<p>Given an integer array <code>nums</code>, return <em>the <strong>third distinct maximum</strong> number in this array. If the third maximum does not exist, return the <strong>maximum</strong> number</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,2,1]
<strong>Output:</strong> 1
<strong>Explanation:</strong>
The first distinct maximum is 3.
The second distinct maximum is 2.
The third distinct maximum is 1.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2]
<strong>Output:</strong> 2
<strong>Explanation:</strong>
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.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,2,3,1]
<strong>Output:</strong> 1
<strong>Explanation:</strong>
The first distinct maximum is 3.
The second distinct maximum is 2 (both 2&#39;s are counted together since they have the same value).
The third distinct maximum is 1.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>4</sup></code></li>
	<li><code>-2<sup>31</sup> &lt;= nums[i] &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

<p>&nbsp;</p>
<strong>Follow up:</strong> Can you find an <code>O(n)</code> solution?
#include <limits>

const int down_infinity = std::numeric_limits<int>::min();

class Solution {
public:
    int thirdMax(vector<int>& nums) {
        unordered_set<int> used;
        int max = down_infinity, max2 = down_infinity, max3 = down_infinity;
        bool maxSet = false, max2Set = false, max3Set = false;
        int aux, aux2;
        for(int _ : nums){
            if(used.find(_) == used.end() && _ >= max3){
                used.insert(_);
                if(_ >= max2){
                    if(_ >= max){
                        aux = max;
                        aux2 = max2;
                        max = _;
                        max2 = aux;
                        max3 = aux2;
                        max3Set = max2Set;
                        max2Set = maxSet;
                        maxSet = true;
                    } else {
                        aux = max2;
                        max2 = _;
                        max3 = aux;
                        max3Set = max2Set;
                        max2Set = true;
                    }
                } else {max3Set = true; max3 = _;}
            }
        }
        cout << max << " " << max2 << " " << max3 << " " << max3Set << endl;
        if(!max3Set) return max;
        return max3;
    }
};
12500