From d75a2eb691d4d4e80ffbc9420b078ed0a64b03e7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E7=8E=8B=E4=BD=9C=E5=8B=8B?= <59754483+Zuoxun@users.noreply.github.com> Date: Sat, 7 Oct 2023 21:38:02 +0800 Subject: [PATCH] Add Unbounded knapsack in C code (#832) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit * Update vector.h 增加功能列表： 获取向量的第 i 个元素 设置向量的第 i 个元素 向量扩容 向量缩容 向量插入元素 向量删除元素 向量交换元素 向量是否为空 向量是否已满 向量是否相等 对向量内部进行排序（升序/降序） 对向量某段数据排序（升序/降序） * Create hanota.c * 新增binary_search_recur.c * Update vector.h * Delete codes/c/chapter_divide_and_conquer directory * Update vector.h * Create binary_search_recur.c * Delete codes/chapter_divide_and_conquer directory * Update vector.h * old vector.h * Create unbounded_knapsack.c * Update unbounded_knapsack.c * Update unbounded_knapsack.c * Create CMakeLists.txt * Update unbounded_knapsack.c --------- Co-authored-by: Yudong Jin --- .../CMakeLists.txt | 3 +- .../unbounded_knapsack.c | 72 +++++++++++++++++++ 2 files changed, 74 insertions(+), 1 deletion(-) create mode 100644 codes/c/chapter_dynamic_programming/unbounded_knapsack.c diff --git a/codes/c/chapter_dynamic_programming/CMakeLists.txt b/codes/c/chapter_dynamic_programming/CMakeLists.txt index b54139627..292b26f3c 100644 --- a/codes/c/chapter_dynamic_programming/CMakeLists.txt +++ b/codes/c/chapter_dynamic_programming/CMakeLists.txt @@ -1,3 +1,4 @@ +add_executable(min_cost_climbing_stairs_dp min_cost_climbing_stairs_dp.c) add_executable(min_path_sum min_path_sum.c) add_executable(knapsack knapsack.c) -add_executable(min_cost_climbing_stairs_dp min_cost_climbing_stairs_dp.c) +add_executable(unbounded_knapsack unbounded_knapsack.c) diff --git a/codes/c/chapter_dynamic_programming/unbounded_knapsack.c b/codes/c/chapter_dynamic_programming/unbounded_knapsack.c new file mode 100644 index 000000000..ac221f732 --- /dev/null +++ b/codes/c/chapter_dynamic_programming/unbounded_knapsack.c @@ -0,0 +1,72 @@ +/** + * File: unbounded_knapsack.c + * Created Time: 2023-10-02 + * Author: Zuoxun (845242523@qq.com) + */ + +#include "../utils/common.h" + +/* 求最大值 */ +int max(int a, int b) { + return a > b ? a : b; +} + +/* 完全背包：动态规划 */ +int unboundedKnapsackDP(int wgt[], int val[], int cap, int wgtSize) { + int n = wgtSize; + // 初始化 dp 表 + int dp[n + 1][cap + 1]; + memset(dp, 0, sizeof(dp)); + // 状态转移 + for (int i = 1; i <= n; i++) { + for (int c = 1; c <= cap; c++) { + if (wgt[i - 1] > c) { + // 若超过背包容量，则不选物品 i + dp[i][c] = dp[i - 1][c]; + } else { + // 不选和选物品 i 这两种方案的较大值 + dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]); + } + } + } + return dp[n][cap]; +} + +/* 完全背包：空间优化后的动态规划 */ +int unboundedKnapsackDPComp(int wgt[], int val[], int cap, int wgtSize) { + int n = wgtSize; + // 初始化 dp 表 + int dp[cap + 1]; + memset(dp, 0, sizeof(dp)); + // 状态转移 + for (int i = 1; i <= n; i++) { + for (int c = 1; c <= cap; c++) { + if (wgt[i - 1] > c) { + // 若超过背包容量，则不选物品 i + dp[c] = dp[c]; + } else { + // 不选和选物品 i 这两种方案的较大值 + dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]); + } + } + } + return dp[cap]; +} + +/* Driver code */ +int main() { + int wgt[] = {1, 2, 3}; + int val[] = {5, 11, 15}; + int wgtSize = sizeof(wgt) / sizeof(wgt[0]); + int cap = 4; + + // 动态规划 + int res = unboundedKnapsackDP(wgt, val, cap, wgtSize); + printf("不超过背包容量的最大物品价值为 %d\n", res); + + // 空间优化后的动态规划 + res = unboundedKnapsackDPComp(wgt, val, cap, wgtSize); + printf("不超过背包容量的最大物品价值为 %d\n", res); + + return 0; +}