Solution: Minimize Maximum Value in a Grid
Explore how to transform a matrix by replacing its values while preserving relative order in rows and columns. This lesson guides you through sorting and updating strategies that minimize the matrix's maximum value. Understand key steps like flattening, sorting, and using auxiliary arrays to efficiently assign new values, preparing you to solve similar matrix optimization problems.
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Statement
You are given an m x n integer matrix, grid, containing distinct positive integers.
Your task is to replace each integer in the matrix with a positive integer such that the following conditions are satisfied:
1. Preserve relative order: The relative order of every two elements that are in the same row or column should stay the same after the replacements.
2. Minimize maximum value: The maximum number in the matrix after the replacement should be as small as possible.
The relative order is preserved if, for all pairs of elements in the original matrix, the following condition holds:
If grid[r1][c1] > grid[r2][c2] and either r1 == r2 or c1 == c2, then the corresponding replacement values must also satisfy grid[r1][c1] > grid[r2][c2].
For example, if grid = [[2, 4, 5], [6, 3, 8]], valid replacements could be:
[[1, 2, 3], [2, 1, 4]][[1, 2, 3], [3, 1, 4]]
Return the resulting matrix after the replacement. If there are multiple valid solutions, return any of them.
Constraints:
mgrid.lengthn...