# LeetCode 1331. Rank Transform of an Array

## 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 <= 105`
• `-109 <= arr[i] <= 109`

## 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).