<p>You are given a binary matrix <code>matrix</code> of size <code>m x n</code>, and you are allowed to rearrange the <strong>columns</strong> of the <code>matrix</code> in any order.</p>

<p>Return <em>the area of the largest submatrix within </em><code>matrix</code><em> where <strong>every</strong> element of the submatrix is </em><code>1</code><em> after reordering the columns optimally.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/12/29/screenshot-2020-12-30-at-40536-pm.png" style="width: 500px; height: 240px;" />
<pre>
<strong>Input:</strong> matrix = [[0,0,1],[1,1,1],[1,0,1]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> You can rearrange the columns as shown above.
The largest submatrix of 1s, in bold, has an area of 4.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/12/29/screenshot-2020-12-30-at-40852-pm.png" style="width: 500px; height: 62px;" />
<pre>
<strong>Input:</strong> matrix = [[1,0,1,0,1]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> You can rearrange the columns as shown above.
The largest submatrix of 1s, in bold, has an area of 3.
</pre>

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

<pre>
<strong>Input:</strong> matrix = [[1,1,0],[1,0,1]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> Notice that you must rearrange entire columns, and there is no way to make a submatrix of 1s larger than an area of 2.
</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;= m * n &lt;= 10<sup>5</sup></code></li>
	<li><code>matrix[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

class Solution {
public:
    int largestSubmatrix(vector<vector<int>>& matrix) {
        int n = matrix.size();
        int m = matrix[0].size();
        vector<vector<int>> prefix(n,vector<int> (m));
        for(int j=0;j<m;j++)
        {
            prefix[0][j] = matrix[0][j];
        }
        vector<int> temp=prefix[0];
        sort(temp.begin(),temp.end(),greater<int>());
        int ans = 0;
        for(int i=0;i<m;i++)
        {
            if(temp[i])
            ans = max(ans,(i+1));
            else
            break;
        }
        for(int i=1;i<n;i++)
        {
            for(int j=0;j<m;j++)
            {
                if(matrix[i][j])
                {
                    prefix[i][j]+= matrix[i][j] + prefix[i-1][j];
                }
            }
            vector<int> tem=prefix[i];
            // tem.push_back(prefix[i]);
            sort(tem.begin(),tem.end(),greater<int>());
            for(int k=0;k<m;k++)
            {
                ans = max(ans,(k+1)*tem[k]);
            }
        }
        for(int i=0;i<n;i++)
        {
            for(int j=0;j<m;j++)
            cout<<prefix[i][j]<<" ";
            cout<<endl;
        }
        return ans;
    }
};
101800