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15. Best Time to Buy and Sell Stock

easyAsked at PayPal

Find the maximum profit from a single buy-sell transaction in a price array. PayPal treats this as a core financial-reasoning problem — interviewers look for candidates who can frame it as tracking running minimum and maximum gain.

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

Source citations

Public interview reports confirming this problem appears in PayPal loops.

  • Glassdoor (2026)— PayPal SWE L3 candidate reported stock problem as first coding question
  • Blind (2025)— Multiple PayPal reports cite stock buy/sell in phone screens and OAs

Problem

You are given an array prices where prices[i] is the price of a given stock on the ith day. You want to maximize your profit by choosing a single day to buy one stock and choosing a different day in the future to sell that stock. Return the maximum profit you can achieve from this transaction. If you cannot achieve any profit, return 0.

Constraints

  • 1 <= prices.length <= 100000
  • 0 <= prices[i] <= 10000

Examples

Example 1

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

Explanation: Buy on day 2 (price=1), sell on day 5 (price=6), profit = 6-1 = 5

Example 2

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

Explanation: No transaction yields a profit; return 0

Approaches

1. Brute force (all pairs)

Try every buy-sell pair (i, j) where i < j and track the maximum difference.

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

Tradeoff: O(n^2) — too slow for 100k prices; mention it as the naive baseline before optimizing.

2. Single-pass minimum tracker

Track the lowest price seen so far and update the maximum profit on every step. Profit at each day = current price minus the best buy price seen before it. One loop, constant space.

Time
O(n)
Space
O(1)
function maxProfit(prices) {
  let minPrice = Infinity;
  let maxProfit = 0;
  for (const price of prices) {
    if (price < minPrice) {
      minPrice = price;      // found a cheaper buy day
    } else if (price - minPrice > maxProfit) {
      maxProfit = price - minPrice; // new best profit
    }
  }
  return maxProfit;
}

Tradeoff: Kadane's-style insight: we never need to look back once we track the running minimum. At PayPal, frame this as 'optimal trade execution with a single market position'.

PayPal-specific tips

PayPal interviews focus on payment processing, fraud detection logic, financial reconciliation algorithms, and distributed transaction design. Hash maps, sliding windows, and two-pointer techniques appear frequently.

Common mistakes

  • Initializing minPrice to 0 instead of Infinity, making day-0 high prices never candidates for minimum
  • Returning a negative profit instead of 0 when prices only decrease
  • Selling before buying — not enforcing j > i in the brute force or assuming buy and sell on same day is valid

Follow-up questions

An interviewer at PayPal may pivot to one of these next:

  • Allow multiple transactions (buy/sell as many times as you want) — LC 122
  • Allow at most two transactions — LC 123
  • Add a cooldown of one day between sell and next buy — LC 309

Solve it now

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Output

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FAQ

Can you buy and sell on the same day?

No — the problem says you must sell on a DIFFERENT future day, so profit would be zero anyway. Clarify this with the interviewer if not stated.

Why does PayPal ask financial-themed algorithm problems?

PayPal evaluates whether candidates can reason about time-ordered financial data, which mirrors real ledger and pricing-engine work. Framing your solution in financial terms signals domain awareness.

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