746. Min Cost Climbing Stairs

Min Cost Climbing Stairs (LeetCode 746) is a Easy Data Structures and Algorithms interview problem you can solve, run and submit on Thita.ai. It belongs to the Dynamic Programming (DP) Patterns pattern, in the 1D Array (Fibonacci Style) subpattern.

• NeetCode 150 · #100 of 150 · 1-D Dynamic Programming
• NeetCode 250 · #175 of 250 · 1-D Dynamic Programming

How to solve Min Cost Climbing Stairs

Min Cost Climbing Stairs is a Fibonacci Style DP problem, part of Dynamic Programming (DP) Patterns. Solve problems with Fibonacci-like recurrence: climbing stairs, house robber, decode ways.

Work towards the solution in these steps:

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]

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

The Min Cost Climbing Stairs solution and editorial walks through the full approach with reference code.

Problem statement

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.

You can either start from the step with index 0, or the step with index 1.

Return the minimum cost to reach the top of the floor.

Example 1:

Input: cost = [10,15,20] Output: 15 Explanation: You will start at index 1. - Pay 15 and climb two steps to reach the top. The total cost is 15.

Example 2:

Input: cost = [1,100,1,1,1,100,1,1,100,1] Output: 6 Explanation: You will start at index 0. - Pay 1 and climb two steps to reach index 2. - Pay 1 and climb two steps to reach index 4. - Pay 1 and climb two steps to reach index 6. - Pay 1 and climb one step to reach index 7. - Pay 1 and climb two steps to reach index 9. - Pay 1 and climb one step to reach the top. The total cost is 6.

Constraints:

- 2 <= cost.length <= 1000

- 0 <= cost[i] <= 999

Topics and companies

Topics: Array, Dynamic Programming.

Reported in interviews at Adobe, Amazon, Apple, Bloomberg, Goldman Sachs, Google, Microsoft, Uber, VMware, Yahoo.

How to practise Min Cost Climbing Stairs on Thita.ai

Starter code is provided in C, C#, C++, Go, Java, JavaScript and Python. Your solution runs against 5 test cases for this problem, with the AI coach available for a hint when you are stuck rather than a finished answer. The reference solution runs in O(n) time and O(1) space.

Open Min Cost Climbing Stairs in the code editor, or read the Min Cost Climbing Stairs editorial for a worked solution with its approach and complexity analysis.

Where Min Cost Climbing Stairs sits in the DSA pattern sheet

• Dynamic Programming (DP) Patterns pattern guide
• 1D Array (Fibonacci Style) subpattern
• The full DSA patterns sheet

Problems related to Min Cost Climbing Stairs

Other problems that use the same 1D Array (Fibonacci Style) and Dynamic Programming (DP) Patterns techniques:

• Climbing Stairs — Easy, same subpattern
• Decode Ways — Medium, same subpattern
• Delete and Earn — Medium, same subpattern
• Fibonacci Number — Easy, same subpattern
• House Robber — Medium, same subpattern
• House Robber II — Medium, same subpattern

Min Cost Climbing Stairs FAQ