<p>There is a rectangular brick wall in front of you with <code>n</code> rows of bricks. The <code>i<sup>th</sup></code> row has some number of bricks each of the same height (i.e., one unit) but they can be of different widths. The total width of each row is the same.</p>

<p>Draw a vertical line from the top to the bottom and cross the least bricks. If your line goes through the edge of a brick, then the brick is not considered as crossed. You cannot draw a line just along one of the two vertical edges of the wall, in which case the line will obviously cross no bricks.</p>

<p>Given the 2D array <code>wall</code> that contains the information about the wall, return <em>the minimum number of crossed bricks after drawing such a vertical line</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/24/cutwall-grid.jpg" style="width: 493px; height: 577px;" />
<pre>
<strong>Input:</strong> wall = [[1,2,2,1],[3,1,2],[1,3,2],[2,4],[3,1,2],[1,3,1,1]]
<strong>Output:</strong> 2
</pre>

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

<pre>
<strong>Input:</strong> wall = [[1],[1],[1]]
<strong>Output:</strong> 3
</pre>

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

<ul>
	<li><code>n == wall.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>
	<li><code>1 &lt;= wall[i].length &lt;= 10<sup>4</sup></code></li>
	<li><code>1 &lt;= sum(wall[i].length) &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>sum(wall[i])</code> is the same for each row <code>i</code>.</li>
	<li><code>1 &lt;= wall[i][j] &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

class Solution {
public:
    int leastBricks(vector<vector<int>>& wall) {
        int n = wall.size(), m = wall[0].size(), totalWidth = 0;
        vector<int> rows(n, 0);
        int bricksCrossed = n;

        for(int brick : wall[0])
            totalWidth += brick;

        for(int i = 0; i < n; i++) {
            for(int j = 1; j < wall[i].size(); j++)
                wall[i][j] += wall[i][j - 1];
        }

        // for(auto row : wall) {
        //     for(int i = 0; i < row.size(); i++)
        //         cout<<row[i]<<", ";
        //     cout<<endl;
        // }

        int width = 0;
        while(width < totalWidth) {
            int minWidth = INT_MAX, bricks = 0;
            for(int i = 0; i < n; i++) {
                int col = rows[i];
                minWidth = min(minWidth, wall[i][col]);
                if(wall[i][col] <= width) {
                    rows[i]++;
                }
                else {
                    bricks++;
                }
            }
            width = minWidth;
            // cout<<"bricks: "<<bricks<<" width: "<<width<<endl;
            bricksCrossed = min(bricksCrossed, bricks);
        }

        return bricksCrossed;
    }
};
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