Best Time to Buy and Sell Stock III

Best Time to Buy and Sell Stock III is a Hard 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 Stock problems subpattern.

Problem statement

You are given an array prices where prices[i] is the price of a given stock on the ith day.

Find the maximum profit you can achieve. You may complete at most two transactions.

Note: You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).

Example 1: Input: prices = [3,3,5,0,0,3,1,4] Output: 6 Explanation: Buy on day 4 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.

Then buy on day 7 (price = 1) and sell on day 8 (price = 4), profit = 4-1 = 3.

Example 2: Input: prices = [1,2,3,4,5] Output: 4 Explanation: Buy on day 1 (price = 1) and sell on day 5 (price = 5), profit = 5-1 = 4.

Note that you cannot buy on day 1, buy on day 2 and sell them later, as you are engaging multiple transactions at the same time. You must sell before buying again.

Example 3: Input: prices = [7,6,4,3,1] Output: 0 Explanation: In this case, no transaction is done, i.e. max profit = 0.

Example 4: Input: prices = [1] Output: 0

Constraints: 1 <= prices.length <= 105 0 <= prices[i] <= 105

Topics and companies

Topics: Array, Dynamic Programming.

Reported in interviews at Amazon, Google.

How to practise Best Time to Buy and Sell Stock III on Thita.ai

Starter code is provided in C, C#, C++, dart, elixir, erlang, Go, Java, JavaScript, Kotlin, PHP, Python, python3, racket, Ruby, Rust, Scala, Swift and TypeScript. 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(n) space.

Open Best Time to Buy and Sell Stock III in the code editor, or read the Best Time to Buy and Sell Stock III editorial for a worked solution with its approach and complexity analysis.

Where Best Time to Buy and Sell Stock III sits in the DSA pattern sheet

Problems related to Best Time to Buy and Sell Stock III

Other problems that use the same Stock problems and Dynamic Programming (DP) Patterns techniques:

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