diff --git a/codes/csharp/chapter_dynamic_programming/knapsack.cs b/codes/csharp/chapter_dynamic_programming/knapsack.cs new file mode 100644 index 000000000..08ffe5470 --- /dev/null +++ b/codes/csharp/chapter_dynamic_programming/knapsack.cs @@ -0,0 +1,115 @@ +/** +* File: knapsack.cs +* Created Time: 2023-07-07 +* Author: hpstory (hpstory1024@163.com) +*/ + +namespace hello_algo.chapter_dynamic_programming; + +public class knapsack { + /* 0-1 背包:暴力搜索 */ + public int knapsack_dfs(int[] weight, int[] val, int i, int c) { + // 若已选完所有物品或背包无容量,则返回价值 0 + if (i == 0 || c == 0) { + return 0; + } + // 若超过背包容量,则只能不放入背包 + if (weight[i - 1] > c) { + return knapsack_dfs(weight, val, i - 1, c); + } + // 计算不放入和放入物品 i 的最大价值 + int no = knapsack_dfs(weight, val, i - 1, c); + int yes = knapsack_dfs(weight, val, i - 1, c - weight[i - 1]) + val[i - 1]; + // 返回两种方案中价值更大的那一个 + return Math.Max(no, yes); + } + + /* 0-1 背包:记忆化搜索 */ + public int knapsack_dfs_mem(int[] weight, int[] val, int[][] mem, int i, int c) { + // 若已选完所有物品或背包无容量,则返回价值 0 + if (i == 0 || c == 0) { + return 0; + } + // 若已有记录,则直接返回 + if (mem[i][c] != -1) { + return mem[i][c]; + } + // 若超过背包容量,则只能不放入背包 + if (weight[i - 1] > c) { + return knapsack_dfs_mem(weight, val, mem, i - 1, c); + } + // 计算不放入和放入物品 i 的最大价值 + int no = knapsack_dfs_mem(weight, val, mem, i - 1, c); + int yes = knapsack_dfs_mem(weight, val, mem, i - 1, c - weight[i - 1]) + val[i - 1]; + // 记录并返回两种方案中价值更大的那一个 + mem[i][c] = Math.Max(no, yes); + return mem[i][c]; + } + + /* 0-1 背包:动态规划 */ + public int knapsack_dp(int[] weight, int[] val, int cap) { + int n = weight.Length; + // 初始化 dp 列表 + int[,] dp = new int[n + 1, cap + 1]; + // 状态转移 + for (int i = 1; i <= n; i++) { + for (int c = 1; c <= cap; c++) { + if (weight[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] = Math.Max(dp[i - 1, c - weight[i - 1]] + val[i - 1], dp[i - 1, c]); + } + } + } + return dp[n, cap]; + } + + /* 0-1 背包:状态压缩后的动态规划 */ + public int knapsack_dp_comp(int[] weight, int[] val, int cap) { + int n = weight.Length; + // 初始化 dp 列表 + int[] dp = new int[cap + 1]; + // 状态转移 + for (int i = 1; i <= n; i++) { + // 倒序遍历 + for (int c = cap; c > 0; c--) { + if (weight[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] = Math.Max(dp[c - weight[i - 1]] + val[i - 1], dp[c]); + } + } + } + return dp[cap]; + } + + [Test] + public void Test() { + int[] weight = { 10, 20, 30, 40, 50 }; + int[] val = { 60, 100, 120, 160, 200 }; + int cap = 50; + int n = weight.Length; + + // 暴力搜索 + Console.WriteLine(knapsack_dfs(weight, val, n, cap)); + + // 记忆化搜索 + int[][] mem = new int[n + 1][]; + for (int i = 0; i <= n; i++) { + mem[i] = new int[cap + 1]; + Array.Fill(mem[i], -1); + } + + Console.WriteLine(knapsack_dfs_mem(weight, val, mem, n, cap)); + + // 动态规划 + Console.WriteLine(knapsack_dp(weight, val, cap)); + + // 状态压缩后的动态规划 + Console.WriteLine(knapsack_dp_comp(weight, val, cap)); + } +}