70 - Climbing Stairs

#easy

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

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

Example 1:
Input: n = 2
Output: 2
Explanation: There are two ways to climb to the top.

1. 1 step + 1 step
2. 2 steps

Example 2:
Input: n = 3
Output: 3
Explanation: There are three ways to climb to the top.

1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step

class Solution {
public:
    int climbStairs(int n) {
        if ( n <= 2 ) return n;
        // 第三階 = 前兩階方法數相加
        vector<int> dp( n + 1 );
        dp[0] = 0;
        dp[1] = 1;
        dp[2] = 2;
        for ( int i = 3; i <= n; i++ ) {
            dp[i] = dp[i-1] + dp[i-2];
        }

        return dp[n];
    }
};