Can All Values Be Rearranged into an Arithmetic Progression?
Company: Google
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: easy
Interview Round: Other
### Problem
Determine whether every entry of arr can be reordered so that consecutive differences are all equal. Return true or false; no particular rearrangement is requested.
```cpp
class Solution {
public:
bool canMakeArithmeticProgression(vector<int>& arr);
};
```
### Examples
**Example 1:**
```text
Input: arr = [4,-2,1]
Output: true
Explanation: Sorting gives[-2,1,4],whose consecutive differences are both3.
```
**Example 2:**
```text
Input: arr = [2,2,5]
Output: false
Explanation: Sorted consecutive differences are0 and3,and no arithmetic progression uses exactly these values.
```
### Constraints
- arr has length 2 to 1000.
- Each value lies in `[-1000000,1000000]`.
### Contract considerations
The boolean result is deterministic even if multiple arrangements would work.
```hint Read the boundary condition
All supplied occurrences must appear in the rearrangement. Include duplicate values, negative values, and arrays of length two.
```
### Boundary reminders
The boolean result is deterministic even if multiple arrangements would work.
Overview: Can All Values Be Rearranged into an Arithmetic Progression?. Determine whether every entry of arr can be reordered so that consecutive differences are all equal.