Climbing Stairs [LEETCODE]

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?

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Fisrt, I tried recursive way.

class Solution {
public:
    int climbStairs(int n) {
        // Recursively
        if(0 == n) return 0;
        if(1 == n) return 1;
        return climbStairs(n - 1) + climbStairs(n - 2);
    }
};

But this solution exceed time limit.

So let's think about it. One step has only 1 way , 2 steps have two ways.

Thus N steps have two ways to reach destination: N-1 steps plus one step; N-2 steps plus two steps.

So S[n] = S[n-1] + S[n-2]

Here' s the code:

class Solution {
public:
    int climbStairs(int n) {
        // Recursively
        if(0 == n) return 0;
        if(1 == n) return 1;
        int *step = new int[n+1];
        step[0] = 0;
        step[1] = 1;
        step[2] = 2;
        for(int i =3; i <=n ; i++){
            step[i] = step[i-1] + step[i-2];
        }
        return step[n];
    }
};

Remind to allocate n+1 space to store steps from 0 to n.