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Chapter 0. Preface
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Chapter 0. Preface
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0.1 About this book
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0.2 How to read
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0.3 Summary
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Chapter 1. Encounter with algorithms
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Chapter 1. Encounter with algorithms
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1.1 Algorithms are everywhere
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1.2 What is an algorithm
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1.3 Summary
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Chapter 2. Complexity analysis
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Chapter 2. Complexity analysis
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2.1 Algorithm efficiency assessment
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2.2 Iteration and recursion
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2.3 Time complexity
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2.4 Space complexity
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2.5 Summary
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Chapter 3. Data structures
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Chapter 3. Data structures
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3.1 Classification of data structures
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3.2 Basic data types
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3.3 Number encoding *
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3.4 Character encoding *
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3.5 Summary
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Chapter 4. Array and linked list
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Chapter 4. Array and linked list
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4.1 Array
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4.2 Linked list
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4.3 List
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4.4 Memory and cache *
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4.5 Summary
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Chapter 5. Stack and queue
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Chapter 5. Stack and queue
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5.1 Stack
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5.2 Queue
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5.3 Double-ended queue
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5.4 Summary
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Chapter 6. Hash table
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Chapter 6. Hash table
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6.1 Hash table
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6.2 Hash collision
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6.3 Hash algorithm
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6.4 Summary
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Chapter 7. Tree
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Chapter 7. Tree
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< a href = "../../chapter_tree/binary_tree/" class = "md-nav__link" >
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7.1 Binary tree
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7.2 Binary tree traversal
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7.3 Array Representation of tree
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7.4 Binary Search tree
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< a href = "../../chapter_tree/avl_tree/" class = "md-nav__link" >
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7.5 AVL tree *
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7.6 Summary
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< a href = "../../chapter_heap/" class = "md-nav__link " >
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Chapter 8. Heap
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Chapter 8. Heap
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< a href = "../../chapter_heap/heap/" class = "md-nav__link" >
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8.1 Heap
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8.2 Building a heap
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8.3 Top-k problem
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8.4 Summary
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< a href = "../../chapter_graph/" class = "md-nav__link " >
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Chapter 9. Graph
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Chapter 9. Graph
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9.1 Graph
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9.2 Basic graph operations
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9.3 Graph traversal
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9.4 Summary
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_searching/" class = "md-nav__link " >
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Chapter 10. Searching
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Chapter 10. Searching
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< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
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10.1 Binary search
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10.2 Binary search insertion
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< a href = "../../chapter_searching/binary_search_edge/" class = "md-nav__link" >
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10.3 Binary search boundaries
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< a href = "../../chapter_searching/replace_linear_by_hashing/" class = "md-nav__link" >
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10.4 Hashing optimization strategies
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< a href = "../../chapter_searching/searching_algorithm_revisited/" class = "md-nav__link" >
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10.5 Search algorithms revisited
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10.6 Summary
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_sorting/" class = "md-nav__link " >
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Chapter 11. Sorting
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Chapter 11. Sorting
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11.1 Sorting algorithms
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11.2 Selection sort
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11.3 Bubble sort
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11.4 Insertion sort
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11.5 Quick sort
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11.6 Merge sort
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11.7 Heap sort
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11.8 Bucket sort
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11.9 Counting sort
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11.10 Radix sort
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11.11 Summary
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< a href = "../../chapter_divide_and_conquer/" class = "md-nav__link " >
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Chapter 12. Divide and conquer
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Chapter 12. Divide and conquer
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12.1 Divide and conquer algorithms
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< a href = "../../chapter_divide_and_conquer/binary_search_recur/" class = "md-nav__link" >
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12.2 Divide and conquer search strategy
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12.3 Building binary tree problem
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< a href = "../../chapter_divide_and_conquer/hanota_problem/" class = "md-nav__link" >
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12.4 Tower of Hanoi Problem
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12.5 Summary
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< h1 id = "152-fractional-knapsack-problem" > 15.2 Fractional knapsack problem< a class = "headerlink" href = "#152-fractional-knapsack-problem" title = "Permanent link" > ¶ < / a > < / h1 >
< div class = "admonition question" >
< p class = "admonition-title" > Question< / p >
< p > Given < span class = "arithmatex" > \(n\)< / span > items, the weight of the < span class = "arithmatex" > \(i\)< / span > -th item is < span class = "arithmatex" > \(wgt[i-1]\)< / span > and its value is < span class = "arithmatex" > \(val[i-1]\)< / span > , and a knapsack with a capacity of < span class = "arithmatex" > \(cap\)< / span > . Each item can be chosen only once, < strong > but a part of the item can be selected, with its value calculated based on the proportion of the weight chosen< / strong > , what is the maximum value of the items in the knapsack under the limited capacity? An example is shown in Figure 15-3.< / p >
< / div >
< p > < a class = "glightbox" href = "../fractional_knapsack_problem.assets/fractional_knapsack_example.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Example data of the fractional knapsack problem" class = "animation-figure" src = "../fractional_knapsack_problem.assets/fractional_knapsack_example.png" / > < / a > < / p >
< p align = "center" > Figure 15-3 Example data of the fractional knapsack problem < / p >
< p > The fractional knapsack problem is very similar overall to the 0-1 knapsack problem, involving the current item < span class = "arithmatex" > \(i\)< / span > and capacity < span class = "arithmatex" > \(c\)< / span > , aiming to maximize the value within the limited capacity of the knapsack.< / p >
< p > The difference is that, in this problem, only a part of an item can be chosen. As shown in Figure 15-4, < strong > we can arbitrarily split the items and calculate the corresponding value based on the weight proportion< / strong > .< / p >
< ol >
< li > For item < span class = "arithmatex" > \(i\)< / span > , its value per unit weight is < span class = "arithmatex" > \(val[i-1] / wgt[i-1]\)< / span > , referred to as the unit value.< / li >
< li > Suppose we put a part of item < span class = "arithmatex" > \(i\)< / span > with weight < span class = "arithmatex" > \(w\)< / span > into the knapsack, then the value added to the knapsack is < span class = "arithmatex" > \(w \times val[i-1] / wgt[i-1]\)< / span > .< / li >
< / ol >
< p > < a class = "glightbox" href = "../fractional_knapsack_problem.assets/fractional_knapsack_unit_value.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Value per unit weight of the item" class = "animation-figure" src = "../fractional_knapsack_problem.assets/fractional_knapsack_unit_value.png" / > < / a > < / p >
< p align = "center" > Figure 15-4 Value per unit weight of the item < / p >
< h3 id = "1-greedy-strategy-determination" > 1. Greedy strategy determination< a class = "headerlink" href = "#1-greedy-strategy-determination" title = "Permanent link" > ¶ < / a > < / h3 >
< p > Maximizing the total value of the items in the knapsack < strong > essentially means maximizing the value per unit weight< / strong > . From this, the greedy strategy shown in Figure 15-5 can be deduced.< / p >
< ol >
< li > Sort the items by their unit value from high to low.< / li >
< li > Iterate over all items, < strong > greedily choosing the item with the highest unit value in each round< / strong > .< / li >
< li > If the remaining capacity of the knapsack is insufficient, use part of the current item to fill the knapsack.< / li >
< / ol >
< p > < a class = "glightbox" href = "../fractional_knapsack_problem.assets/fractional_knapsack_greedy_strategy.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Greedy strategy of the fractional knapsack problem" class = "animation-figure" src = "../fractional_knapsack_problem.assets/fractional_knapsack_greedy_strategy.png" / > < / a > < / p >
< p align = "center" > Figure 15-5 Greedy strategy of the fractional knapsack problem < / p >
< h3 id = "2-code-implementation" > 2. Code implementation< a class = "headerlink" href = "#2-code-implementation" title = "Permanent link" > ¶ < / a > < / h3 >
< p > We have created an < code > Item< / code > class in order to sort the items by their unit value. We loop and make greedy choices until the knapsack is full, then exit and return the solution:< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "1:14" > < input checked = "checked" id = "__tabbed_1_1" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_2" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_3" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_4" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_5" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_6" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_7" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_8" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_9" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_10" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_11" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_12" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_13" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_14" name = "__tabbed_1" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_1_1" > Python< / label > < label for = "__tabbed_1_2" > C++< / label > < label for = "__tabbed_1_3" > Java< / label > < label for = "__tabbed_1_4" > C#< / label > < label for = "__tabbed_1_5" > Go< / label > < label for = "__tabbed_1_6" > Swift< / label > < label for = "__tabbed_1_7" > JS< / label > < label for = "__tabbed_1_8" > TS< / label > < label for = "__tabbed_1_9" > Dart< / label > < label for = "__tabbed_1_10" > Rust< / label > < label for = "__tabbed_1_11" > C< / label > < label for = "__tabbed_1_12" > Kotlin< / label > < label for = "__tabbed_1_13" > Ruby< / label > < label for = "__tabbed_1_14" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "k" > class< / span > < span class = "nc" > Item< / span > < span class = "p" > :< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 物品" " " < / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "k" > def< / span > < span class = "fm" > __init__< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > w< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > ,< / span > < span class = "n" > v< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > w< / span > < span class = "o" > =< / span > < span class = "n" > w< / span > < span class = "c1" > # 物品重量< / span >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > v< / span > < span class = "o" > =< / span > < span class = "n" > v< / span > < span class = "c1" > # 物品价值< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < span class = "k" > def< / span > < span class = "nf" > fractional_knapsack< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ],< / span > < span class = "n" > val< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ],< / span > < span class = "n" > cap< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-0-9" name = "__codelineno-0-9" href = "#__codelineno-0-9" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 分数背包：贪心" " " < / span >
< a id = "__codelineno-0-10" name = "__codelineno-0-10" href = "#__codelineno-0-10" > < / a > < span class = "c1" > # 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-0-11" name = "__codelineno-0-11" href = "#__codelineno-0-11" > < / a > < span class = "n" > items< / span > < span class = "o" > =< / span > < span class = "p" > [< / span > < span class = "n" > Item< / span > < span class = "p" > (< / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "n" > v< / span > < span class = "p" > )< / span > < span class = "k" > for< / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "n" > v< / span > < span class = "ow" > in< / span > < span class = "nb" > zip< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > < span class = "p" > ,< / span > < span class = "n" > val< / span > < span class = "p" > )]< / span >
< a id = "__codelineno-0-12" name = "__codelineno-0-12" href = "#__codelineno-0-12" > < / a > < span class = "c1" > # 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-0-13" name = "__codelineno-0-13" href = "#__codelineno-0-13" > < / a > < span class = "n" > items< / span > < span class = "o" > .< / span > < span class = "n" > sort< / span > < span class = "p" > (< / span > < span class = "n" > key< / span > < span class = "o" > =< / span > < span class = "k" > lambda< / span > < span class = "n" > item< / span > < span class = "p" > :< / span > < span class = "n" > item< / span > < span class = "o" > .< / span > < span class = "n" > v< / span > < span class = "o" > /< / span > < span class = "n" > item< / span > < span class = "o" > .< / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "n" > reverse< / span > < span class = "o" > =< / span > < span class = "kc" > True< / span > < span class = "p" > )< / span >
< a id = "__codelineno-0-14" name = "__codelineno-0-14" href = "#__codelineno-0-14" > < / a > < span class = "c1" > # 循环贪心选择< / span >
< a id = "__codelineno-0-15" name = "__codelineno-0-15" href = "#__codelineno-0-15" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-0-16" name = "__codelineno-0-16" href = "#__codelineno-0-16" > < / a > < span class = "k" > for< / span > < span class = "n" > item< / span > < span class = "ow" > in< / span > < span class = "n" > items< / span > < span class = "p" > :< / span >
< a id = "__codelineno-0-17" name = "__codelineno-0-17" href = "#__codelineno-0-17" > < / a > < span class = "k" > if< / span > < span class = "n" > item< / span > < span class = "o" > .< / span > < span class = "n" > w< / span > < span class = "o" > < =< / span > < span class = "n" > cap< / span > < span class = "p" > :< / span >
< a id = "__codelineno-0-18" name = "__codelineno-0-18" href = "#__codelineno-0-18" > < / a > < span class = "c1" > # 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-0-19" name = "__codelineno-0-19" href = "#__codelineno-0-19" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > item< / span > < span class = "o" > .< / span > < span class = "n" > v< / span >
< a id = "__codelineno-0-20" name = "__codelineno-0-20" href = "#__codelineno-0-20" > < / a > < span class = "n" > cap< / span > < span class = "o" > -=< / span > < span class = "n" > item< / span > < span class = "o" > .< / span > < span class = "n" > w< / span >
< a id = "__codelineno-0-21" name = "__codelineno-0-21" href = "#__codelineno-0-21" > < / a > < span class = "k" > else< / span > < span class = "p" > :< / span >
< a id = "__codelineno-0-22" name = "__codelineno-0-22" href = "#__codelineno-0-22" > < / a > < span class = "c1" > # 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-0-23" name = "__codelineno-0-23" href = "#__codelineno-0-23" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "o" > .< / span > < span class = "n" > v< / span > < span class = "o" > /< / span > < span class = "n" > item< / span > < span class = "o" > .< / span > < span class = "n" > w< / span > < span class = "p" > )< / span > < span class = "o" > *< / span > < span class = "n" > cap< / span >
< a id = "__codelineno-0-24" name = "__codelineno-0-24" href = "#__codelineno-0-24" > < / a > < span class = "c1" > # 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-0-25" name = "__codelineno-0-25" href = "#__codelineno-0-25" > < / a > < span class = "k" > break< / span >
< a id = "__codelineno-0-26" name = "__codelineno-0-26" href = "#__codelineno-0-26" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* 物品 */< / span >
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "k" > class< / span > < span class = "w" > < / span > < span class = "nc" > Item< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-3" name = "__codelineno-1-3" href = "#__codelineno-1-3" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "o" > :< / span >
< a id = "__codelineno-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品重量< / span >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品价值< / span >
< a id = "__codelineno-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / a >
< a id = "__codelineno-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > (< / span > < span class = "n" > w< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > (< / span > < span class = "n" > v< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / a > < span class = "p" > };< / span >
< a id = "__codelineno-1-10" name = "__codelineno-1-10" href = "#__codelineno-1-10" > < / a >
< a id = "__codelineno-1-11" name = "__codelineno-1-11" href = "#__codelineno-1-11" > < / a > < span class = "cm" > /* 分数背包：贪心 */< / span >
< a id = "__codelineno-1-12" name = "__codelineno-1-12" href = "#__codelineno-1-12" > < / a > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "nf" > fractionalKnapsack< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > wgt< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > val< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-13" name = "__codelineno-1-13" href = "#__codelineno-1-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-1-14" name = "__codelineno-1-14" href = "#__codelineno-1-14" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > Item< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-15" name = "__codelineno-1-15" href = "#__codelineno-1-15" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > wgt< / span > < span class = "p" > .< / span > < span class = "n" > size< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-16" name = "__codelineno-1-16" href = "#__codelineno-1-16" > < / a > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > Item< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]));< / span >
< a id = "__codelineno-1-17" name = "__codelineno-1-17" href = "#__codelineno-1-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-18" name = "__codelineno-1-18" href = "#__codelineno-1-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-1-19" name = "__codelineno-1-19" href = "#__codelineno-1-19" > < / a > < span class = "w" > < / span > < span class = "n" > sort< / span > < span class = "p" > (< / span > < span class = "n" > items< / span > < span class = "p" > .< / span > < span class = "n" > begin< / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > .< / span > < span class = "n" > end< / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "p" > [](< / span > < span class = "n" > Item< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > a< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > b< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > double< / span > < span class = "p" > )< / span > < span class = "n" > a< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > a< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > double< / span > < span class = "p" > )< / span > < span class = "n" > b< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "p" > });< / span >
< a id = "__codelineno-1-20" name = "__codelineno-1-20" href = "#__codelineno-1-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环贪心选择< / span >
< a id = "__codelineno-1-21" name = "__codelineno-1-21" href = "#__codelineno-1-21" > < / a > < span class = "w" > < / span > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-22" name = "__codelineno-1-22" href = "#__codelineno-1-22" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "k" > auto< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > item< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-23" name = "__codelineno-1-23" href = "#__codelineno-1-23" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-24" name = "__codelineno-1-24" href = "#__codelineno-1-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-1-25" name = "__codelineno-1-25" href = "#__codelineno-1-25" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-26" name = "__codelineno-1-26" href = "#__codelineno-1-26" > < / a > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-27" name = "__codelineno-1-27" href = "#__codelineno-1-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-28" name = "__codelineno-1-28" href = "#__codelineno-1-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-1-29" name = "__codelineno-1-29" href = "#__codelineno-1-29" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > double< / span > < span class = "p" > )< / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-30" name = "__codelineno-1-30" href = "#__codelineno-1-30" > < / a > < span class = "w" > < / span > < span class = "c1" > // 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-1-31" name = "__codelineno-1-31" href = "#__codelineno-1-31" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-32" name = "__codelineno-1-32" href = "#__codelineno-1-32" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-33" name = "__codelineno-1-33" href = "#__codelineno-1-33" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-34" name = "__codelineno-1-34" href = "#__codelineno-1-34" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-35" name = "__codelineno-1-35" href = "#__codelineno-1-35" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "cm" > /* 物品 */< / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "kd" > class< / span > < span class = "nc" > Item< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品重量< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品价值< / span >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "w" > < / span > < span class = "kd" > public< / span > < span class = "w" > < / span > < span class = "nf" > Item< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "na" > w< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "na" > v< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-2-11" name = "__codelineno-2-11" href = "#__codelineno-2-11" > < / a >
< a id = "__codelineno-2-12" name = "__codelineno-2-12" href = "#__codelineno-2-12" > < / a > < span class = "cm" > /* 分数背包：贪心 */< / span >
< a id = "__codelineno-2-13" name = "__codelineno-2-13" href = "#__codelineno-2-13" > < / a > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "nf" > fractionalKnapsack< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > wgt< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-14" name = "__codelineno-2-14" href = "#__codelineno-2-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-2-15" name = "__codelineno-2-15" href = "#__codelineno-2-15" > < / a > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "o" > [< / span > < span class = "n" > wgt< / span > < span class = "p" > .< / span > < span class = "na" > length< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-16" name = "__codelineno-2-16" href = "#__codelineno-2-16" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > wgt< / span > < span class = "p" > .< / span > < span class = "na" > length< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-17" name = "__codelineno-2-17" href = "#__codelineno-2-17" > < / a > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-18" name = "__codelineno-2-18" href = "#__codelineno-2-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-19" name = "__codelineno-2-19" href = "#__codelineno-2-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-2-20" name = "__codelineno-2-20" href = "#__codelineno-2-20" > < / a > < span class = "w" > < / span > < span class = "n" > Arrays< / span > < span class = "p" > .< / span > < span class = "na" > sort< / span > < span class = "p" > (< / span > < span class = "n" > items< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Comparator< / span > < span class = "p" > .< / span > < span class = "na" > comparingDouble< / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "w" > < / span > < span class = "o" > -> < / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "p" > ((< / span > < span class = "kt" > double< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > w< / span > < span class = "p" > )));< / span >
< a id = "__codelineno-2-21" name = "__codelineno-2-21" href = "#__codelineno-2-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环贪心选择< / span >
< a id = "__codelineno-2-22" name = "__codelineno-2-22" href = "#__codelineno-2-22" > < / a > < span class = "w" > < / span > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-23" name = "__codelineno-2-23" href = "#__codelineno-2-23" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > Item< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-24" name = "__codelineno-2-24" href = "#__codelineno-2-24" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > w< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-25" name = "__codelineno-2-25" href = "#__codelineno-2-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-2-26" name = "__codelineno-2-26" href = "#__codelineno-2-26" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > v< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-27" name = "__codelineno-2-27" href = "#__codelineno-2-27" > < / a > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > w< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-28" name = "__codelineno-2-28" href = "#__codelineno-2-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-29" name = "__codelineno-2-29" href = "#__codelineno-2-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-2-30" name = "__codelineno-2-30" href = "#__codelineno-2-30" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > double< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > w< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-31" name = "__codelineno-2-31" href = "#__codelineno-2-31" > < / a > < span class = "w" > < / span > < span class = "c1" > // 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-2-32" name = "__codelineno-2-32" href = "#__codelineno-2-32" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-33" name = "__codelineno-2-33" href = "#__codelineno-2-33" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-34" name = "__codelineno-2-34" href = "#__codelineno-2-34" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-35" name = "__codelineno-2-35" href = "#__codelineno-2-35" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-36" name = "__codelineno-2-36" href = "#__codelineno-2-36" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* 物品 */< / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "k" > class< / span > < span class = "w" > < / span > < span class = "nf" > Item< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品重量< / span >
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品价值< / span >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / a >
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "cm" > /* 分数背包：贪心 */< / span >
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / a > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "nf" > FractionalKnapsack< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > wgt< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-9" name = "__codelineno-3-9" href = "#__codelineno-3-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "p" > [< / span > < span class = "n" > wgt< / span > < span class = "p" > .< / span > < span class = "n" > Length< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-3-11" name = "__codelineno-3-11" href = "#__codelineno-3-11" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > wgt< / span > < span class = "p" > .< / span > < span class = "n" > Length< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-12" name = "__codelineno-3-12" href = "#__codelineno-3-12" > < / a > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-3-13" name = "__codelineno-3-13" href = "#__codelineno-3-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-14" name = "__codelineno-3-14" href = "#__codelineno-3-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-3-15" name = "__codelineno-3-15" href = "#__codelineno-3-15" > < / a > < span class = "w" > < / span > < span class = "n" > Array< / span > < span class = "p" > .< / span > < span class = "n" > Sort< / span > < span class = "p" > (< / span > < span class = "n" > items< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > x< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > y< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > => < / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > y< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > y< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ).< / span > < span class = "n" > CompareTo< / span > < span class = "p" > (< / span > < span class = "n" > x< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > x< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-3-16" name = "__codelineno-3-16" href = "#__codelineno-3-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环贪心选择< / span >
< a id = "__codelineno-3-17" name = "__codelineno-3-17" href = "#__codelineno-3-17" > < / a > < span class = "w" > < / span > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-18" name = "__codelineno-3-18" href = "#__codelineno-3-18" > < / a > < span class = "w" > < / span > < span class = "k" > foreach< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > Item< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-19" name = "__codelineno-3-19" href = "#__codelineno-3-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-20" name = "__codelineno-3-20" href = "#__codelineno-3-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-3-21" name = "__codelineno-3-21" href = "#__codelineno-3-21" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-22" name = "__codelineno-3-22" href = "#__codelineno-3-22" > < / a > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-23" name = "__codelineno-3-23" href = "#__codelineno-3-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-24" name = "__codelineno-3-24" href = "#__codelineno-3-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-3-25" name = "__codelineno-3-25" href = "#__codelineno-3-25" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > double< / span > < span class = "p" > )< / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-26" name = "__codelineno-3-26" href = "#__codelineno-3-26" > < / a > < span class = "w" > < / span > < span class = "c1" > // 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-3-27" name = "__codelineno-3-27" href = "#__codelineno-3-27" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-28" name = "__codelineno-3-28" href = "#__codelineno-3-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-29" name = "__codelineno-3-29" href = "#__codelineno-3-29" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-30" name = "__codelineno-3-30" href = "#__codelineno-3-30" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-31" name = "__codelineno-3-31" href = "#__codelineno-3-31" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "cm" > /* 物品 */< / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a > < span class = "kd" > type< / span > < span class = "w" > < / span > < span class = "nx" > Item< / span > < span class = "w" > < / span > < span class = "kd" > struct< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "w" > < / span > < span class = "nx" > w< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "c1" > // 物品重量< / span >
< a id = "__codelineno-4-4" name = "__codelineno-4-4" href = "#__codelineno-4-4" > < / a > < span class = "w" > < / span > < span class = "nx" > v< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "c1" > // 物品价值< / span >
< a id = "__codelineno-4-5" name = "__codelineno-4-5" href = "#__codelineno-4-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / a >
< a id = "__codelineno-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "cm" > /* 分数背包：贪心 */< / span >
< a id = "__codelineno-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > fractionalKnapsack< / span > < span class = "p" > (< / span > < span class = "nx" > wgt< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cap< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > float64< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-9" name = "__codelineno-4-9" href = "#__codelineno-4-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-4-10" name = "__codelineno-4-10" href = "#__codelineno-4-10" > < / a > < span class = "w" > < / span > < span class = "nx" > items< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "nx" > Item< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "nx" > wgt< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-4-11" name = "__codelineno-4-11" href = "#__codelineno-4-11" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "p" > < < / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "nx" > wgt< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-12" name = "__codelineno-4-12" href = "#__codelineno-4-12" > < / a > < span class = "w" > < / span > < span class = "nx" > items< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > Item< / span > < span class = "p" > {< / span > < span class = "nx" > wgt< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]}< / span >
< a id = "__codelineno-4-13" name = "__codelineno-4-13" href = "#__codelineno-4-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-14" name = "__codelineno-4-14" href = "#__codelineno-4-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-4-15" name = "__codelineno-4-15" href = "#__codelineno-4-15" > < / a > < span class = "w" > < / span > < span class = "nx" > sort< / span > < span class = "p" > .< / span > < span class = "nx" > Slice< / span > < span class = "p" > (< / span > < span class = "nx" > items< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kd" > func< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-16" name = "__codelineno-4-16" href = "#__codelineno-4-16" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nb" > float64< / span > < span class = "p" > (< / span > < span class = "nx" > items< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ].< / span > < span class = "nx" > v< / span > < span class = "p" > )< / span > < span class = "o" > /< / span > < span class = "nb" > float64< / span > < span class = "p" > (< / span > < span class = "nx" > items< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ].< / span > < span class = "nx" > w< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > > < / span > < span class = "w" > < / span > < span class = "nb" > float64< / span > < span class = "p" > (< / span > < span class = "nx" > items< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "p" > ].< / span > < span class = "nx" > v< / span > < span class = "p" > )< / span > < span class = "o" > /< / span > < span class = "nb" > float64< / span > < span class = "p" > (< / span > < span class = "nx" > items< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "p" > ].< / span > < span class = "nx" > w< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-17" name = "__codelineno-4-17" href = "#__codelineno-4-17" > < / a > < span class = "w" > < / span > < span class = "p" > })< / span >
< a id = "__codelineno-4-18" name = "__codelineno-4-18" href = "#__codelineno-4-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环贪心选择< / span >
< a id = "__codelineno-4-19" name = "__codelineno-4-19" href = "#__codelineno-4-19" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mf" > 0.0< / span >
< a id = "__codelineno-4-20" name = "__codelineno-4-20" href = "#__codelineno-4-20" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > _< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > item< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "k" > range< / span > < span class = "w" > < / span > < span class = "nx" > items< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-21" name = "__codelineno-4-21" href = "#__codelineno-4-21" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > cap< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-22" name = "__codelineno-4-22" href = "#__codelineno-4-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-4-23" name = "__codelineno-4-23" href = "#__codelineno-4-23" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nb" > float64< / span > < span class = "p" > (< / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > v< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-24" name = "__codelineno-4-24" href = "#__codelineno-4-24" > < / a > < span class = "w" > < / span > < span class = "nx" > cap< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span >
< a id = "__codelineno-4-25" name = "__codelineno-4-25" href = "#__codelineno-4-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-26" name = "__codelineno-4-26" href = "#__codelineno-4-26" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-4-27" name = "__codelineno-4-27" href = "#__codelineno-4-27" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nb" > float64< / span > < span class = "p" > (< / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > v< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "nb" > float64< / span > < span class = "p" > (< / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nb" > float64< / span > < span class = "p" > (< / span > < span class = "nx" > cap< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-28" name = "__codelineno-4-28" href = "#__codelineno-4-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-4-29" name = "__codelineno-4-29" href = "#__codelineno-4-29" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span >
< a id = "__codelineno-4-30" name = "__codelineno-4-30" href = "#__codelineno-4-30" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-31" name = "__codelineno-4-31" href = "#__codelineno-4-31" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-32" name = "__codelineno-4-32" href = "#__codelineno-4-32" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-4-33" name = "__codelineno-4-33" href = "#__codelineno-4-33" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "cm" > /* 物品 */< / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a > < span class = "kd" > class< / span > < span class = "nc" > Item< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "kd" > var< / span > < span class = "nv" > w< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "c1" > // 物品重量< / span >
< a id = "__codelineno-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a > < span class = "kd" > var< / span > < span class = "nv" > v< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "c1" > // 物品价值< / span >
< a id = "__codelineno-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / a >
< a id = "__codelineno-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < span class = "kd" > init< / span > < span class = "p" > (< / span > < span class = "n" > w< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > ,< / span > < span class = "n" > v< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / a > < span class = "kc" > self< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > =< / span > < span class = "n" > w< / span >
< a id = "__codelineno-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "kc" > self< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "p" > =< / span > < span class = "n" > v< / span >
< a id = "__codelineno-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-10" name = "__codelineno-5-10" href = "#__codelineno-5-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-11" name = "__codelineno-5-11" href = "#__codelineno-5-11" > < / a >
< a id = "__codelineno-5-12" name = "__codelineno-5-12" href = "#__codelineno-5-12" > < / a > < span class = "cm" > /* 分数背包：贪心 */< / span >
< a id = "__codelineno-5-13" name = "__codelineno-5-13" href = "#__codelineno-5-13" > < / a > < span class = "kd" > func< / span > < span class = "nf" > fractionalKnapsack< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ],< / span > < span class = "n" > val< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ],< / span > < span class = "n" > cap< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "nb" > Double< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-14" name = "__codelineno-5-14" href = "#__codelineno-5-14" > < / a > < span class = "c1" > // 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-5-15" name = "__codelineno-5-15" href = "#__codelineno-5-15" > < / a > < span class = "kd" > var< / span > < span class = "nv" > items< / span > < span class = "p" > =< / span > < span class = "n" > zip< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > < span class = "p" > ,< / span > < span class = "n" > val< / span > < span class = "p" > ).< / span > < span class = "bp" > map< / span > < span class = "p" > {< / span > < span class = "n" > Item< / span > < span class = "p" > (< / span > < span class = "n" > w< / span > < span class = "p" > :< / span > < span class = "nv" > $0< / span > < span class = "p" > ,< / span > < span class = "n" > v< / span > < span class = "p" > :< / span > < span class = "nv" > $1< / span > < span class = "p" > )< / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-16" name = "__codelineno-5-16" href = "#__codelineno-5-16" > < / a > < span class = "c1" > // 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-5-17" name = "__codelineno-5-17" href = "#__codelineno-5-17" > < / a > < span class = "n" > items< / span > < span class = "p" > .< / span > < span class = "bp" > sort< / span > < span class = "p" > {< / span > < span class = "o" > -< / span > < span class = "p" > (< / span > < span class = "nb" > Double< / span > < span class = "p" > (< / span > < span class = "nv" > $0< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "p" > )< / span > < span class = "o" > /< / span > < span class = "nb" > Double< / span > < span class = "p" > (< / span > < span class = "nv" > $0< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ))< / span > < span class = "o" > < < / span > < span class = "o" > -< / span > < span class = "p" > (< / span > < span class = "nb" > Double< / span > < span class = "p" > (< / span > < span class = "nv" > $1< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "p" > )< / span > < span class = "o" > /< / span > < span class = "nb" > Double< / span > < span class = "p" > (< / span > < span class = "nv" > $1< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ))< / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-18" name = "__codelineno-5-18" href = "#__codelineno-5-18" > < / a > < span class = "c1" > // 循环贪心选择< / span >
< a id = "__codelineno-5-19" name = "__codelineno-5-19" href = "#__codelineno-5-19" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > =< / span > < span class = "mf" > 0.0< / span >
< a id = "__codelineno-5-20" name = "__codelineno-5-20" href = "#__codelineno-5-20" > < / a > < span class = "kd" > var< / span > < span class = "nv" > cap< / span > < span class = "p" > =< / span > < span class = "n" > cap< / span >
< a id = "__codelineno-5-21" name = "__codelineno-5-21" href = "#__codelineno-5-21" > < / a > < span class = "k" > for< / span > < span class = "n" > item< / span > < span class = "k" > in< / span > < span class = "n" > items< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-22" name = "__codelineno-5-22" href = "#__codelineno-5-22" > < / a > < span class = "k" > if< / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "o" > < =< / span > < span class = "n" > cap< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-23" name = "__codelineno-5-23" href = "#__codelineno-5-23" > < / a > < span class = "c1" > // 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-5-24" name = "__codelineno-5-24" href = "#__codelineno-5-24" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "nb" > Double< / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "p" > )< / span >
< a id = "__codelineno-5-25" name = "__codelineno-5-25" href = "#__codelineno-5-25" > < / a > < span class = "n" > cap< / span > < span class = "o" > -=< / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span >
< a id = "__codelineno-5-26" name = "__codelineno-5-26" href = "#__codelineno-5-26" > < / a > < span class = "p" > }< / span > < span class = "k" > else< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-27" name = "__codelineno-5-27" href = "#__codelineno-5-27" > < / a > < span class = "c1" > // 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-5-28" name = "__codelineno-5-28" href = "#__codelineno-5-28" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "nb" > Double< / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "p" > )< / span > < span class = "o" > /< / span > < span class = "nb" > Double< / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > )< / span > < span class = "o" > *< / span > < span class = "nb" > Double< / span > < span class = "p" > (< / span > < span class = "n" > cap< / span > < span class = "p" > )< / span >
< a id = "__codelineno-5-29" name = "__codelineno-5-29" href = "#__codelineno-5-29" > < / a > < span class = "c1" > // 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-5-30" name = "__codelineno-5-30" href = "#__codelineno-5-30" > < / a > < span class = "k" > break< / span >
< a id = "__codelineno-5-31" name = "__codelineno-5-31" href = "#__codelineno-5-31" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-32" name = "__codelineno-5-32" href = "#__codelineno-5-32" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-33" name = "__codelineno-5-33" href = "#__codelineno-5-33" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-5-34" name = "__codelineno-5-34" href = "#__codelineno-5-34" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "cm" > /* 物品 */< / span >
< a id = "__codelineno-6-2" name = "__codelineno-6-2" href = "#__codelineno-6-2" > < / a > < span class = "kd" > class< / span > < span class = "w" > < / span > < span class = "nx" > Item< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-3" name = "__codelineno-6-3" href = "#__codelineno-6-3" > < / a > < span class = "w" > < / span > < span class = "kr" > constructor< / span > < span class = "p" > (< / span > < span class = "nx" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > v< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-4" name = "__codelineno-6-4" href = "#__codelineno-6-4" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > w< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品重量< / span >
< a id = "__codelineno-6-5" name = "__codelineno-6-5" href = "#__codelineno-6-5" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > v< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > v< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品价值< / span >
< a id = "__codelineno-6-6" name = "__codelineno-6-6" href = "#__codelineno-6-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-7" name = "__codelineno-6-7" href = "#__codelineno-6-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-6-8" name = "__codelineno-6-8" href = "#__codelineno-6-8" > < / a >
< a id = "__codelineno-6-9" name = "__codelineno-6-9" href = "#__codelineno-6-9" > < / a > < span class = "cm" > /* 分数背包：贪心 */< / span >
< a id = "__codelineno-6-10" name = "__codelineno-6-10" href = "#__codelineno-6-10" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > fractionalKnapsack< / span > < span class = "p" > (< / span > < span class = "nx" > wgt< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-11" name = "__codelineno-6-11" href = "#__codelineno-6-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-6-12" name = "__codelineno-6-12" href = "#__codelineno-6-12" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > items< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > wgt< / span > < span class = "p" > .< / span > < span class = "nx" > map< / span > < span class = "p" > ((< / span > < span class = "nx" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > => < / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nx" > Item< / span > < span class = "p" > (< / span > < span class = "nx" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]));< / span >
< a id = "__codelineno-6-13" name = "__codelineno-6-13" href = "#__codelineno-6-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-6-14" name = "__codelineno-6-14" href = "#__codelineno-6-14" > < / a > < span class = "w" > < / span > < span class = "nx" > items< / span > < span class = "p" > .< / span > < span class = "nx" > sort< / span > < span class = "p" > ((< / span > < span class = "nx" > a< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > => < / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "p" > .< / span > < span class = "nx" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > a< / span > < span class = "p" > .< / span > < span class = "nx" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "nx" > a< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span > < span class = "p" > );< / span >
< a id = "__codelineno-6-15" name = "__codelineno-6-15" href = "#__codelineno-6-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环贪心选择< / span >
< a id = "__codelineno-6-16" name = "__codelineno-6-16" href = "#__codelineno-6-16" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-17" name = "__codelineno-6-17" href = "#__codelineno-6-17" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > item< / span > < span class = "w" > < / span > < span class = "k" > of< / span > < span class = "w" > < / span > < span class = "nx" > items< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-18" name = "__codelineno-6-18" href = "#__codelineno-6-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-19" name = "__codelineno-6-19" href = "#__codelineno-6-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-6-20" name = "__codelineno-6-20" href = "#__codelineno-6-20" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > v< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-21" name = "__codelineno-6-21" href = "#__codelineno-6-21" > < / a > < span class = "w" > < / span > < span class = "nx" > cap< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-22" name = "__codelineno-6-22" href = "#__codelineno-6-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-23" name = "__codelineno-6-23" href = "#__codelineno-6-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-6-24" name = "__codelineno-6-24" href = "#__codelineno-6-24" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nx" > cap< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-25" name = "__codelineno-6-25" href = "#__codelineno-6-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-6-26" name = "__codelineno-6-26" href = "#__codelineno-6-26" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-27" name = "__codelineno-6-27" href = "#__codelineno-6-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-28" name = "__codelineno-6-28" href = "#__codelineno-6-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-29" name = "__codelineno-6-29" href = "#__codelineno-6-29" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-30" name = "__codelineno-6-30" href = "#__codelineno-6-30" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* 物品 */< / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a > < span class = "kd" > class< / span > < span class = "w" > < / span > < span class = "nx" > Item< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "w" > < / span > < span class = "nx" > w< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品重量< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a > < span class = "w" > < / span > < span class = "nx" > v< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品价值< / span >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a >
< a id = "__codelineno-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / a > < span class = "w" > < / span > < span class = "kr" > constructor< / span > < span class = "p" > (< / span > < span class = "nx" > w< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > v< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > w< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > v< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > v< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-10" name = "__codelineno-7-10" href = "#__codelineno-7-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-7-11" name = "__codelineno-7-11" href = "#__codelineno-7-11" > < / a >
< a id = "__codelineno-7-12" name = "__codelineno-7-12" href = "#__codelineno-7-12" > < / a > < span class = "cm" > /* 分数背包：贪心 */< / span >
< a id = "__codelineno-7-13" name = "__codelineno-7-13" href = "#__codelineno-7-13" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > fractionalKnapsack< / span > < span class = "p" > (< / span > < span class = "nx" > wgt< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [],< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [],< / span > < span class = "w" > < / span > < span class = "nx" > cap< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-14" name = "__codelineno-7-14" href = "#__codelineno-7-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-7-15" name = "__codelineno-7-15" href = "#__codelineno-7-15" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > items< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > Item< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > wgt< / span > < span class = "p" > .< / span > < span class = "nx" > map< / span > < span class = "p" > ((< / span > < span class = "nx" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > => < / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nx" > Item< / span > < span class = "p" > (< / span > < span class = "nx" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]));< / span >
< a id = "__codelineno-7-16" name = "__codelineno-7-16" href = "#__codelineno-7-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-7-17" name = "__codelineno-7-17" href = "#__codelineno-7-17" > < / a > < span class = "w" > < / span > < span class = "nx" > items< / span > < span class = "p" > .< / span > < span class = "nx" > sort< / span > < span class = "p" > ((< / span > < span class = "nx" > a< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > => < / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "p" > .< / span > < span class = "nx" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > a< / span > < span class = "p" > .< / span > < span class = "nx" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "nx" > a< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-18" name = "__codelineno-7-18" href = "#__codelineno-7-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环贪心选择< / span >
< a id = "__codelineno-7-19" name = "__codelineno-7-19" href = "#__codelineno-7-19" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-20" name = "__codelineno-7-20" href = "#__codelineno-7-20" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > item< / span > < span class = "w" > < / span > < span class = "k" > of< / span > < span class = "w" > < / span > < span class = "nx" > items< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-21" name = "__codelineno-7-21" href = "#__codelineno-7-21" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-22" name = "__codelineno-7-22" href = "#__codelineno-7-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-7-23" name = "__codelineno-7-23" href = "#__codelineno-7-23" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > v< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-24" name = "__codelineno-7-24" href = "#__codelineno-7-24" > < / a > < span class = "w" > < / span > < span class = "nx" > cap< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-25" name = "__codelineno-7-25" href = "#__codelineno-7-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-26" name = "__codelineno-7-26" href = "#__codelineno-7-26" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-7-27" name = "__codelineno-7-27" href = "#__codelineno-7-27" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nx" > cap< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-28" name = "__codelineno-7-28" href = "#__codelineno-7-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-7-29" name = "__codelineno-7-29" href = "#__codelineno-7-29" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-30" name = "__codelineno-7-30" href = "#__codelineno-7-30" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-31" name = "__codelineno-7-31" href = "#__codelineno-7-31" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-32" name = "__codelineno-7-32" href = "#__codelineno-7-32" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-33" name = "__codelineno-7-33" href = "#__codelineno-7-33" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* 物品 */< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "kd" > class< / span > < span class = "w" > < / span > < span class = "nc" > Item< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品重量< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品价值< / span >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "p" > (< / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "p" > );< / span >
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "cm" > /* 分数背包：贪心 */< / span >
< a id = "__codelineno-8-10" name = "__codelineno-8-10" href = "#__codelineno-8-10" > < / a > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "n" > fractionalKnapsack< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > wgt< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-11" name = "__codelineno-8-11" href = "#__codelineno-8-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-8-12" name = "__codelineno-8-12" href = "#__codelineno-8-12" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Item< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "p" > .< / span > < span class = "n" > generate< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > < span class = "p" > .< / span > < span class = "n" > length< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > => < / span > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]));< / span >
< a id = "__codelineno-8-13" name = "__codelineno-8-13" href = "#__codelineno-8-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-8-14" name = "__codelineno-8-14" href = "#__codelineno-8-14" > < / a > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > .< / span > < span class = "n" > sort< / span > < span class = "p" > ((< / span > < span class = "n" > a< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > => < / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > b< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ).< / span > < span class = "n" > compareTo< / span > < span class = "p" > (< / span > < span class = "n" > a< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > a< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-8-15" name = "__codelineno-8-15" href = "#__codelineno-8-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环贪心选择< / span >
< a id = "__codelineno-8-16" name = "__codelineno-8-16" href = "#__codelineno-8-16" > < / a > < span class = "w" > < / span > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-17" name = "__codelineno-8-17" href = "#__codelineno-8-17" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > Item< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-18" name = "__codelineno-8-18" href = "#__codelineno-8-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-19" name = "__codelineno-8-19" href = "#__codelineno-8-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-8-20" name = "__codelineno-8-20" href = "#__codelineno-8-20" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-21" name = "__codelineno-8-21" href = "#__codelineno-8-21" > < / a > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-22" name = "__codelineno-8-22" href = "#__codelineno-8-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-23" name = "__codelineno-8-23" href = "#__codelineno-8-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-8-24" name = "__codelineno-8-24" href = "#__codelineno-8-24" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-25" name = "__codelineno-8-25" href = "#__codelineno-8-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-8-26" name = "__codelineno-8-26" href = "#__codelineno-8-26" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-27" name = "__codelineno-8-27" href = "#__codelineno-8-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-8-28" name = "__codelineno-8-28" href = "#__codelineno-8-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-8-29" name = "__codelineno-8-29" href = "#__codelineno-8-29" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-30" name = "__codelineno-8-30" href = "#__codelineno-8-30" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a > < span class = "cm" > /* 物品 */< / span >
< a id = "__codelineno-9-2" name = "__codelineno-9-2" href = "#__codelineno-9-2" > < / a > < span class = "k" > struct< / span > < span class = "nc" > Item< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-3" name = "__codelineno-9-3" href = "#__codelineno-9-3" > < / a > < span class = "w" > < / span > < span class = "n" > w< / span > : < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "c1" > // 物品重量< / span >
< a id = "__codelineno-9-4" name = "__codelineno-9-4" href = "#__codelineno-9-4" > < / a > < span class = "w" > < / span > < span class = "n" > v< / span > : < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "c1" > // 物品价值< / span >
< a id = "__codelineno-9-5" name = "__codelineno-9-5" href = "#__codelineno-9-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-9-6" name = "__codelineno-9-6" href = "#__codelineno-9-6" > < / a >
< a id = "__codelineno-9-7" name = "__codelineno-9-7" href = "#__codelineno-9-7" > < / a > < span class = "k" > impl< / span > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-8" name = "__codelineno-9-8" href = "#__codelineno-9-8" > < / a > < span class = "w" > < / span > < span class = "k" > fn< / span > < span class = "nf" > new< / span > < span class = "p" > (< / span > < span class = "n" > w< / span > : < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > v< / span > : < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "nc" > Self< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-9" name = "__codelineno-9-9" href = "#__codelineno-9-9" > < / a > < span class = "w" > < / span > < span class = "bp" > Self< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-10" name = "__codelineno-9-10" href = "#__codelineno-9-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-11" name = "__codelineno-9-11" href = "#__codelineno-9-11" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-9-12" name = "__codelineno-9-12" href = "#__codelineno-9-12" > < / a >
< a id = "__codelineno-9-13" name = "__codelineno-9-13" href = "#__codelineno-9-13" > < / a > < span class = "cm" > /* 分数背包：贪心 */< / span >
< a id = "__codelineno-9-14" name = "__codelineno-9-14" href = "#__codelineno-9-14" > < / a > < span class = "k" > fn< / span > < span class = "nf" > fractional_knapsack< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > : < span class = "kp" > & < / span > < span class = "p" > [< / span > < span class = "kt" > i32< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > val< / span > : < span class = "kp" > & < / span > < span class = "p" > [< / span > < span class = "kt" > i32< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > : < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "kt" > f64< / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-15" name = "__codelineno-9-15" href = "#__codelineno-9-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-9-16" name = "__codelineno-9-16" href = "#__codelineno-9-16" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > wgt< / span >
< a id = "__codelineno-9-17" name = "__codelineno-9-17" href = "#__codelineno-9-17" > < / a > < span class = "w" > < / span > < span class = "p" > .< / span > < span class = "n" > iter< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-9-18" name = "__codelineno-9-18" href = "#__codelineno-9-18" > < / a > < span class = "w" > < / span > < span class = "p" > .< / span > < span class = "n" > zip< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > .< / span > < span class = "n" > iter< / span > < span class = "p" > ())< / span >
< a id = "__codelineno-9-19" name = "__codelineno-9-19" href = "#__codelineno-9-19" > < / a > < span class = "w" > < / span > < span class = "p" > .< / span > < span class = "n" > map< / span > < span class = "p" > (< / span > < span class = "o" > |< / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > v< / span > < span class = "p" > )< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "n" > Item< / span > ::< span class = "n" > new< / span > < span class = "p" > (< / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-9-20" name = "__codelineno-9-20" href = "#__codelineno-9-20" > < / a > < span class = "w" > < / span > < span class = "p" > .< / span > < span class = "n" > collect< / span > ::< span class = "o" > < < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "n" > Item< / span > < span class = "o" > > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-9-21" name = "__codelineno-9-21" href = "#__codelineno-9-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-9-22" name = "__codelineno-9-22" href = "#__codelineno-9-22" > < / a > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > .< / span > < span class = "n" > sort_by< / span > < span class = "p" > (< / span > < span class = "o" > |< / span > < span class = "n" > a< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-23" name = "__codelineno-9-23" href = "#__codelineno-9-23" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > b< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "k" > as< / span > < span class = "w" > < / span > < span class = "kt" > f64< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "k" > as< / span > < span class = "w" > < / span > < span class = "kt" > f64< / span > < span class = "p" > )< / span >
< a id = "__codelineno-9-24" name = "__codelineno-9-24" href = "#__codelineno-9-24" > < / a > < span class = "w" > < / span > < span class = "p" > .< / span > < span class = "n" > partial_cmp< / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "p" > (< / span > < span class = "n" > a< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "k" > as< / span > < span class = "w" > < / span > < span class = "kt" > f64< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > a< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "k" > as< / span > < span class = "w" > < / span > < span class = "kt" > f64< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-9-25" name = "__codelineno-9-25" href = "#__codelineno-9-25" > < / a > < span class = "w" > < / span > < span class = "p" > .< / span > < span class = "n" > unwrap< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-9-26" name = "__codelineno-9-26" href = "#__codelineno-9-26" > < / a > < span class = "w" > < / span > < span class = "p" > });< / span >
< a id = "__codelineno-9-27" name = "__codelineno-9-27" href = "#__codelineno-9-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环贪心选择< / span >
< a id = "__codelineno-9-28" name = "__codelineno-9-28" href = "#__codelineno-9-28" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0.0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-29" name = "__codelineno-9-29" href = "#__codelineno-9-29" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > items< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-30" name = "__codelineno-9-30" href = "#__codelineno-9-30" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-31" name = "__codelineno-9-31" href = "#__codelineno-9-31" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-9-32" name = "__codelineno-9-32" href = "#__codelineno-9-32" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "k" > as< / span > < span class = "w" > < / span > < span class = "kt" > f64< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-33" name = "__codelineno-9-33" href = "#__codelineno-9-33" > < / a > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-34" name = "__codelineno-9-34" href = "#__codelineno-9-34" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-35" name = "__codelineno-9-35" href = "#__codelineno-9-35" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-9-36" name = "__codelineno-9-36" href = "#__codelineno-9-36" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "k" > as< / span > < span class = "w" > < / span > < span class = "kt" > f64< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "k" > as< / span > < span class = "w" > < / span > < span class = "kt" > f64< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "k" > as< / span > < span class = "w" > < / span > < span class = "kt" > f64< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-37" name = "__codelineno-9-37" href = "#__codelineno-9-37" > < / a > < span class = "w" > < / span > < span class = "c1" > // 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-9-38" name = "__codelineno-9-38" href = "#__codelineno-9-38" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-39" name = "__codelineno-9-39" href = "#__codelineno-9-39" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-40" name = "__codelineno-9-40" href = "#__codelineno-9-40" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-41" name = "__codelineno-9-41" href = "#__codelineno-9-41" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-9-42" name = "__codelineno-9-42" href = "#__codelineno-9-42" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "cm" > /* 物品 */< / span >
< a id = "__codelineno-10-2" name = "__codelineno-10-2" href = "#__codelineno-10-2" > < / a > < span class = "k" > typedef< / span > < span class = "w" > < / span > < span class = "k" > struct< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-3" name = "__codelineno-10-3" href = "#__codelineno-10-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品重量< / span >
< a id = "__codelineno-10-4" name = "__codelineno-10-4" href = "#__codelineno-10-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品价值< / span >
< a id = "__codelineno-10-5" name = "__codelineno-10-5" href = "#__codelineno-10-5" > < / a > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-6" name = "__codelineno-10-6" href = "#__codelineno-10-6" > < / a >
< a id = "__codelineno-10-7" name = "__codelineno-10-7" href = "#__codelineno-10-7" > < / a > < span class = "cm" > /* 分数背包：贪心 */< / span >
< a id = "__codelineno-10-8" name = "__codelineno-10-8" href = "#__codelineno-10-8" > < / a > < span class = "kt" > float< / span > < span class = "w" > < / span > < span class = "nf" > fractionalKnapsack< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > wgt< / span > < span class = "p" > [],< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > [],< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > itemCount< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-9" name = "__codelineno-10-9" href = "#__codelineno-10-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-10-10" name = "__codelineno-10-10" href = "#__codelineno-10-10" > < / a > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > items< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > malloc< / span > < span class = "p" > (< / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "n" > Item< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > itemCount< / span > < span class = "p" > );< / span >
< a id = "__codelineno-10-11" name = "__codelineno-10-11" href = "#__codelineno-10-11" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > itemCount< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-12" name = "__codelineno-10-12" href = "#__codelineno-10-12" > < / a > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > Item< / span > < span class = "p" > ){.< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > wgt< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]};< / span >
< a id = "__codelineno-10-13" name = "__codelineno-10-13" href = "#__codelineno-10-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-14" name = "__codelineno-10-14" href = "#__codelineno-10-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-10-15" name = "__codelineno-10-15" href = "#__codelineno-10-15" > < / a > < span class = "w" > < / span > < span class = "n" > qsort< / span > < span class = "p" > (< / span > < span class = "n" > items< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > size_t< / span > < span class = "p" > )< / span > < span class = "n" > itemCount< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "n" > Item< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > sortByValueDensity< / span > < span class = "p" > );< / span >
< a id = "__codelineno-10-16" name = "__codelineno-10-16" href = "#__codelineno-10-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环贪心选择< / span >
< a id = "__codelineno-10-17" name = "__codelineno-10-17" href = "#__codelineno-10-17" > < / a > < span class = "w" > < / span > < span class = "kt" > float< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0.0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-18" name = "__codelineno-10-18" href = "#__codelineno-10-18" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > itemCount< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-19" name = "__codelineno-10-19" href = "#__codelineno-10-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > items< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ].< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-20" name = "__codelineno-10-20" href = "#__codelineno-10-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-10-21" name = "__codelineno-10-21" href = "#__codelineno-10-21" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ].< / span > < span class = "n" > v< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-22" name = "__codelineno-10-22" href = "#__codelineno-10-22" > < / a > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ].< / span > < span class = "n" > w< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-23" name = "__codelineno-10-23" href = "#__codelineno-10-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-24" name = "__codelineno-10-24" href = "#__codelineno-10-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-10-25" name = "__codelineno-10-25" href = "#__codelineno-10-25" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > float< / span > < span class = "p" > )< / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ].< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ].< / span > < span class = "n" > v< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-26" name = "__codelineno-10-26" href = "#__codelineno-10-26" > < / a > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-27" name = "__codelineno-10-27" href = "#__codelineno-10-27" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-28" name = "__codelineno-10-28" href = "#__codelineno-10-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-29" name = "__codelineno-10-29" href = "#__codelineno-10-29" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-30" name = "__codelineno-10-30" href = "#__codelineno-10-30" > < / a > < span class = "w" > < / span > < span class = "n" > free< / span > < span class = "p" > (< / span > < span class = "n" > items< / span > < span class = "p" > );< / span >
< a id = "__codelineno-10-31" name = "__codelineno-10-31" href = "#__codelineno-10-31" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-32" name = "__codelineno-10-32" href = "#__codelineno-10-32" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.kt< / span > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "cm" > /* 物品 */< / span >
< a id = "__codelineno-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / a > < span class = "kd" > class< / span > < span class = "w" > < / span > < span class = "nc" > Item< / span > < span class = "p" > (< / span >
< a id = "__codelineno-11-3" name = "__codelineno-11-3" href = "#__codelineno-11-3" > < / a > < span class = "w" > < / span > < span class = "kd" > val< / span > < span class = "w" > < / span > < span class = "nv" > w< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "c1" > // 物品< / span >
< a id = "__codelineno-11-4" name = "__codelineno-11-4" href = "#__codelineno-11-4" > < / a > < span class = "w" > < / span > < span class = "kd" > val< / span > < span class = "w" > < / span > < span class = "nv" > v< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "w" > < / span > < span class = "c1" > // 物品价值< / span >
< a id = "__codelineno-11-5" name = "__codelineno-11-5" href = "#__codelineno-11-5" > < / a > < span class = "p" > )< / span >
< a id = "__codelineno-11-6" name = "__codelineno-11-6" href = "#__codelineno-11-6" > < / a >
< a id = "__codelineno-11-7" name = "__codelineno-11-7" href = "#__codelineno-11-7" > < / a > < span class = "cm" > /* 分数背包：贪心 */< / span >
< a id = "__codelineno-11-8" name = "__codelineno-11-8" href = "#__codelineno-11-8" > < / a > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > fractionalKnapsack< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > IntArray< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > _val< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > IntArray< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "p" > ):< / span > < span class = "w" > < / span > < span class = "kt" > Double< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-9" name = "__codelineno-11-9" href = "#__codelineno-11-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-11-10" name = "__codelineno-11-10" href = "#__codelineno-11-10" > < / a > < span class = "w" > < / span > < span class = "kd" > var< / span > < span class = "w" > < / span > < span class = "nv" > cap< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > c< / span >
< a id = "__codelineno-11-11" name = "__codelineno-11-11" href = "#__codelineno-11-11" > < / a > < span class = "w" > < / span > < span class = "kd" > val< / span > < span class = "w" > < / span > < span class = "nv" > items< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > arrayOfNulls< / span > < span class = "o" > < < / span > < span class = "n" > Item< / span > < span class = "o" > > < / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > < span class = "p" > .< / span > < span class = "na" > size< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-12" name = "__codelineno-11-12" href = "#__codelineno-11-12" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > wgt< / span > < span class = "p" > .< / span > < span class = "na" > indices< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-13" name = "__codelineno-11-13" href = "#__codelineno-11-13" > < / a > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > _val< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-14" name = "__codelineno-11-14" href = "#__codelineno-11-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-15" name = "__codelineno-11-15" href = "#__codelineno-11-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-11-16" name = "__codelineno-11-16" href = "#__codelineno-11-16" > < / a > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > .< / span > < span class = "na" > sortBy< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > Item? < / span > < span class = "o" > -> < / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "o" > !!< / span > < span class = "p" > .< / span > < span class = "na" > v< / span > < span class = "p" > .< / span > < span class = "na" > toDouble< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > w< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-17" name = "__codelineno-11-17" href = "#__codelineno-11-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环贪心选择< / span >
< a id = "__codelineno-11-18" name = "__codelineno-11-18" href = "#__codelineno-11-18" > < / a > < span class = "w" > < / span > < span class = "kd" > var< / span > < span class = "w" > < / span > < span class = "nv" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0.0< / span >
< a id = "__codelineno-11-19" name = "__codelineno-11-19" href = "#__codelineno-11-19" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-20" name = "__codelineno-11-20" href = "#__codelineno-11-20" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "o" > !!< / span > < span class = "p" > .< / span > < span class = "na" > w< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-21" name = "__codelineno-11-21" href = "#__codelineno-11-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-11-22" name = "__codelineno-11-22" href = "#__codelineno-11-22" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > v< / span >
< a id = "__codelineno-11-23" name = "__codelineno-11-23" href = "#__codelineno-11-23" > < / a > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > w< / span >
< a id = "__codelineno-11-24" name = "__codelineno-11-24" href = "#__codelineno-11-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-25" name = "__codelineno-11-25" href = "#__codelineno-11-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-11-26" name = "__codelineno-11-26" href = "#__codelineno-11-26" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > v< / span > < span class = "p" > .< / span > < span class = "na" > toDouble< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > w< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > cap< / span >
< a id = "__codelineno-11-27" name = "__codelineno-11-27" href = "#__codelineno-11-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-11-28" name = "__codelineno-11-28" href = "#__codelineno-11-28" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span >
< a id = "__codelineno-11-29" name = "__codelineno-11-29" href = "#__codelineno-11-29" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-30" name = "__codelineno-11-30" href = "#__codelineno-11-30" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-31" name = "__codelineno-11-31" href = "#__codelineno-11-31" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-11-32" name = "__codelineno-11-32" href = "#__codelineno-11-32" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.rb< / span > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / a > < span class = "o" > [< / span > < span class = "n" > class< / span > < span class = "o" > ]< / span > < span class = "p" > {< / span > < span class = "no" > Item< / span > < span class = "p" > }< / span > < span class = "o" > -[< / span > < span class = "n" > func< / span > < span class = "o" > ]< / span > < span class = "p" > {}< / span >
< a id = "__codelineno-12-2" name = "__codelineno-12-2" href = "#__codelineno-12-2" > < / a >
< a id = "__codelineno-12-3" name = "__codelineno-12-3" href = "#__codelineno-12-3" > < / a > < span class = "o" > [< / span > < span class = "n" > class< / span > < span class = "o" > ]< / span > < span class = "p" > {}< / span > < span class = "o" > -[< / span > < span class = "n" > func< / span > < span class = "o" > ]< / span > < span class = "p" > {< / span > < span class = "n" > fractional_knapsack< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< p > Apart from sorting, in the worst case, the entire list of items needs to be traversed, < strong > hence the time complexity is < span class = "arithmatex" > \(O(n)\)< / span > < / strong > , where < span class = "arithmatex" > \(n\)< / span > is the number of items.< / p >
< p > Since an < code > Item< / code > object list is initialized, < strong > the space complexity is < span class = "arithmatex" > \(O(n)\)< / span > < / strong > .< / p >
< h3 id = "3-correctness-proof" > 3. Correctness proof< a class = "headerlink" href = "#3-correctness-proof" title = "Permanent link" > ¶ < / a > < / h3 >
< p > Using proof by contradiction. Suppose item < span class = "arithmatex" > \(x\)< / span > has the highest unit value, and some algorithm yields a maximum value < code > res< / code > , but the solution does not include item < span class = "arithmatex" > \(x\)< / span > .< / p >
< p > Now remove a unit weight of any item from the knapsack and replace it with a unit weight of item < span class = "arithmatex" > \(x\)< / span > . Since the unit value of item < span class = "arithmatex" > \(x\)< / span > is the highest, the total value after replacement will definitely be greater than < code > res< / code > . < strong > This contradicts the assumption that < code > res< / code > is the optimal solution, proving that the optimal solution must include item < span class = "arithmatex" > \(x\)< / span > < / strong > .< / p >
< p > For other items in this solution, we can also construct the above contradiction. Overall, < strong > items with greater unit value are always better choices< / strong > , proving that the greedy strategy is effective.< / p >
< p > As shown in Figure 15-6, if the item weight and unit value are viewed as the horizontal and vertical axes of a two-dimensional chart respectively, the fractional knapsack problem can be transformed into "seeking the largest area enclosed within a limited horizontal axis range". This analogy can help us understand the effectiveness of the greedy strategy from a geometric perspective.< / p >
< p > < a class = "glightbox" href = "../fractional_knapsack_problem.assets/fractional_knapsack_area_chart.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Geometric representation of the fractional knapsack problem" class = "animation-figure" src = "../fractional_knapsack_problem.assets/fractional_knapsack_area_chart.png" / > < / a > < / p >
< p align = "center" > Figure 15-6 Geometric representation of the fractional knapsack problem < / p >
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< script > document $ . subscribe ( ( ) => { const lightbox = GLightbox ( { "touchNavigation" : true , "loop" : false , "zoomable" : true , "draggable" : false , "openEffect" : "zoom" , "closeEffect" : "zoom" , "slideEffect" : "none" } ) ; } ) < / script > < / body >
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