70. 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

public class Solution {
    public int climbStairs(int n) {
        int a=1;
        int b=2;
        if(n==1)return a;
        if(n==2)return b;
        for(int i=3;i<=n;i++){
            int index=a;
            a=b;
            b=index+a;
        }
        return b;
    }
}

class Solution {
    public int climbStairs(int n) {
        int[] memory = new int[n+1];
        return climb(n, memory);
    }
    
    public int climb(int n, int[] memory) {
        if(n <= 2) {
            return n;
        }
        if(memory[n] != 0) {
            return memory[n];
        }
        memory[n] = climb(n-1, memory) + climb(n-2, memory);
        return memory[n];
    }
}

class Solution {
    public int climbStairs(int n) {
        if (n <= 0) return 0;
        else if (n == 1) return 1;
        else if (n == 2) return 2;
        
        int[] arr = new int[n + 1];
        arr[1] = 1;
        arr[2] = 2;
        
        for (int i = 3; i < n + 1; i++) {
            arr[i] = arr[i -1] + arr[i - 2];
        }   
        return arr[n]; 
    }
}