LeetCode 169: Majority Element — Python Solution

Solve LeetCode 169: Majority Element in Python with a Boyer-Moore voting 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

Treat equal values as votes for the current candidate and different values as cancellations. A guaranteed majority survives every possible cancellation.

Algorithm

1. Treat equal values as votes for the current candidate and different values as cancellations. A guaranteed majority survives every possible cancellation.
2. Maintain this invariant: The candidate represents the unmatched votes in the processed prefix.
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 majorityElement(self, nums):
        candidate, votes = None, 0
        for value in nums:
            if votes == 0:
                candidate = value
            votes += 1 if value == candidate else -1
        return candidate

Why this is correct

The proof follows the maintained state: The candidate represents the unmatched votes in the processed prefix. 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

The majority can change as the scan progresses; negative values are ordinary keys.

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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