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

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 no = knapsackDFS(weight, val, i - 1, c);
-        int yes = knapsack_dfs(weight, val, i - 1, c - weight[i - 1]) + val[i - 1];
+        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 no = knapsackDFSMem(weight, val, mem, i - 1, c);
-        int yes = knapsack_dfs_mem(weight, val, mem, i - 1, c - weight[i - 1]) + val[i - 1];
+        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));
     }
 }

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));
+    }
+}