Best Time to Buy and Sell Stock
Reported by candidates from Bloomberg's online assessment. Pattern, common pitfall, and the honest play if you blank under the timer.
The mistake that sinks a first attempt on this one is grabbing the global min and global max and subtracting. Bloomberg reportedly asked Best Time to Buy and Sell Stock in September 2020, and the sell day has to come after the buy day. That one rule trips people who rush. It's a single pass over an array, no fancy structure. If you've got the OA in a day or two, you can learn this in ten minutes. And if your brain locks up mid-assessment, StealthCoder runs invisibly on screen as a safety net so you're not stuck staring at a blank editor.
The problem
You are given an integer array prices, where prices[i] is the price of one share on day i. Choose at most one day to buy and one later day to sell. Return the maximum profit. If no profitable transaction exists, return 0. Function maxProfit(prices: int[]) → long Examples Example 1 prices = [7,1,5,3,6,4] return = 5 Buy at price 1 and sell later at price 6 for profit 5. Example 2 prices = [7,6,4,3,1] return = 0 Every later price is lower, so the best choice is not to trade. Example 3 prices = [3,3,5,0,0,3,1,4] return = 4 Buy at a price of 0 and sell later at 4. Constraints 1 <= prices.length <= 200000 0 <= prices[i] <= 10^9
Reported by candidates. Source: FastPrep
Pattern and pitfall
The trick is to scan once and track the lowest price seen so far. At each day, compute price minus that running minimum, and keep the best result. Start the best at 0, which handles the case where prices only fall, like [7,6,4,3,1]. The common pitfall is the global min and max subtraction. On [3,3,5,0,0,3,1,4] the max is 5 and the min is 0, but the 0 comes after the 5, so that fails. The right answer is 4. The other pitfall is a nested loop. With up to 200000 prices, O(n^2) will time out, so you need O(n) time and O(1) space. Prices go up to 10^9, and a difference fits easily in a 64-bit integer, so use a long if your language needs it. If you blank on the running-min idea during the live OA, StealthCoder can surface the one-pass solution so you can type it cleanly.
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Best Time to Buy and Sell Stock FAQ
How hard is Best Time to Buy and Sell Stock really?+
It's easy once you see it. The whole solution is one loop with two variables. Most failures come from overthinking it or ignoring the order rule. If you can explain why the running minimum works, you're done in a few minutes.
What's the trick to this problem?+
Track the minimum price seen so far as you walk the array. At every day, check whether selling today beats your best profit. Update the minimum after that check. You never need to look backward, which keeps it linear.
Why does subtracting the global min from the global max fail?+
Because the max can appear before the min. In [7,6,4,3,1] the max is first, so that subtraction gives a negative profit that can't be made. The sell must come after the buy, so the order matters, not just the values.
What should I return when prices only go down?+
Return 0. The problem says to skip trading when no profit exists. Initialize your best profit to 0 and only update it when a positive gain shows up. That covers decreasing arrays and single-element inputs automatically.
How do I prepare for this in 48 hours?+
Write the one-pass solution from memory twice, then test it on the three examples plus a single-element array. Check your handling of equal prices and large values up to 10^9. Bloomberg reportedly asked it in September 2020, so expect similar array questions.