DSA interview question

Best Time to Buy and Sell Stock

Medium · Algorithms · Topics: dynamic programming, array

The problem

This is the foundational version of your trading bot backend, before any of the fee/cooldown/k-transaction rules existed. Given an array prices where prices[i] is the stock price on day i, you're allowed to complete at most one transaction (buy on one day, sell on a later day). Return the maximum profit you can achieve. If no profit is possible, return 0.

Function signature

int maxProfit(vector<int>& prices);

Test cases

Input `prices`	Output	Explanation
`[7,1,5,3,6,4]`	5	Buy@1, sell@6 → profit 5
`[7,6,4,3,1]`	0	Strictly decreasing — no profitable trade, return 0
`[1,2,3,4,5]`	4	Buy@1, sell@5 → profit 4
`[1]`	0	Single day — no transaction possible
`[]`	0	Empty array
`[2,4,1]`	2	Buy@2, sell@4 → profit 2 (buying at 1 comes too late to sell higher)
`[3,3,3,3]`	0	No price movement — no profit possible

(Always check: you must buy before you sell — selling can never happen on an earlier or same day as buying.)

How interviewers phrase it

"You're given prices of a stock over n days. You can buy once and sell once. Maximize profit."
"What's the maximum difference prices[j] - prices[i] for j > i?"
Often the very first problem in a "stock trading" interview series, used as a warm-up before layering constraints.

Clarifying questions to ask

Can I choose not to transact at all if no profitable trade exists? (i.e., is 0 a valid answer?)
Must I sell on a strictly later day than I buy (no same-day buy-sell)?
Are prices guaranteed non-negative integers?
What's the expected size of prices? (Confirms O(n) is expected over O(n²) brute force.)
Can the array be empty or have just one element — what should I return then?

Follow-ups to expect

"Can you do this in O(n) instead of O(n²)?"
"What if you could do unlimited transactions instead of just one?"
"What if you could do at most two transactions?"
"What if you could do at most k transactions?"
"What if there's a transaction fee or cooldown?"
"Can you also return the actual buy/sell days, not just the profit?"

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