1632. Rank Transform of a Matrix

https://leetcode.com/problems/rank-transform-of-a-matrix

Description

Given an m x n matrix, return a new matrix answer where answer[row][col] is the rank of matrix[row][col].

The rank is an integer that represents how large an element is compared to other elements. It is calculated using the following rules:

• The rank is an integer starting from 1.

• If two elements p and q are in the same row or column, then:

  • If p < q then rank(p) < rank(q)

  • If p == q then rank(p) == rank(q)

  • If p > q then rank(p) > rank(q)

• The rank should be as small as possible.

It is guaranteed that answer is unique under the given rules.

Example 1:

**Input:** matrix = [[1,2],[3,4]]
**Output:** [[1,2],[2,3]]
**Explanation:**
The rank of matrix[0][0] is 1 because it is the smallest integer in its row and column.
The rank of matrix[0][1] is 2 because matrix[0][1] > matrix[0][0] and matrix[0][0] is rank 1.
The rank of matrix[1][0] is 2 because matrix[1][0] > matrix[0][0] and matrix[0][0] is rank 1.
The rank of matrix[1][1] is 3 because matrix[1][1] > matrix[0][1], matrix[1][1] > matrix[1][0], and both matrix[0][1] and matrix[1][0] are rank 2.

Example 2:

**Input:** matrix = [[7,7],[7,7]]
**Output:** [[1,1],[1,1]]

Example 3:

**Input:** matrix = [[20,-21,14],[-19,4,19],[22,-47,24],[-19,4,19]]
**Output:** [[4,2,3],[1,3,4],[5,1,6],[1,3,4]]

Example 4:

**Input:** matrix = [[7,3,6],[1,4,5],[9,8,2]]
**Output:** [[5,1,4],[1,2,3],[6,3,1]]

Constraints:

• m == matrix.length

• n == matrix[i].length

• 1 <= m, n <= 500

• -109 <= matrix[row][col] <= 109

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