Climbing Stairs

Problem

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?

Solution Approach

Expected Time Complexity: $O(n)$

Click - to see solution code

C++

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