Climbing Stairs

Description

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.

Example 1:

Input: 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps

Example 2:

Input: 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

Solution

Let dp[i] denote the number of ways to climb to stair $i, i \ge 1$.

Recursive formula: dp[i] = dp[i-1] + dp[i-2].

Base cases: dp[0] = dp[1] = 1.

class Solution {
public:
    int climbStairs(int n) {
        int prev2 = 1, prev1 = 1;
        for(int i = 2; i <= n; ++i){
            int curr = prev2 + prev1;
            prev2 = prev1;
            prev1 = curr;
        }
        return prev1;
    }
};