1632 - Rank Transform of a Matrix.

Hard

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:

• The rank should be as small as possible.

The test cases are generated so 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 matrix0 is 1 because it is the smallest integer in its row and column.

The rank of matrix1 is 2 because matrix1> matrix0 and matrix0 is rank 1.

The rank of matrix0 is 2 because matrix0> matrix0 and matrix0 is rank 1.

The rank of matrix1 is 3 because matrix1> matrix1, matrix1> matrix0, and both matrix1 and matrix0 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]

Constraints:

• m == matrix.length

• n == matrix[i].length

• 1 <= m, n <= 500

• <code>-10⁹<= matrixcol<= 10⁹</code>