Best Time to Buy and Sell Stock

Question

Given daily prices, compute the maximum profit obtainable by buying once and selling once later. You may choose not to trade, in which case the profit is `0`.

```python
def max_profit(prices: list[int]) -> int: ...
```

Prices are non-negative integers. An empty or one-day input returns `0`. Solve the problem in `O(n)` time and `O(1)` auxiliary space.

## Staged follow-ups

1. Allow any number of non-overlapping transactions while holding at most one share.
2. Add a fixed transaction fee or a one-day cooldown after selling.
3. Return the chosen buy and sell days with deterministic tie-breaking.