{ "data": { "question": { "questionId": "1845", "questionFrontendId": "1727", "categoryTitle": "Algorithms", "boundTopicId": 559179, "title": "Largest Submatrix With Rearrangements", "titleSlug": "largest-submatrix-with-rearrangements", "content": "

You are given a binary matrix matrix of size m x n, and you are allowed to rearrange the columns of the matrix in any order.

\n\n

Return the area of the largest submatrix within matrix where every element of the submatrix is 1 after reordering the columns optimally.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: matrix = [[0,0,1],[1,1,1],[1,0,1]]\nOutput: 4\nExplanation: You can rearrange the columns as shown above.\nThe largest submatrix of 1s, in bold, has an area of 4.\n
\n\n

Example 2:

\n\"\"\n
\nInput: matrix = [[1,0,1,0,1]]\nOutput: 3\nExplanation: You can rearrange the columns as shown above.\nThe largest submatrix of 1s, in bold, has an area of 3.\n
\n\n

Example 3:

\n\n
\nInput: matrix = [[1,1,0],[1,0,1]]\nOutput: 2\nExplanation: Notice that you must rearrange entire columns, and there is no way to make a submatrix of 1s larger than an area of 2.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "重新排列后的最大子矩阵", "translatedContent": "

给你一个二进制矩阵 matrix ，它的大小为 m x n ，你可以将 matrix 中的 列 按任意顺序重新排列。

\n\n

请你返回最优方案下将 matrix 重新排列后，全是 1 的子矩阵面积。

\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
\n输入：matrix = [[0,0,1],[1,1,1],[1,0,1]]\n输出：4\n解释：你可以按照上图方式重新排列矩阵的每一列。\n最大的全 1 子矩阵是上图中加粗的部分，面积为 4 。\n
\n\n

示例 2：

\n\n

\"\"

\n\n
\n输入：matrix = [[1,0,1,0,1]]\n输出：3\n解释：你可以按照上图方式重新排列矩阵的每一列。\n最大的全 1 子矩阵是上图中加粗的部分，面积为 3 。\n
\n\n

示例 3：

\n\n
\n输入：matrix = [[1,1,0],[1,0,1]]\n输出：2\n解释：由于你只能整列整列重新排布，所以没有比面积为 2 更大的全 1 子矩形。
\n\n

示例 4：

\n\n
\n输入：matrix = [[0,0],[0,0]]\n输出：0\n解释：由于矩阵中没有 1 ，没有任何全 1 的子矩阵，所以面积为 0 。
\n\n

 

\n\n

提示：

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