Maximize Trading Profit with a One-Day Cooldown
Company: Amazon
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Other
# Maximize Trading Profit with a One-Day Cooldown
Given daily prices `prices`, return the maximum profit obtainable by buying and selling one share at a time. You may make multiple transactions, but you must sell a held share before buying another.
After selling on a day, you cannot buy on the immediately following day. This is a one-day cooldown. You may choose to make no transaction.
### Function
`int maxProfit(vector<int>& prices)`
### Example 1
```text
Input: prices = [2,6,1,2,7]
Output: 9
```
Buy at `2` on day `0` and sell at `6` on day `1`, earning `4`. Day `2` is the cooldown. Buy at `2` on day `3` and sell at `7` on day `4`, earning `5` more.
### Example 2
```text
Input: prices = [9,6,3]
Output: 0
```
No profitable completed transaction is available.
### Constraints
- `1 <= prices.length <= 5000`.
- `0 <= prices[i] <= 1000`.
### Clarifications
Profit is cash earned from completed sales minus purchase costs. Return the maximum profit value, not the sequence of trades. A price of zero is valid. An unfinished purchase is not itself a completed profit.
### What a Strong Answer Covers
- How sale history affects eligibility to buy on a later day.
- Why simultaneous ownership of multiple shares is excluded.
- A single day, declining prices, and a tempting purchase during cooldown.
- A correctness argument and time/storage bounds.
Overview: Practice maximizing repeated trading profit with a one-day wait after each sale. Track purchase eligibility, preserve single-share ownership, and handle zero prices and unprofitable inputs.
