Climbing Stairs Problem Solution

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?

Example :

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

Climbing Stairs Problem Solution

Problem Solution In Python

def climbStairs(self, n: int) -> int:
        def dp(n, cache):
            if n not in cache:
                cache[n] = dp(n-1, cache) + dp(n-2, cache)
            return cache[n]
        return dp(n, {1: 1, 2: 2})

Problem Solution In Java

class Solution {    
    int [] cache = new int[46];    
    public int climbStairs(int n) {  
        if(n < 0) return 0;
        if(n == 0) return 1;        
        int val = cache[n];        
        if(val != 0)
            return val;        
        val = climbStairs(n - 1) + climbStairs(n - 2);       
        cache[n] = val;        
        return val;
    }
}

Problem Solution In C++

class Solution {
public:
    int climbStairs(int n) {
        vector<int>dp;
        dp.resize(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];
    }
};

Problem Solution In C

int climbStairs(int n){
    int* a = (int*)malloc(sizeof(int)*2);
    
    a[0] = 1;
    a[1] = 1;
    
    for (int i=2;i<=n;i++){
        a[i%2] =  a[0] + a[1];
    }
    return a[n%2];
}