Best Time to Buy and Sell Stock

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.

Examples

The brute-force approach

Try every pair of days (buy day i, sell day j where j > i) and track the best profit seen.

max_profit = 0

for i in 0 .. n - 1:
    for j in i + 1 .. n - 1:    # ← nested loop is the bottleneck
        profit = prices[j] - prices[i]
        max_profit = max(max_profit, profit)

return max_profit

Checking every buy-sell pair is O(n²). For a year of daily prices (~365 days) that's 66,000 comparisons, manageable, but for multi-year histories it blows up fast.

Spotting the pattern

This is a Tracking Minimum problem. The key question to ask yourself:

Can I track the lowest price seen so far and compute the best profit at each step?

Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.