746. Min Cost Climbing Stairs

How to solve Min Cost Climbing Stairs (LeetCode 746): the approach in brief

The problem

You are given an integer array cost where cost[i] is the cost of ith step on a staircase. Once you pay the cost, you can either climb one or two steps.

Pattern

Min Cost Climbing Stairs is a Dynamic Programming (DP) Patterns problem, in the 1D Array (Fibonacci Style) subpattern. The pattern covers fibonacci, Kadane, knapsack, LCS, LIS, edit distance, grid paths, and word break

Solve problems with Fibonacci-like recurrence: climbing stairs, house robber, decode ways.

Approach outline

1. Build an array dp where dp[i] is the minimum cost to climb to the top starting from the ith staircase.
2. Assuming we have n staircase labeled from 0 to n - 1 and assuming the top is n, then dp[n] = 0, marking that if you are at the top, the cost is 0.
3. Now, looping from n - 1 to 0, the dp[i] = cost[i] + min(dp[i + 1], dp[i + 2]). The answer will be the minimum of dp[0] and dp[1]

Complexity

The reference solution runs in O(n) time and O(1) space.

Asked at

Min Cost Climbing Stairs has been reported in interviews at Adobe, Amazon, Apple, Bloomberg, Goldman Sachs, Google, Microsoft, Uber.