PPractick

The problem

Your trading bot backend just got its most relaxed ruleset yet — no fee, no cooldown, no transaction limit. Given an array prices where prices[i] is the stock price on day i, you can buy and sell as many times as you want, but you must hold at most one share at a time (sell before buying again). Return the maximum profit achievable.

Function signature

int maxProfit(vector<int>& prices);

Test cases

Input prices	Output	Explanation
[7,1,5,3,6,4]	7	Buy@1,sell@5 (4), buy@3,sell@6 (3) → total 7
[1,2,3,4,5]	4	Buy@1, sell@5 — one continuous uptrend, capture the whole rise
[7,6,4,3,1]	0	Strictly decreasing — no profitable trade
[1]	0	Single day — no transaction possible
[]	0	Empty array
[1,7,2,3,6,7,6,7]	13	Buy@1,sell@7(6), buy@2,sell@3(1), buy@6,sell@7(1)... verify total with code

(Always verify: with unlimited transactions and no fee, capturing every single positive day-to-day delta is always optimal — confirm this intuition matches brute force before trusting the greedy.)

How interviewers phrase it

• "You can buy and sell stock as many times as you like. Maximize total profit."
• "This is the unlimited-transaction version — no fee, no cooldown, no cap on trade count."
• Often used as a warm-up before asking the fee/cooldown/k-transaction variants, to check baseline understanding of the greedy insight.

Clarifying questions to ask

1. Can I hold at most one share at a time (must sell before buying again)?
2. Is there any transaction fee, or is this purely unconstrained?
3. Can I buy and sell on the same day (net zero effect), or is that disallowed entirely?
4. What's the expected size of prices? (Confirms O(n) greedy is expected, not something more complex.)
5. Are prices guaranteed non-negative integers?

Follow-ups to expect

1. "Can you prove the greedy approach is optimal?"
2. "What if there's a transaction fee?"
3. "What if there's a cooldown after selling?"
4. "What if there's a cap of k transactions?"
5. "Can you solve this with DP instead of greedy, to build intuition for the constrained variants?"
6. "What's the maximum possible number of transactions in the worst case?"

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