Third Maximum Number

LeetCode 414 · Easy

Understand

Return the third-largest distinct integer. If fewer than three distinct values exist, return the largest.

Input	Output	Reason
[3, 2, 1]	1	Three distinct values
[1, 2]	2	Third value is absent
[2, 2, 3, 1]	1	Repeated 2 counts once

Match

A fixed number of running maxima. Each new number enters at most one rank; displaced candidates shift down.

Plan

After each iteration, the three variables hold the largest three distinct values seen so far. Missing ranks use negative infinity, which is outside this problem’s integer domain. Shift lower ranks before replacing the higher ones.

Implement: submitted Python solution

class Solution:
    def thirdMax(self, nums: list[int]) -> int:
        largest = float('-inf')
        largest2 = float('-inf')
        largest3 = float('-inf')

        for num in nums:
            if num > largest:
                largest3 = largest2
                largest2 = largest
                largest = num
            elif largest > num:
                if num > largest2:
                    largest3 = largest2
                    largest2 = num
                elif largest2 > num and num > largest3:
                    largest3 = num

        return largest if largest3 == float('-inf') else largest3

Review

Next number	First	Second	Third
2	2	missing	missing
2	2	missing	missing
3	3	2	missing
1	3	2	1

Strict comparisons exclude duplicates. Returning the maximum when the third rank is missing is part of this problem’s contract.

Comparison direction

Write ranges from smallest to largest:

lower < candidate < upper
# means:
lower < candidate and candidate < upper

With largest = 10, largest2 = 6, and num = 8:

largest2 < num < largest        # 6 < 8 < 10: True
largest > num > largest2        # 10 > 8 > 6: True
largest > num and num > largest2  # also True
largest < num < largest2        # 10 < 8 < 6: False

Use num for one item, and nums for the whole list.

Evaluate

O(n) time, O(1) auxiliary space. Three variables use constant storage: O(3) simplifies to O(1).

Revision cue

Why must the previous second move into third before the second variable is replaced? Trace a duplicate maximum and an input containing only two distinct values.

Study record: acceptance was reported by the learner. Implementation was reviewed by inspection; comparison direction was clarified afterward. This is not an independently observed LeetCode submission.