feat(csharp): add csharp code for charper dynamic programming (#574)

* feat(csharp): add csharp code for charper dynamic programming

* add climbing_stairs_constraint_dp

codes/csharp/chapter_dynamic_programming/climbing_stairs_backtrack.cs

@@ -0,0 +1,41 @@
+/**
+* File: climbing_stairs_backtrack.cs
+* Created Time: 2023-06-30
+* Author: hpstory (hpstory1024@163.com)
+*/
+
+namespace hello_algo.chapter_dynamic_programming; 
+
+public class climbing_stairs_backtrack {
+    /* 回溯 */
+    public void backtrack(List<int> choices, int state, int n, List<int> res) {
+        // 当爬到第 n 阶时，方案数量加 1
+        if (state == n)
+            res[0]++;
+        // 遍历所有选择
+        foreach (int choice in choices) {
+            // 剪枝：不允许越过第 n 阶
+            if (state + choice > n)
+                break;
+            // 尝试：做出选择，更新状态
+            backtrack(choices, state + choice, n, res);
+            // 回退
+        }
+    }
+
+    /* 爬楼梯：回溯 */
+    public int climbingStairsBacktrack(int n) {
+        List<int> choices = new List<int> { 1, 2 }; // 可选择向上爬 1 或 2 阶
+        int state = 0; // 从第 0 阶开始爬
+        List<int> res = new List<int> { 0 }; // 使用 res[0] 记录方案数量
+        backtrack(choices, state, n, res);
+        return res[0];
+    }
+
+    [Test]
+    public void Test() {
+        int n = 9;
+        int res = climbingStairsBacktrack(n);
+        Console.WriteLine($"爬 {n} 阶楼梯共有 {res} 种方案");
+    }
+}

codes/csharp/chapter_dynamic_programming/climbing_stairs_constraint_dp.cs

@@ -0,0 +1,36 @@
+/**
+* File: climbing_stairs_constraint_dp.cs
+* Created Time: 2023-07-03
+* Author: hpstory (hpstory1024@163.com)
+*/
+
+namespace hello_algo.chapter_dynamic_programming;
+
+public class climbing_stairs_constraint_dp {
+    /* 带约束爬楼梯：动态规划 */
+    public int climbingStairsConstraintDP(int n) {
+        if (n == 1 || n == 2) {
+            return n;
+        }
+        // 初始化 dp 列表，用于存储子问题的解
+        int[,] dp = new int[n + 1, 3];
+        // 初始状态：预设最小子问题的解
+        dp[1, 1] = 1;
+        dp[1, 2] = 0;
+        dp[2, 1] = 0;
+        dp[2, 2] = 1;
+        // 状态转移：从较小子问题逐步求解较大子问题
+        for (int i = 3; i <= n; i++) {
+            dp[i, 1] = dp[i - 1, 2];
+            dp[i, 2] = dp[i - 2, 1] + dp[i - 2, 2];
+        }
+        return dp[n, 1] + dp[n, 2];
+    }
+
+    [Test]
+    public void Test() {
+        int n = 9;
+        int res = climbingStairsConstraintDP(n);
+        Console.WriteLine($"爬 {n} 阶楼梯共有 {res} 种方案");
+    }
+}

codes/csharp/chapter_dynamic_programming/climbing_stairs_dfs.cs

@@ -0,0 +1,31 @@
+/**
+* File: climbing_stairs_dfs.cs
+* Created Time: 2023-06-30
+* Author: hpstory (hpstory1024@163.com)
+*/
+
+namespace hello_algo.chapter_dynamic_programming; 
+
+public class climbing_stairs_dfs {
+    /* 搜索 */
+    public int dfs(int i) {
+        // 已知 dp[1] 和 dp[2] ，返回之
+        if (i == 1 || i == 2)
+            return i;
+        // dp[i] = dp[i-1] + dp[i-2]
+        int count = dfs(i - 1) + dfs(i - 2);
+        return count;
+    }
+
+    /* 爬楼梯：搜索 */
+    public int climbingStairsDFS(int n) {
+        return dfs(n);
+    }
+
+    [Test]
+    public void Test() {
+        int n = 9;
+        int res = climbingStairsDFS(n);
+        Console.WriteLine($"爬 {n} 阶楼梯共有 {res} 种方案");
+    }
+}

codes/csharp/chapter_dynamic_programming/climbing_stairs_dfs_mem.cs

@@ -0,0 +1,39 @@
+/**
+* File: climbing_stairs_dfs_mem.cs
+* Created Time: 2023-06-30
+* Author: hpstory (hpstory1024@163.com)
+*/
+
+namespace hello_algo.chapter_dynamic_programming;
+
+public class climbing_stairs_dfs_mem {
+    /* 记忆化搜索 */
+    public int dfs(int i, int[] mem) {
+        // 已知 dp[1] 和 dp[2] ，返回之
+        if (i == 1 || i == 2)
+            return i;
+        // 若存在记录 dp[i] ，则直接返回之
+        if (mem[i] != -1)
+            return mem[i];
+        // dp[i] = dp[i-1] + dp[i-2]
+        int count = dfs(i - 1, mem) + dfs(i - 2, mem);
+        // 记录 dp[i]
+        mem[i] = count;
+        return count;
+    }
+
+    /* 爬楼梯：记忆化搜索 */
+    public int climbingStairsDFSMem(int n) {
+        // mem[i] 记录爬到第 i 阶的方案总数，-1 代表无记录
+        int[] mem = new int[n + 1];
+        Array.Fill(mem, -1);
+        return dfs(n, mem);
+    }
+
+    [Test]
+    public void Test() {
+        int n = 9;
+        int res = climbingStairsDFSMem(n);
+        Console.WriteLine($"爬 {n} 阶楼梯共有 {res} 种方案");
+    }
+}

codes/csharp/chapter_dynamic_programming/climbing_stairs_dp.cs

@@ -0,0 +1,49 @@
+/**
+* File: climbing_stairs_dp.cs
+* Created Time: 2023-06-30
+* Author: hpstory (hpstory1024@163.com)
+*/
+
+namespace hello_algo.chapter_dynamic_programming; 
+
+public class climbing_stairs_dp {
+    /* 爬楼梯：动态规划 */
+    public int climbingStairsDP(int n) {
+        if (n == 1 || n == 2)
+            return n;
+        // 初始化 dp 列表，用于存储子问题的解
+        int[] dp = new int[n + 1];
+        // 初始状态：预设最小子问题的解
+        dp[1] = 1;
+        dp[2] = 2;
+        // 状态转移：从较小子问题逐步求解较大子问题
+        for (int i = 3; i <= n; i++) {
+            dp[i] = dp[i - 1] + dp[i - 2];
+        }
+        return dp[n];
+    }
+
+    /* 爬楼梯：状态压缩后的动态规划 */
+    public int climbingStairsDPComp(int n) {
+        if (n == 1 || n == 2)
+            return n;
+        int a = 1, b = 2;
+        for (int i = 3; i <= n; i++) {
+            int tmp = b;
+            b = a + b;
+            a = tmp;
+        }
+        return b;
+    }
+
+    [Test]
+    public void Test() {
+        int n = 9;
+
+        int res = climbingStairsDP(n);
+        Console.WriteLine($"爬 {n} 阶楼梯共有 {res} 种方案");
+
+        res = climbingStairsDPComp(n);
+        Console.WriteLine($"爬 {n} 阶楼梯共有 {res} 种方案");
+    }
+}

codes/csharp/chapter_dynamic_programming/min_cost_climbing_stairs_dp.cs

@@ -0,0 +1,53 @@
+/**
+* File: min_cost_climbing_stairs_dp.cs
+* Created Time: 2023-06-30
+* Author: hpstory (hpstory1024@163.com)
+*/
+
+namespace hello_algo.chapter_dynamic_programming;
+
+public class min_cost_climbing_stairs_dp {
+    /* 爬楼梯最小代价：动态规划 */
+    public int minCostClimbingStairsDP(int[] cost) {
+        int n = cost.Length - 1;
+        if (n == 1 || n == 2)
+            return cost[n];
+        // 初始化 dp 列表，用于存储子问题的解
+        int[] dp = new int[n + 1];
+        // 初始状态：预设最小子问题的解
+        dp[1] = cost[1];
+        dp[2] = cost[2];
+        // 状态转移：从较小子问题逐步求解较大子问题
+        for (int i = 3; i <= n; i++) {
+            dp[i] = Math.Min(dp[i - 1], dp[i - 2]) + cost[i];
+        }
+        return dp[n];
+    }
+
+    /* 爬楼梯最小代价：状态压缩后的动态规划 */
+    public int minCostClimbingStairsDPComp(int[] cost) {
+        int n = cost.Length - 1;
+        if (n == 1 || n == 2)
+            return cost[n];
+        int a = cost[1], b = cost[2];
+        for (int i = 3; i <= n; i++) {
+            int tmp = b;
+            b = Math.Min(a, tmp) + cost[i];
+            a = tmp;
+        }
+        return b;
+    }
+
+    [Test]
+    public void Test() {
+        int[] cost = { 0, 1, 10, 1, 1, 1, 10, 1, 1, 10, 1 };
+        Console.WriteLine("输入楼梯的代价列表为");
+        PrintUtil.PrintList(cost);
+
+        int res = minCostClimbingStairsDP(cost);
+        Console.WriteLine($"爬完楼梯的最低代价为 {res}");
+
+        res = minCostClimbingStairsDPComp(cost);
+        Console.WriteLine($"爬完楼梯的最低代价为 {res}");
+    }
+}

codes/csharp/utils/PrintUtil.cs

@@ -18,7 +18,7 @@ public class Trunk {
 
 public class PrintUtil {
     /* Print a list */
-    public static void PrintList<T>(List<T> list) {
+    public static void PrintList<T>(IList<T> list) {
         Console.WriteLine("[" + string.Join(", ", list) + "]");
     }