LeetCode 169: Majority Element — Python Solution

LeetCode 169: Majority Element is an Easy array / string problem. This Python walkthrough develops a Boyer-Moore voting solution, ties every code decision to a concrete invariant, and includes the regression check used before publication.

This independent guide paraphrases the task rather than reproducing LeetCode’s prompt. Use the official page for the exact statement, examples, constraints, and submission runner.

Recognizing the pattern

Array and string questions usually reward a precise index invariant. Decide which prefix or suffix is already final before mutating the next position.

For this problem specifically, treat equal values as votes for the current candidate and different values as cancellations. A guaranteed majority survives every possible cancellation. The invariant worth writing beside the code is: The candidate represents the unmatched votes in the processed prefix.

Step-by-step algorithm

1. Identify the input state consumed by majorityElement(nums) and initialize the data required by the Boyer-Moore voting pattern.
2. Treat equal values as votes for the current candidate and different values as cancellations. A guaranteed majority survives every possible cancellation.
3. After each update, verify the page’s central invariant: The candidate represents the unmatched votes in the processed prefix.
4. Finish only after the boundary behavior is covered: The majority can change as the scan progresses; negative values are ordinary keys.

Python solution

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

Reading the implementation

The main entry point is majorityElement(nums). The named working state includes candidate, votes; those variables make the Boyer-Moore voting state visible instead of hiding it in incidental control flow.

A single main loop advances the algorithm, which is the key reason the traversal does not revisit already resolved input unnecessarily. In concrete terms, treat equal values as votes for the current candidate and different values as cancellations. A guaranteed majority survives every possible cancellation.

Correctness argument

Initialization. The data structure starts with exactly the information known before any input element is processed.

Preservation. Treat equal values as votes for the current candidate and different values as cancellations. A guaranteed majority survives every possible cancellation. Each update records the current item without invalidating earlier decisions; consequently, the candidate represents the unmatched votes in the processed prefix.

Termination. The traversal consumes a finite input or finite state space. At the end, the invariant covers the complete input, which is precisely the condition required for the returned result.

Complexity and trade-offs

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

A copied output buffer can simplify reasoning, but the in-place version reduces auxiliary memory when mutation is allowed. That comparison is useful in an interview because it explains why the final implementation is preferable, not merely that it passes.

Regression check

The published implementation belongs to a 100-problem suite that is compiled and exercised behaviorally before deployment.

One reference assertion from that suite is shown below. It targets the normal path while the edge conditions in the next section cover the failure-prone boundaries.

assert Solution().majorityElement([2,2,1,1,1,2,2]) == 2

Common mistakes and edge cases

• Problem-specific boundary: The majority can change as the scan progresses; negative values are ordinary keys.
• Pattern-level pitfall: Do not let a write operation destroy input that a later read still needs; write direction and boundary conventions matter.
• Invariant check: after every update, confirm that the candidate represents the unmatched votes in the processed prefix.

Interview review checklist

• Explain why Boyer-Moore voting matches the structure of this input.
• State the invariant in one sentence before tracing code: The candidate represents the unmatched votes in the processed prefix.
• Derive O(n) time and O(1) extra space from how many times each element or state is visited.
• Test the boundary explicitly: The majority can change as the scan progresses; negative values are ordinary keys.

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