【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,);
        if(n<) return n;
        dp[] = ;
        dp[] = ;
        for(int i=; i<n; i++) {
            dp[i] = dp[i-] + dp[i-];
        }
        return dp[n-];
    }
};

Solution 2 ()

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

Solution 2

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

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