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Challenge Points: 30
Level: HardYou are given a matrix with m rows and n columns. Your task is to create another matrix of the same size, where each cell contains the rank of the value at that position.
A rank is a positive integer that represents the relative order of the value compared to all other numbers in the same row or column. The ranking must follow these conditions:
The smallest possible rank is 1.
If two cells lie in the same row or column:
If one value is smaller, its rank must also be smaller.
If both values are equal, their ranks must be equal.
If one value is larger, its rank must be larger.
The resulting rank matrix must follow all constraints while keeping ranks as small as possible.
Input is guaranteed so that there is only one unique valid rank configuration.
Input: matrix = [[2,2,1],[1,2,2]]
Output: [[2,2,1],[1,2,2]]
Explanation:
Equal numbers in the same row/column share the same rank.
Input: matrix = [[4,6],[3,5]]
Output: [[2,3],[1,2]]
Explanation:
3 is the smallest → rank 1 4 is next → rank 2 5 → rank 2 (same row as 3 but greater) 6 → rank 3
Input: matrix = [[9,3,8],[2,7,6],[1,4,5]]
Output: [6,1,5, 2,5,4, 1,2,3]
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