<p>Given an <code>m x n</code> matrix of <strong>distinct </strong>numbers, return <em>all <strong>lucky numbers</strong> in the matrix in <strong>any </strong>order</em>.</p>

<p>A <strong>lucky number</strong> is an element of the matrix such that it is the minimum element in its row and maximum in its column.</p>

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

<pre>
<strong>Input:</strong> matrix = [[3,7,8],[9,11,13],[15,16,17]]
<strong>Output:</strong> [15]
<strong>Explanation:</strong> 15 is the only lucky number since it is the minimum in its row and the maximum in its column.
</pre>

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

<pre>
<strong>Input:</strong> matrix = [[1,10,4,2],[9,3,8,7],[15,16,17,12]]
<strong>Output:</strong> [12]
<strong>Explanation:</strong> 12 is the only lucky number since it is the minimum in its row and the maximum in its column.
</pre>

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

<pre>
<strong>Input:</strong> matrix = [[7,8],[1,2]]
<strong>Output:</strong> [7]
<strong>Explanation:</strong> 7 is the only lucky number since it is the minimum in its row and the maximum in its column.
</pre>

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

<ul>
	<li><code>m == mat.length</code></li>
	<li><code>n == mat[i].length</code></li>
	<li><code>1 &lt;= n, m &lt;= 50</code></li>
	<li><code>1 &lt;= matrix[i][j] &lt;= 10<sup>5</sup></code>.</li>
	<li>All elements in the matrix are distinct.</li>
</ul>

class Solution {
public:
    vector<int> luckyNumbers (vector<vector<int>>& matrix) {
        int rows = matrix.size();
        int cols = matrix[0].size();

        int row_maximum_of_minimums = 0;
        for (const auto& row : matrix) {
            row_maximum_of_minimums = max(*min_element(row.begin(), row.end()), row_maximum_of_minimums);
        }

        int col_minimum_of_maximums = INT_MAX;
        for (int col_ind = 0; col_ind < cols; ++col_ind) {
            int col_maximum = 0;
            for (int row_ind = 0; row_ind < rows; ++row_ind) {
                col_maximum = max(col_maximum, matrix[row_ind][col_ind]);
            }
            col_minimum_of_maximums = min(col_maximum, col_minimum_of_maximums);
        }

        return row_maximum_of_minimums == col_minimum_of_maximums ? vector<int>{col_minimum_of_maximums} : vector<int>{};
    }
};
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