LeetCode 70. Climbing Stairs

Description

https://leetcode.com/problems/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

Explanation

The total distinct ways to climb to i th stair is actually the sum of the distinct ways of i – 2 and i – 1 stairs.

Java Solution

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

Python Solution

class Solution:
    def climbStairs(self, n: int) -> int:
        
        f = []
        
        f.append(1)
        f.append(2)
        
        for i in range(2, n):
            f.append(f[i - 1] + f[i - 2])
            
        return f[n - 1]
  • Time complexity: O(n). Single loop up to n.
  • Space complexity: O(n). dp array of size n is used.

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