<p>Write an efficient algorithm that searches for a value <code>target</code> in an <code>m x n</code> integer matrix <code>matrix</code>. This matrix has the following properties:</p>

<ul>
	<li>Integers in each row are sorted in ascending from left to right.</li>
	<li>Integers in each column are sorted in ascending from top to bottom.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/24/searchgrid2.jpg" style="width: 300px; height: 300px;" />
<pre>
<strong>Input:</strong> matrix = [[1,4,7,11,15],[2,5,8,12,19],[3,6,9,16,22],[10,13,14,17,24],[18,21,23,26,30]], target = 5
<strong>Output:</strong> true
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/24/searchgrid.jpg" style="width: 300px; height: 300px;" />
<pre>
<strong>Input:</strong> matrix = [[1,4,7,11,15],[2,5,8,12,19],[3,6,9,16,22],[10,13,14,17,24],[18,21,23,26,30]], target = 20
<strong>Output:</strong> false
</pre>

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

<ul>
	<li><code>m == matrix.length</code></li>
	<li><code>n == matrix[i].length</code></li>
	<li><code>1 &lt;= n, m &lt;= 300</code></li>
	<li><code>-10<sup>9</sup> &lt;= matrix[i][j] &lt;= 10<sup>9</sup></code></li>
	<li>All the integers in each row are <strong>sorted</strong> in ascending order.</li>
	<li>All the integers in each column are <strong>sorted</strong> in ascending order.</li>
	<li><code>-10<sup>9</sup> &lt;= target &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution {
public:
    bool searchMatrix(vector<vector<int>> const& matrix, int const target) {
        size_t const M = matrix.size();
        size_t const N = matrix[0].size();

        for (size_t i = 0; i < M; ++i) {
            if (matrix[i][0] <= target && matrix[i][N - 1] >= target) {
                // we found row where target could be located

                ssize_t l = 0;
                ssize_t r = N - 1;
                while (l <= r) {
                    ssize_t const mid = (l + r) / 2;
                    int val = matrix[i][mid];

                    if (val == target) {
                        return true;
                    }

                    if (val < target) {
                        l = mid + 1;
                    } else {
                        r = mid - 1;
                    }
                }
            }
        }
        return false;
    }
};
17300