diff --git a/chapter_computational_complexity/iteration_and_recursion.md b/chapter_computational_complexity/iteration_and_recursion.md index b6642fa73..c51cbc34a 100644 --- a/chapter_computational_complexity/iteration_and_recursion.md +++ b/chapter_computational_complexity/iteration_and_recursion.md @@ -60,7 +60,15 @@ status: new === "Go" ```go title="iteration.go" - [class]{}-[func]{forLoop} + /* for 循环 */ + func forLoop(n int) int { + res := 0 + // 循环求和 1, 2, ..., n-1, n + for i := 1; i <= n; i++ { + res += i + } + return res + } ``` === "JS" @@ -84,7 +92,15 @@ status: new === "C#" ```csharp title="iteration.cs" - [class]{iteration}-[func]{forLoop} + /* for 循环 */ + int forLoop(int n) { + int res = 0; + // 循环求和 1, 2, ..., n-1, n + for (int i = 1; i <= n; i++) { + res += i; + } + return res; + } ``` === "Swift" @@ -182,7 +198,19 @@ status: new === "Go" ```go title="iteration.go" - [class]{}-[func]{whileLoop} + /* while 循环 */ + func whileLoop(n int) int { + res := 0 + // 初始化条件变量 + i := 1 + // 循环求和 1, 2, ..., n-1, n + for i <= n { + res += i + // 更新条件变量 + i++ + } + return res + } ``` === "JS" @@ -206,7 +234,17 @@ status: new === "C#" ```csharp title="iteration.cs" - [class]{iteration}-[func]{whileLoop} + /* while 循环 */ + int whileLoop(int n) { + int res = 0; + int i = 1; // 初始化条件变量 + // 循环求和 1, 2, ..., n-1, n + while (i <= n) { + res += i; + i += 1; // 更新条件变量 + } + return res; + } ``` === "Swift" @@ -302,7 +340,20 @@ status: new === "Go" ```go title="iteration.go" - [class]{}-[func]{whileLoopII} + /* while 循环(两次更新) */ + func whileLoopII(n int) int { + res := 0 + // 初始化条件变量 + i := 1 + // 循环求和 1, 4, ... + for i <= n { + res += i + // 更新条件变量 + i++ + i *= 2 + } + return res + } ``` === "JS" @@ -326,7 +377,19 @@ status: new === "C#" ```csharp title="iteration.cs" - [class]{iteration}-[func]{whileLoopII} + /* while 循环(两次更新) */ + int whileLoopII(int n) { + int res = 0; + int i = 1; // 初始化条件变量 + // 循环求和 1, 2, 4, 5... + while (i <= n) { + res += i; + i += 1; // 更新条件变量 + res += i; + i *= 2; // 更新条件变量 + } + return res; + } ``` === "Swift" @@ -422,7 +485,18 @@ status: new === "Go" ```go title="iteration.go" - [class]{}-[func]{nestedForLoop} + /* 双层 for 循环 */ + func nestedForLoop(n int) string { + res := "" + // 循环 i = 1, 2, ..., n-1, n + for i := 1; i <= n; i++ { + for j := 1; j <= n; j++ { + // 循环 j = 1, 2, ..., n-1, n + res += fmt.Sprintf("(%d, %d), ", i, j) + } + } + return res + } ``` === "JS" @@ -446,7 +520,18 @@ status: new === "C#" ```csharp title="iteration.cs" - [class]{iteration}-[func]{nestedForLoop} + /* 双层 for 循环 */ + string nestedForLoop(int n) { + StringBuilder res = new StringBuilder(); + // 循环 i = 1, 2, ..., n-1, n + for (int i = 1; i <= n; i++) { + // 循环 j = 1, 2, ..., n-1, n + for (int j = 1; j <= n; j++) { + res.Append($"({i}, {j}), "); + } + } + return res.ToString(); + } ``` === "Swift" @@ -556,7 +641,17 @@ status: new === "Go" ```go title="recursion.go" - [class]{}-[func]{recur} + /* 递归 */ + func recur(n int) int { + // 终止条件 + if n == 1 { + return 1 + } + // 递:递归调用 + res := recur(n - 1) + // 归:返回结果 + return n + res + } ``` === "JS" @@ -580,7 +675,16 @@ status: new === "C#" ```csharp title="recursion.cs" - [class]{recursion}-[func]{recur} + /* 递归 */ + int recur(int n) { + // 终止条件 + if (n == 1) + return 1; + // 递:递归调用 + int res = recur(n - 1); + // 归:返回结果 + return n + res; + } ``` === "Swift" @@ -696,7 +800,15 @@ status: new === "Go" ```go title="recursion.go" - [class]{}-[func]{tailRecur} + /* 尾递归 */ + func tailRecur(n int, res int) int { + // 终止条件 + if n == 0 { + return res + } + // 尾递归调用 + return tailRecur(n-1, res+n) + } ``` === "JS" @@ -720,7 +832,14 @@ status: new === "C#" ```csharp title="recursion.cs" - [class]{recursion}-[func]{tailRecur} + /* 尾递归 */ + int tailRecur(int n, int res) { + // 终止条件 + if (n == 0) + return res; + // 尾递归调用 + return tailRecur(n - 1, res + n); + } ``` === "Swift" @@ -826,7 +945,17 @@ status: new === "Go" ```go title="recursion.go" - [class]{}-[func]{fib} + /* 斐波那契数列:递归 */ + func fib(n int) int { + // 终止条件 f(1) = 0, f(2) = 1 + if n == 1 || n == 2 { + return n - 1 + } + // 递归调用 f(n) = f(n-1) + f(n-2) + res := fib(n-1) + fib(n-2) + // 返回结果 f(n) + return res + } ``` === "JS" @@ -850,7 +979,16 @@ status: new === "C#" ```csharp title="recursion.cs" - [class]{recursion}-[func]{fib} + /* 斐波那契数列:递归 */ + int fib(int n) { + // 终止条件 f(1) = 0, f(2) = 1 + if (n == 1 || n == 2) + return n - 1; + // 递归调用 f(n) = f(n-1) + f(n-2) + int res = fib(n - 1) + fib(n - 2); + // 返回结果 f(n) + return res; + } ``` === "Swift" diff --git a/chapter_heap/build_heap.md b/chapter_heap/build_heap.md index d482706bc..b59cee050 100644 --- a/chapter_heap/build_heap.md +++ b/chapter_heap/build_heap.md @@ -73,7 +73,7 @@ comments: true func newMaxHeap(nums []any) *maxHeap { // 将列表元素原封不动添加进堆 h := &maxHeap{data: nums} - for i := len(h.data) - 1; i >= 0; i-- { + for i := h.parent(len(h.data) - 1); i >= 0; i-- { // 堆化除叶节点以外的其他所有节点 h.siftDown(i) } @@ -118,7 +118,7 @@ comments: true maxHeap *h = (maxHeap *)malloc(sizeof(maxHeap)); h->size = size; memcpy(h->data, nums, size * sizeof(int)); - for (int i = size - 1; i >= 0; i--) { + for (int i = parent(size - 1); i >= 0; i--) { // 堆化除叶节点以外的其他所有节点 siftDown(h, i); }