Min Cost Climbing Stairs

Asked byAmazonAdobeBloomberg

Problem

Given an array where cost[i] is the cost of stepping on stair i, you may start from step 0 or step 1 and climb one or two steps at a time. Return the minimum cost to reach the top (one step past the last stair).

Examples

Example 1

Input:cost = [10,15,20]

Output:15

Start at index 1, pay 15, and step directly to the top.

Example 2

Input:cost = [1,100,1,1,1,100,1,1,100,1]

Output:6

Constraints

2 <= cost.length <= 1000

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How to approach it: the 1-D Dynamic Programming pattern

Break a problem into overlapping subproblems along a single dimension — like "the answer up to index i" — solve each one once, and reuse the result instead of recomputing it.

Look for this pattern when

A greedy or purely recursive approach recomputes the same subproblem repeatedly.
The problem asks for a count, a minimum/maximum, or a yes/no reachability over a sequence, where the answer at position `i` depends on answers at earlier positions.

Read the full 1-D Dynamic Programming guide →

Video walkthroughs

Original problem on LeetCode ↗