LeetCode 121: Best Time to Buy and Sell Stock — Python Solution

Solve LeetCode 121: Best Time to Buy and Sell Stock in Python with a running minimum approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

Track the cheapest price seen before today and the best profit from selling today or earlier.

Algorithm

1. Track the cheapest price seen before today and the best profit from selling today or earlier.
2. Maintain this invariant: The minimum is the best legal buy price for the current sell day.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def maxProfit(self, prices):
        cheapest, best = float("inf"), 0
        for price in prices:
            cheapest = min(cheapest, price)
            best = max(best, price - cheapest)
        return best

Why this is correct

The proof follows the maintained state: The minimum is the best legal buy price for the current sell day. Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O(n) time and O(1) extra space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

Descending prices return zero; the buy must occur before the sale.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

Browse the searchable 100 LeetCode Python Solutions hub. Previous: 189. Rotate Array · Next: 122. Best Time to Buy and Sell Stock II