Min Cost Climbing Stairs — DSA Visualizer

Problem

Cost array for each step. You can start at step 0 or 1. Pay cost[i] to climb from step i (then climb 1 or 2 steps). Return minimum cost to reach the top.

Example

[10,15,20] → 15 (start at index 1, pay 15, climb 2 to top)

Constraints: 2 ≤ cost.length ≤ 1000

Cost Array & DP

Variables

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a (dp[i-2])

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b (dp[i-1])

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min cost

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Step Logic

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Algorithm

a=cost[0], b=cost[1] (base)

For i=2..n-1: c = cost[i] + min(a,b); a=b; b=c

Return min(a, b)

Time

O(n)

Space

O(1)

Why This Works

dp[i] = min cost to reach top from step i. You can jump 1 or 2 steps. Answer is min(dp[n-1], dp[n-2]) since you can finish from either of the last two steps.