1632-rank-transform-of-a-matrix.adoc

1632. Rank Transform of a Matrix

{leetcode}/problems/rank-transform-of-a-matrix/[LeetCode - 1632. Rank Transform of a Matrix ^]

Given an m x n matrix, return a new matrix _`answer` where `answer[row] 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: <img alt="" src="https://assets.leetcode.com/uploads/2020/10/18/rank1.jpg" style="width: 442px; height: 162px;" />

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: <img alt="" src="https://assets.leetcode.com/uploads/2020/10/18/rank2.jpg" style="width: 442px; height: 162px;" />

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

Example 3: <img alt="" src="https://assets.leetcode.com/uploads/2020/10/18/rank3.jpg" style="width: 601px; height: 322px;" />

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

思路分析

一刷

link:{sourcedir}/_1632_RankTransformOfAMatrix.java[role=include]

参考资料