From 5ea016816a9da3139a9ab45f89ead18ffaced672 Mon Sep 17 00:00:00 2001 From: hpstory <33348162+hpstory@users.noreply.github.com> Date: Mon, 10 Jul 2023 17:34:54 +0800 Subject: [PATCH] fix(csharp): fix csharp method name in knapsack (#592) * fix(csharp): fix csharp method name in knapsack * feat(csharp): add csharp code for min path sum * move INF define into method * change INF to int max value --- .../chapter_dynamic_programming/knapsack.cs | 28 ++-- .../min_path_sum.cs | 124 ++++++++++++++++++ 2 files changed, 138 insertions(+), 14 deletions(-) create mode 100644 codes/csharp/chapter_dynamic_programming/min_path_sum.cs diff --git a/codes/csharp/chapter_dynamic_programming/knapsack.cs b/codes/csharp/chapter_dynamic_programming/knapsack.cs index 1e46f4d1b..ca1a24566 100644 --- a/codes/csharp/chapter_dynamic_programming/knapsack.cs +++ b/codes/csharp/chapter_dynamic_programming/knapsack.cs @@ -8,24 +8,24 @@ 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) { + public int knapsackDFS(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); + return knapsackDFS(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]; + int no = knapsackDFS(weight, val, i - 1, c); + int yes = knapsackDFS(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) { + public int knapsackDFSMem(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; @@ -36,18 +36,18 @@ public class knapsack { } // 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); + return knapsackDFSMem(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]; + int no = knapsackDFSMem(weight, val, mem, i - 1, c); + int yes = knapsackDFSMem(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) { + public int knapsackDP(int[] weight, int[] val, int cap) { int n = weight.Length; // 初始化 dp 表 int[,] dp = new int[n + 1, cap + 1]; @@ -67,7 +67,7 @@ public class knapsack { } /* 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) { + public int knapsackDPComp(int[] weight, int[] val, int cap) { int n = weight.Length; // 初始化 dp 表 int[] dp = new int[cap + 1]; @@ -95,7 +95,7 @@ public class knapsack { int n = weight.Length; // 暴力搜索 - Console.WriteLine(knapsack_dfs(weight, val, n, cap)); + Console.WriteLine(knapsackDFS(weight, val, n, cap)); // 记忆化搜索 int[][] mem = new int[n + 1][]; @@ -104,12 +104,12 @@ public class knapsack { Array.Fill(mem[i], -1); } - Console.WriteLine(knapsack_dfs_mem(weight, val, mem, n, cap)); + Console.WriteLine(knapsackDFSMem(weight, val, mem, n, cap)); // 动态规划 - Console.WriteLine(knapsack_dp(weight, val, cap)); + Console.WriteLine(knapsackDP(weight, val, cap)); // 状态压缩后的动态规划 - Console.WriteLine(knapsack_dp_comp(weight, val, cap)); + Console.WriteLine(knapsackDPComp(weight, val, cap)); } } diff --git a/codes/csharp/chapter_dynamic_programming/min_path_sum.cs b/codes/csharp/chapter_dynamic_programming/min_path_sum.cs new file mode 100644 index 000000000..183bac467 --- /dev/null +++ b/codes/csharp/chapter_dynamic_programming/min_path_sum.cs @@ -0,0 +1,124 @@ +/** +* File: min_path_sum.cs +* Created Time: 2023-07-10 +* Author: hpstory (hpstory1024@163.com) +*/ + +namespace hello_algo.chapter_dynamic_programming; + +public class min_path_sum { + /* 最小路径和：暴力搜索 */ + public int minPathSumDFS(int[][] grid, int i, int j) { + // 若为左上角单元格，则终止搜索 + if (i == 0 && j == 0){ + return grid[0][0]; + } + // 若行列索引越界，则返回 +∞ 代价 + if (i < 0 || j < 0) { + return int.MaxValue; + } + // 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价 + int left = minPathSumDFS(grid, i - 1, j); + int up = minPathSumDFS(grid, i, j - 1); + // 返回从左上角到 (i, j) 的最小路径代价 + return Math.Min(left, up) + grid[i][j]; + } + + /* 最小路径和：记忆化搜索 */ + public int minPathSumDFSMem(int[][] grid, int[][] mem, int i, int j) { + // 若为左上角单元格，则终止搜索 + if (i == 0 && j == 0) { + return grid[0][0]; + } + // 若行列索引越界，则返回 +∞ 代价 + if (i < 0 || j < 0) { + return int.MaxValue; + } + // 若已有记录，则直接返回 + if (mem[i][j] != -1) { + return mem[i][j]; + } + // 左边和上边单元格的最小路径代价 + int left = minPathSumDFSMem(grid, mem, i - 1, j); + int up = minPathSumDFSMem(grid, mem, i, j - 1); + // 记录并返回左上角到 (i, j) 的最小路径代价 + mem[i][j] = Math.Min(left, up) + grid[i][j]; + return mem[i][j]; + } + + /* 最小路径和：动态规划 */ + public int minPathSumDP(int[][] grid) { + int n = grid.Length, m = grid[0].Length; + // 初始化 dp 表 + int[,] dp = new int[n, m]; + dp[0, 0] = grid[0][0]; + // 状态转移：首行 + for (int j = 1; j < m; j++) { + dp[0, j] = dp[0, j - 1] + grid[0][j]; + } + // 状态转移：首列 + for (int i = 1; i < n; i++) { + dp[i, 0] = dp[i - 1, 0] + grid[i][0]; + } + // 状态转移：其余行列 + for (int i = 1; i < n; i++) { + for (int j = 1; j < m; j++) { + dp[i, j] = Math.Min(dp[i, j - 1], dp[i - 1, j]) + grid[i][j]; + } + } + return dp[n - 1, m - 1]; + } + + /* 最小路径和：状态压缩后的动态规划 */ + public int minPathSumDPComp(int[][] grid) { + int n = grid.Length, m = grid[0].Length; + // 初始化 dp 表 + int[] dp = new int[m]; + dp[0] = grid[0][0]; + // 状态转移：首行 + for (int j = 1; j < m; j++) { + dp[j] = dp[j - 1] + grid[0][j]; + } + // 状态转移：其余行 + for (int i = 1; i < n; i++) { + // 状态转移：首列 + dp[0] = dp[0] + grid[i][0]; + // 状态转移：其余列 + for (int j = 1; j < m; j++) { + dp[j] = Math.Min(dp[j - 1], dp[j]) + grid[i][j]; + } + } + return dp[m - 1]; + } + + [Test] + public void Test() { + int[][] grid = + { + new int[4] { 1, 3, 1, 5 }, + new int[4] { 2, 2, 4, 2 }, + new int[4] { 5, 3, 2, 1 }, + new int[4] { 4, 3, 5, 2 } + }; + + int n = grid.Length, m = grid[0].Length; + + // 暴力搜索 + Console.WriteLine(minPathSumDFS(grid, n - 1, m - 1)); + + // 记忆化搜索 + int[][] mem = new int[n][]; + for (int i = 0; i < n; i++) { + mem[i] = new int[m]; + Array.Fill(mem[i], -1); + } + + Console.WriteLine(minPathSumDFSMem(grid, mem, n - 1, m - 1)); + + // 动态规划 + Console.WriteLine(minPathSumDP(grid)); + + // 状态压缩后的动态规划 + Console.WriteLine(minPathSumDPComp(grid)); + } +}