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1632. Rank Transform of a Matrix

Difficulty Topics

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.

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 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]]

 

Constraints:

  • m == matrix.length
  • n == matrix[i].length
  • 1 <= m, n <= 500
  • -109 <= matrix[row][col] <= 109

Solution

rank-transform-of-a-matrix.py
class DSU:
    def __init__(self, graph):
        self.p = {i:i for i in graph}

    def find(self, x):
        if self.p[x] != x:
            self.p[x] = self.find(self.p[x])
        return self.p[x]

    def union(self, x, y):
        self.p[self.find(x)] = self.find(y)

    def groups(self):
        ans = defaultdict(list)
        for el in self.p.keys():
            ans[self.find(el)].append(el)
        return ans

class Solution:
    def matrixRankTransform(self, M):
        n, m = len(M), len(M[0])
        rank = [0] * (m + n)
        d = defaultdict(list)

        for i, j in product(range(n), range(m)):
            d[M[i][j]].append([i, j])

        for a in sorted(d):
            graph = [i for i, j in d[a]] + [j + n for i, j in d[a]]
            dsu = DSU(graph)
            for i, j in d[a]: dsu.union(i, j + n)

            for group in dsu.groups().values():
                mx = max(rank[i] for i in group)
                for i in group: rank[i] = mx + 1

            for i, j in d[a]: M[i][j] = rank[i]

        return M