Climbing Stairs

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

n = 5

int[] dp = new int[n+1];

dp[0] = 1, dp[1] = 1;

dp[2] = dp[0] + dp[1] = 2;

dp[3] = dp[2] + dp[1] = 2 + 1 = 3;

dp[4] = dp[3] + dp[2] = 3 + 2 = 5;

dp[5] = dp[4] + dp[3] = 5 + 3 = 8;

Code

public class Solution {
    public int ClimbStairs(int n) {
        //Edge Case
        if(n < 2)
            return 1;
        
        int[] dp = new int[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];
    }
}

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