## Description

https://leetcode.com/problems/rank-transform-of-an-array/

Given an array of integers `arr`

, replace each element with its rank.

The rank represents how large the element is. The rank has the following rules:

- Rank is an integer starting from 1.
- The larger the element, the larger the rank. If two elements are equal, their rank must be the same.
- Rank should be as small as possible.

**Example 1:**

Input:arr = [40,10,20,30]Output:[4,1,2,3]Explanation: 40 is the largest element. 10 is the smallest. 20 is the second smallest. 30 is the third smallest.

**Example 2:**

Input:arr = [100,100,100]Output:[1,1,1]Explanation: Same elements share the same rank.

**Example 3:**

Input:arr = [37,12,28,9,100,56,80,5,12]Output:[5,3,4,2,8,6,7,1,3]

**Constraints:**

`0 <= arr.length <= 10`

^{5}`-10`

^{9}<= arr[i] <= 10^{9}

## Explanation

Find and build a map of number’s orders and create a list of orders base on the original list.

## Python Solution

```
class Solution:
def arrayRankTransform(self, arr: List[int]) -> List[int]:
arr_set = set(arr)
sorted_arr = sorted(list(arr_set))
num_map = {}
for i, num in enumerate(sorted_arr):
num_map[num] = i + 1
results = []
for num in arr:
results.append(num_map[num])
return results
```

- Time Complexity: O(N).
- Space Complexity: O(N).