# 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:**

![](https://assets.leetcode.com/uploads/2020/10/18/rank1.jpg)

```
**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:**

![](https://assets.leetcode.com/uploads/2020/10/18/rank2.jpg)

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

**Example 3:**

![](https://assets.leetcode.com/uploads/2020/10/18/rank3.jpg)

```
**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:**

![](https://assets.leetcode.com/uploads/2020/10/18/rank4.jpg)

```
**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`

## ac

```java
```