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12. Best Time to Buy and Sell Stock

easyAsked at Monzo

Given a stream of daily balances on a savings pot, find the maximum profit from one buy and one sell.

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

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 it. Return the maximum profit you can achieve, or 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

Try every pair (i, j) with i < j and track the maximum difference.

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. Running minimum

Sweep once, tracking the smallest price so far and the best profit selling at the current day.

Time
O(n)
Space
O(1)
function maxProfit(prices) {
  let min = Infinity, best = 0;
  for (const p of prices) {
    if (p < min) min = p;
    else if (p - min > best) best = p - min;
  }
  return best;
}

Tradeoff:

Monzo-specific tips

Monzo expects you to articulate the single-pass invariant clearly because their savings-goal analytics rely on this exact pattern.

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Output

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