Data Structures & Algorithms
Dynamic Programming Interview Questions
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Climbing Stairs
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?
class Solution {
climbStairs(n) {
if (n <= 2) return n;
let dp = [0, 1, 2]; for (let i = 3; i <= n; i++) { dp[i] = dp[i - 1] + dp[i - 2]; }
return dp[n]; } }
let dp = [0, 1, 2]; for (let i = 3; i <= n; i++) { dp[i] = dp[i - 1] + dp[i - 2]; }
return dp[n]; } }
This is a classic dynamic programming problem. The number of ways to reach step 'n' is the sum of the ways to reach step 'n-1' and the ways to reach step 'n-2'. This is because you can reach step 'n' either from step 'n-1' by taking one step, or from step 'n-2' by taking two steps. This leads to the Fibonacci sequence recurrence relation.
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