# LeetCode 1502. Can Make Arithmetic Progression From Sequence

## Description

https://leetcode.com/problems/can-make-arithmetic-progression-from-sequence/

Given an array of numbers `arr`. A sequence of numbers is called an arithmetic progression if the difference between any two consecutive elements is the same.

Return `true` if the array can be rearranged to form an arithmetic progression, otherwise, return `false`.

Example 1:

```Input: arr = [3,5,1]
Output: true
Explanation: We can reorder the elements as [1,3,5] or [5,3,1] with differences 2 and -2 respectively, between each consecutive elements.
```

Example 2:

```Input: arr = [1,2,4]
Output: false
Explanation: There is no way to reorder the elements to obtain an arithmetic progression.
```

Constraints:

• `2 <= arr.length <= 1000`
• `-10^6 <= arr[i] <= 10^6`

## Explanation

Sort first. Then compare the differences between numbers.

## Python Solution

``````class Solution:
def canMakeArithmeticProgression(self, arr: List[int]) -> bool:
arr = sorted(arr)

diff = arr[1] - arr[0]
prev = arr[1]

for num in arr[2:]:
if num - prev != diff:
return False
prev = num

return True``````
• Time Complexity: O(NlogN).
• Space Complexity: O(1).