feat: add the section of the introduction to dynamic programming (#571)

* add the section of the introduction to
dynamic programming

* add a code comments.

codes/java/chapter_dynamic_programming/climbing_stairs_backtrack.java

@@ -0,0 +1,44 @@
+/**
+ * File: climbing_stairs_backtrack.java
+ * Created Time: 2023-06-30
+ * Author: Krahets (krahets@163.com)
+ */
+
+package chapter_dynamic_programming;
+
+import java.util.*;
+
+public class climbing_stairs_backtrack {
+    /* 回溯 */
+    public static void backtrack(List<Integer> choices, int state, int n, List<Integer> res) {
+        // 当爬到第 n 阶时，方案数量加 1
+        if (state == n)
+            res.set(0, res.get(0) + 1);
+        // 遍历所有选择
+        for (Integer choice : 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 static int climbingStairsBacktrack(int n) {
+        List<Integer> choices = Arrays.asList(1, 2); // 可选择向上爬 1 或 2 阶
+        int state = 0; // 从第 0 阶开始爬
+        List<Integer> res = new ArrayList<>();
+        res.add(0); // 使用 res[0] 记录方案数量
+        backtrack(choices, state, n, res);
+        return res.get(0);
+    }
+
+    public static void main(String[] args) {
+        int n = 9;
+
+        int res = climbingStairsBacktrack(n);
+        System.out.println(String.format("爬 %d 阶楼梯共有 %d 种方案", n, res));
+    }
+}