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/python/chapter_dynamic_programming/climbing_stairs_backtrack.py

@@ -0,0 +1,37 @@
+"""
+File: climbing_stairs_backtrack.py
+Created Time: 2023-06-30
+Author: Krahets (krahets@163.com)
+"""
+
+
+def backtrack(choices: list[int], state: int, n: int, res: list[int]) -> int:
+    """回溯"""
+    # 当爬到第 n 阶时，方案数量加 1
+    if state == n:
+        res[0] += 1
+    # 遍历所有选择
+    for 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
+
+
+def climbing_stairs_backtrack(n: int) -> int:
+    """爬楼梯：回溯"""
+    choices = [1, 2]  # 可选择向上爬 1 或 2 阶
+    state = 0  # 从第 0 阶开始爬
+    res = [0]  # 使用 res[0] 记录方案数量
+    backtrack(choices, state, n, res)
+    return res[0]
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    n = 9
+
+    res = climbing_stairs_backtrack(n)
+    print(f"爬 {n} 阶楼梯共有 {res} 种方案")