chapter_dynamic_programming: climbing_stairs_backtrack1.c

Author: realwujing

codes/c/chapter_dynamic_programming/climbing_stairs_backtrack1.c

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+#include "../utils/common.h"
+
+/* 回溯 */
+void backtrack(int *choices, int state, int n, int *res, int len) {
+	// 当爬到第 n 阶时，方案数量加 1
+	if (state ==n)
+		res[0]++;
+	// 遍历所有选择
+	for (int i = 0; i < len; i++) {
+		int choice = choices[i];
+		// 剪枝：不允许越过第 n 阶
+		if (state + choice > n)
+			continue;
+		// 尝试：做出选择，更新状态
+		backtrack(choices, state + choice, n ,res, len);
+		// 回退
+	}
+}
+
+/* 爬楼梯：回溯 */
+int climbingStairsBacktrack(int n) {
+	int choices[2] = {1, 2}; // 可选择向上爬 1 阶或 2阶
+	int state = 0;			 // 从第 0 阶开始爬
+	int *res = (int *)malloc(sizeof(int));
+	*res = 0; // 使用 res[0] 记录方案数量
+	int len = sizeof(choices) / sizeof(int);
+	backtrack(choices, state, n ,res, len);
+	int result = *res;
+	free(res);
+	return result;
+}
+
+/* Driver Code */
+int main() {
+	int n = 9;
+	int res = climbingStairsBacktrack(n);
+	printf("爬 %d 阶楼梯共有 %d 种方案\n", n, res);
+
+	return 0;
+}