【LeetCode】070. Climbing Stairs

题目：

You are climbing a stair case. It takes n steps to reach to the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

Note: Given n will be a positive integer.

题解：

　　爬到第n层的方法要么是从第n-1层一步上来的，要不就是从n-2层2步上来的

Solution 1 ()

class Solution {
public:
    int climbStairs(int n) {
        vector<int> dp(n,0);
        if(n<2) return n;
        dp[0] = 1;
        dp[1] = 2;
        for(int i=2; i<n; i++) {
            dp[i] = dp[i-2] + dp[i-1];
        }    
        return dp[n-1];
    }
};

 Solution 2 ()

class Solution {
public:
    int climbStairs(int n) {
        if(n<2) return n;
        int a = 1;
        int b = 2;
        for(int i=2; i<n; i++) {
            b += a;
            a = b - a;
        }    
        return b;
    }
};

 

 Solution 2 

class Solution {
public:
    int climbStairs(int n) {
        const double t = sqrt(5);
        return floor((pow((1 + t) / 2, n + 1) + pow((1 - t) / 2, n + 1)) / t + 0.5);
    }
};

 

斐波那契数列通项公式