hello-algo/codes/c/chapter_dynamic_programming/climbing_stairs_dp.c

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/**
* File: climbing_stairs_dp.c
* Created Time: 2023-09-19
* Author: huawuque404 (huawuque404@163.com)
*/
#include "../utils/common.h"
/* 爬楼梯:动态规划 */
int climbingStairsDP(int n) {
if (n == 1 || n == 2)
return n;
// 初始化 dp 表,用于存储子问题的解
int *dp = (int *)malloc((n + 1) * sizeof(int));
// 初始状态:预设最小子问题的解
dp[1] = 1;
dp[2] = 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] = dp[i - 1] + dp[i - 2];
}
int result = dp[n];
free(dp);
return result;
}
/* 爬楼梯:空间优化后的动态规划 */
int climbingStairsDPComp(int n) {
if (n == 1 || n == 2)
return n;
int a = 1, b = 2;
for (int i = 3; i <= n; i++) {
int tmp = b;
b = a + b;
a = tmp;
}
return b;
}
/* Driver Code */
int main() {
int n = 9;
int res = climbingStairsDP(n);
printf("爬 %d 阶楼梯共有 %d 种方案\n", n, res);
res = climbingStairsDPComp(n);
printf("爬 %d 阶楼梯共有 %d 种方案\n", n, res);
return 0;
}