build

chapter_dynamic_programming/dp_problem_features.md

@@ -123,7 +123,22 @@ $$
 === "C#"
 
     ```csharp title="min_cost_climbing_stairs_dp.cs"
-    [class]{min_cost_climbing_stairs_dp}-[func]{minCostClimbingStairsDP}
+    /* 爬楼梯最小代价：动态规划 */
+    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];
+    }
     ```
 
 === "Swift"
@@ -227,7 +242,19 @@ $$
 === "C#"
 
     ```csharp title="min_cost_climbing_stairs_dp.cs"
-    [class]{min_cost_climbing_stairs_dp}-[func]{minCostClimbingStairsDPComp}
+    /* 爬楼梯最小代价：状态压缩后的动态规划 */
+    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;
+    }
     ```
 
 === "Swift"
@@ -384,7 +411,25 @@ $$
 === "C#"
 
     ```csharp title="climbing_stairs_constraint_dp.cs"
-    [class]{climbing_stairs_constraint_dp}-[func]{climbingStairsConstraintDP}
+    /* 带约束爬楼梯：动态规划 */
+    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];
+    }
     ```
 
 === "Swift"