Update the section of intro to DP.

codes/cpp/chapter_dynamic_programming/climbing_stairs_constraint_dp.cpp

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+/**
+ * File: climbing_stairs_constraint_dp.cpp
+ * Created Time: 2023-07-01
+ * Author: Krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* 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
+    vector<vector<int>> dp(n + 1, vector<int>(3, 0));
+    // 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];
+}
+
+/* Driver Code */
+int main() {
+    int n = 9;
+
+    int res = climbingStairsConstraintDP(n);
+    cout << "爬 " << n << " 阶楼梯共有 " << res << " 种方案" << endl;
+
+    return 0;
+}

codes/java/chapter_dynamic_programming/climbing_stairs_constraint_dp.java

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+/**
+ * File: climbing_stairs_constraint_dp.java
+ * Created Time: 2023-07-01
+ * Author: Krahets (krahets@163.com)
+ */
+
+package chapter_dynamic_programming;
+
+public class climbing_stairs_constraint_dp {
+    /* 带约束爬楼梯：动态规划 */
+    static 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];
+    }
+
+    public static void main(String[] args) {
+        int n = 9;
+
+        int res = climbingStairsConstraintDP(n);
+        System.out.println(String.format("爬 %d 阶楼梯共有 %d 种方案", n, res));
+    }
+}

codes/python/chapter_dynamic_programming/climbing_stairs_constraint_dp.py

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+"""
+File: climbing_stairs_constraint_dp.py
+Created Time: 2023-06-30
+Author: Krahets (krahets@163.com)
+"""
+
+
+def climbing_stairs_constraint_dp(n: int) -> int:
+    """带约束爬楼梯：动态规划"""
+    if n == 1 or n == 2:
+        return n
+    # 初始化 dp 列表，用于存储子问题的解
+    dp = [[0] * 3 for _ in range(n + 1)]
+    # 初始状态：预设最小子问题的解
+    dp[1][1], dp[1][2] = 1, 0
+    dp[2][1], dp[2][2] = 0, 1
+    # 状态转移：从较小子问题逐步求解较大子问题
+    for i in range(3, n + 1):
+        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]
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    n = 9
+
+    res = climbing_stairs_constraint_dp(n)
+    print(f"爬 {n} 阶楼梯共有 {res} 种方案")