题目

算法思路及代码实现

#include 
using namespace std;class Solution {
public:int climbStairs(int n) {int p = 0, q = 0, r = 1;for (int i = 1; i <= n; ++i) {p = q; q = r; r = p + q;}return r;}
};int main()
{Solution solution;int n = 5;int ans = solution.climbStairs(n);cout << ans << endl;    
}

输出：8

#include 
#include 
using namespace std;class Solution {
public:vector> multiply(vector> &a, vector> &b) {vector> c(2, vector(2));for (int i = 0; i < 2; i++) {for (int j = 0; j < 2; j++) {c[i][j] = a[i][0] * b[0][j] + a[i][1] * b[1][j];}}return c;}vector> matrixPow(vector> a, int n) {vector> ret = {{1, 0}, {0, 1}};while (n > 0) {if ((n & 1) == 1) {ret = multiply(ret, a);}n >>= 1;a = multiply(a, a);}return ret;}int climbStairs(int n) {vector> ret = {{1, 1}, {1, 0}};vector> res = matrixPow(ret, n);return res[0][0];}
};int main()
{Solution solution;int n = 5;int ans = solution.climbStairs(n);cout << ans << endl;    
}

#include 
#include 
using namespace std;class Solution {
public:int climbStairs(int n) {double sqrt5 = sqrt(5);double fibn = pow((1 + sqrt5) / 2, n + 1) - pow((1 - sqrt5) / 2, n + 1);return (int)round(fibn / sqrt5);}
};int main()
{Solution solution;int n = 5;int ans = solution.climbStairs(n);cout << ans << endl;    
}