Last updated on October 10th, 2024 at 02:01 am

Here, We see Climbing Stairs LeetCode Solution. This Leetcode problem is done in many programming languages like C++, Java, JavaScript, Python, etc., with different approaches.

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Climbing Stairs LeetCode Solution

Problem Statement

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

Example 2:
Input: n = 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

1. Climbing Stairs Leetcode Solution C++

class Solution {
public:
    int dp[46];
    int climbStairs(int n) {
        if(dp[n]!=0) return dp[n];
  
        if(n==1 || n==2) return n;
        dp[n]=climbStairs(n-1)+climbStairs(n-2);
        return dp[n];
    }
};

1.1 Explanation

• Memoization Array Initialization: An array dp of size 46 is initialized to store the results of subproblems. The size 46 is chosen because it is assumed that n will not exceed 45.
• Check Memoized Value: If the result for n is already computed and stored in dp[n], return that value.
• Base Cases: If n is 1 or 2, return n directly because there is only one way to climb 1 step and two ways to climb 2 steps.
• Recursive Computation with Memoization: Compute the result for n by recursively calling climbStairs(n – 1) and climbStairs(n – 2) and store the result in dp[n].

1.2 Time Complexity

• O(n) due to memoization.

1.3 Space Complexity

• O(n) due to the recursion stack and the dp array.

2. Climbing Stairs Leetcode Solution Java

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

2.1 Explanation

• Base Cases: If n is 0, 1, or 2, return n directly because there are no stairs to climb, one way to climb 1 step, and two ways to climb 2 steps.
• Memoization Array Initialization: Initialize an array mem of size n to store the results of subproblems. Set mem[0] to 1 and mem[1] to 2.
• Iterative Computation: Fill the mem array iteratively using the relation mem[i] = mem[i – 1] + mem[i – 2].
• Return Result: Return the value mem[n – 1], which contains the number of ways to climb n steps.

2.2 Time Complexity

• O(n) due to the single loop that iterates n times.

2.3 Space Complexity

• O(n) due to the mem array.

3. Climbing Stairs Leetcode Solution JavaScript

var climbStairs = function(n) {
    let prev = 0;
    let curr = 1;
    let tmp;
    for(let i = 1; i <= n; i++){
         tmp = prev;
        prev = curr;
      curr += tmp;
   }
   return curr;
};

3.1 Explanation

• Initialize Variables: Initialize prev to 0 and curr to 1. These variables will store the number of ways to climb the previous two steps.
• Iterative Computation: Iterate from 1 to n, updating prev and curr to reflect the number of ways to climb the current step. tmp temporarily holds the value of prev.
• Return Result: Return curr, which contains the number of ways to climb n steps.

3.2 Time Complexity

• O(n) due to the single loop that iterates n times.

3.3 Space Complexity

• O(1) because only a constant amount of extra space is used.

4. Climbing Stairs Leetcode Solution Python

class Solution(object):
    def climbStairs(self, n):
        a, b = 1, 1
        for i in range(n):
            a, b = b, a + b
        return a

4.1 Explanation

• Initialize Variables: Initialize a and b to 1. These variables will store the number of ways to climb the previous two steps.
• Iterative Computation: Iterate from 0 to n-1, updating a and b to reflect the number of ways to climb the current step.
• Return Result: Return a, which contains the number of ways to climb n steps.

4.2 Time Complexity

• O(n) due to the single loop that iterates n times.

4.3 Space Complexity

• O(1) because only a constant amount of extra space is used.