DSA interview question

Best Time to Buy and Sell Stock III

Medium · Algorithms · Topics: dynamic programming, array

The problem

Your trading bot's compliance team has now imposed a stricter cap than before: instead of an arbitrary k, the bot is limited to at most two transactions total in the given trading window. Given an array prices where prices[i] is the stock price on day i, return the maximum profit achievable with at most two buy-sell transaction pairs. You can hold at most one share at a time (must sell before buying again).

Function signature

int maxProfit(vector<int>& prices);

Test cases

Input `prices`	Output	Explanation
`[3,3,5,0,0,3,1,4]`	6	Buy@0, sell@3 (profit 3), then... verify: buy@3,sell@5(2), buy@0,sell@4(4) → 6
`[1,2,3,4,5]`	4	One transaction (buy@1, sell@5) is optimal — second doesn't help
`[7,6,4,3,1]`	0	Strictly decreasing — no profitable trade
`[1]`	0	Single day — no transaction possible
`[]`	0	Empty array
`[1,2,4,2,5,7,2,4,9,0]`	13	Buy@1,sell@7 (6), buy@2,sell@9 (7) → total 13

(Always verify tricky ones like [3,3,5,0,0,3,1,4] with the code — hand-tracing two-transaction cases is error-prone.)

How interviewers phrase it

"You can complete at most two buy-sell transactions. Maximize profit."
"This is a special case of 'Best Time to Buy and Sell Stock IV' with k fixed at 2."
They may start you here specifically to see if you can hardcode/simplify the state machine before generalizing to arbitrary k.

Clarifying questions to ask

Can I hold at most one share at a time (must sell before buying again)?
Does "at most two transactions" mean I could also do zero or one if that's more profitable, or must I do exactly two?
What's the expected size of prices? (Confirms O(n) time with O(1) space is expected here, since k is fixed and small.)
Are prices non-negative integers?
Should I design this as a special case, or should I be ready to generalize to Stock IV afterward?

Follow-ups to expect

"Can you do this in O(1) space?"
"Can you generalize this to at most k transactions?"
"What if there's also a transaction fee?"
**"Can you prove why processing buy1
"What if cooldown is also required between transactions?"
"Why is buy1 initialized to negative infinity (or -prices[0]) but sell1/sell2 to 0?"

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