HARD 1-D Dynamic Programming
123. Best Time to Buy and Sell Stock III
📖 Problem
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 at the same time (i.e., you must sell the stock before you buy again).
🧠 Visual Learning Aid
1 Model the input into the right structure
2 Choose the core technique and invariant
3 Execute step-by-step with a sample
4 Validate complexity and edge cases
JS/TS Refreshers
- •Array methods (`push`, `pop`, `shift`, `slice`)
- •Object/Map/Set usage patterns
- •Function parameter and return typing
- •Array DP table updates
- •State transition thinking
- •Base case initialization
Logical Thinking Concepts
- •Define invariants before coding
- •Check edge cases first (`[]`, single element, duplicates)
- •Estimate time/space before implementation
- •Apply Dynamic Programming reasoning pattern
💡 Approach
- → Track 4 states: first buy, first sell, second buy, second sell
- → buy1 = max profit after first buy (negative)
- → sell1 = max profit after first sell
- → buy2 = max profit after second buy
- → sell2 = max profit after second sell (final answer)
- → Time: O(n), Space: O(1)
🧭 Prerequisites
🛠️ Hints & Pitfalls
Hints
- •Track 4 states: first buy, first sell, second buy, second sell
- •buy1 = max profit after first buy (negative)
- •sell1 = max profit after first sell
Common Pitfalls
- •buy2 = max profit after second buy
- •sell2 = max profit after second sell (final answer)
- •Time: O(n), Space: O(1)
🧪 Test Cases
Hidden tests on submit: 1
Test Case 1
Not run Input:
maxProfit([3,3,5,0,0,3,1,4]); Expected:
6 Test Case 2
Not run Input:
maxProfit([1,2,3,4,5]); Expected:
4 Test Case 3
Not run Input:
maxProfit([7,6,4,3,1]); Expected:
0 📝 Code Editor
📤 Output