Compute Stock Profit with One or Unlimited Transactions
Company: Meta
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Onsite
## Problem
Given daily stock prices, return two values: the maximum profit when at most one
buy-sell transaction is allowed, and the maximum profit when any number of
non-overlapping transactions is allowed. You may hold at most one share at a time,
and a sale must occur after its corresponding purchase.
### Constraints & Assumptions
- The price list contains between 1 and 200,000 positive integers.
- Prices fit in 32-bit signed integers; use 64-bit arithmetic for total profit.
- Buying and selling on the same day adds no profit and is unnecessary.
- Return zero for a strategy that cannot make a positive profit.
### Clarifications
- There are no fees, cooldown periods, or limits beyond the one-share holding rule.
- Unlimited transactions cannot overlap, but a new buy may follow an earlier sale.
- Return `[oneTransactionProfit, unlimitedTransactionsProfit]`.
### Examples
```text
prices = [7, 1, 5, 3, 6, 4]
output = [5, 7]
```
### Hints
```hint One transaction
Track the lowest price seen before each possible selling day.
```
```hint Unlimited transactions
Identify every positive day-to-day increase that can be captured without overlapping holdings.
```
Overview: Compute maximum stock profit for both one transaction and unlimited nonoverlapping transactions in linear time, returning zero when no positive trade is available.
Given a nonempty list of positive daily stock prices, return [oneTransactionProfit, unlimitedTransactionsProfit]. The first value is the maximum profit using at most one buy followed by one later sale. The second is the maximum profit using any number of non-overlapping buy-sell transactions while holding at most one share at a time. There are no fees or cooldowns, a new buy may follow an earlier sale, and a strategy that cannot earn positive profit returns zero.
Constraints
- 1 <= len(prices) <= 200000.
- Every price is a positive signed 32-bit integer.
- A sale must occur after its corresponding purchase, and at most one share may be held at a time.
- There are no fees, cooldown periods, or transaction limits for the unlimited objective.
- Return zero when no positive profit is possible, and use 64-bit arithmetic for total profit.
Examples
Input: ([7, 1, 5, 3, 6, 4],)
Expected Output: [5, 7]
Explanation: This is the source example: one transaction earns five, while two disjoint rises earn seven.
Input: ([5],)
Expected Output: [0, 0]
Explanation: One day permits no positive buy-sell transaction.
Hints
- Track the lowest price before each possible selling day for the one-transaction result.
- For unlimited transactions, capture every positive day-to-day increase.