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16. Best Time to Buy and Sell Stock

easyAsked at Etsy

Maximize profit from one buy and one sell — Etsy uses it to verify single-pass min-tracking.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given an array prices where prices[i] is the stock price on day i, find the maximum profit from buying on one day and selling on a later day. Return 0 if no profit is possible.

Constraints

  • 1 <= prices.length <= 10^5
  • 0 <= prices[i] <= 10^4

Examples

Example 1

Input
prices = [7,1,5,3,6,4]
Output
5

Example 2

Input
prices = [7,6,4,3,1]
Output
0

Approaches

1. Brute force pairs

Check all (i, j) with i < j.

Time
O(n^2)
Space
O(1)
let best = 0;
for (let i = 0; i < prices.length; i++) {
  for (let j = i+1; j < prices.length; j++) {
    best = Math.max(best, prices[j] - prices[i]);
  }
}
return best;

Tradeoff:

2. Track running min

Sweep once, holding the cheapest price seen and the best profit so far.

Time
O(n)
Space
O(1)
function maxProfit(prices) {
  let lo = Infinity, best = 0;
  for (const p of prices) {
    lo = Math.min(lo, p);
    best = Math.max(best, p - lo);
  }
  return best;
}

Tradeoff:

Etsy-specific tips

Etsy will pivot this into 'find the best day to launch a sale on a listing given a 30-day price history' — frame the running-min idea in those terms.

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Output

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