# Third Maximum Number Problem

## Description

LeetCode Problem 414.

Given an integer array nums, return the third distinct maximum number in this array. If the third maximum does not exist, return the maximum number.

Example 1:

``````1
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Input: nums = [3,2,1]
Output: 1
Explanation:
The first distinct maximum is 3.
The second distinct maximum is 2.
The third distinct maximum is 1.
``````

Example 2:

``````1
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Input: nums = [1,2]
Output: 2
Explanation:
The first distinct maximum is 2.
The second distinct maximum is 1.
The third distinct maximum does not exist, so the maximum (2) is returned instead.
``````

Example 3:

``````1
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Input: nums = [2,2,3,1]
Output: 1
Explanation:
The first distinct maximum is 3.
The second distinct maximum is 2 (both 2's are counted together since they have the same value).
The third distinct maximum is 1.
``````

Constraints:

• 1 <= nums.length <= 10^4
• -2^31 <= nums[i] <= 2^31 - 1

## Sample C++ Code

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class Solution {
public:
int thirdMax(vector<int>& nums) {
long long a, b, c;
a = b = c = LLONG_MIN;
for (auto num : nums) {
if (num <= c || num == b || num == a) continue;
c = num;
if (c > b) swap(b, c);
if (b > a) swap(a, b);
}
return c == LLONG_MIN ? a : c;
}
};
``````