LeetCode 122: Best Time to Buy and Sell Stock II — Python Solution

Solve LeetCode 122: Best Time to Buy and Sell Stock II in Python with a greedy positive differences 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

Add every positive day-to-day increase. Each rising run contributes the same profit as buying at its start and selling at its end.

Algorithm

1. Add every positive day-to-day increase. Each rising run contributes the same profit as buying at its start and selling at its end.
2. Maintain this invariant: Accumulated profit equals the maximum realizable profit over processed days with no overlapping positions.
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):
        return sum(max(0, prices[i] - prices[i - 1]) for i in range(1, len(prices)))

Why this is correct

The proof follows the maintained state: Accumulated profit equals the maximum realizable profit over processed days with no overlapping positions. 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

Flat and falling transitions contribute nothing.

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.

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