You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
50 lines
1.1 KiB
50 lines
1.1 KiB
1 year ago
|
/**
|
||
|
|
* File: climbing_stairs_dp.cpp
|
||
|
|
* Created Time: 2023-06-30
|
||
|
|
* Author: Krahets (krahets@163.com)
|
||
|
|
*/
|
||
|
|
|
||
|
|
#include "../utils/common.hpp"
|
||
|
|
|
||
|
|
/* 爬楼梯：动态规划 */
|
||
|
|
int climbingStairsDP(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<int> dp(n + 1);
|
||
|
|
// 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];
|
||
|
|
}
|
||
|
|
return dp[n];
|
||
|
|
}
|
||
|
|
|
||
|
|
/* 爬楼梯：状态压缩后的动态规划 */
|
||
|
|
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);
|
||
|
|
cout << "爬 " << n << " 阶楼梯共有 " << res << " 种方案" << endl;
|
||
|
|
|
||
|
|
res = climbingStairsDPComp(n);
|
||
|
|
cout << "爬 " << n << " 阶楼梯共有 " << res << " 种方案" << endl;
|
||
|
|
|
||
|
|
return 0;
|
||
|
|
}
|