1502 - Can Make Arithmetic Progression From Sequence (Easy)

Problem Link

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

Problem Statement

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

Given an array of numbers arr, 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

Approach 1: Sorting

We sort the array and calculate the first difference. Iterate the rest of the elements to check if they have the same difference between two elements.

C++

Written by @wkw

class Solution {
public:
    bool canMakeArithmeticProgression(vector<int>& arr) {
        // reorder first
        sort(arr.begin(), arr.end());
        // calculate the first difference
        int d = arr[1] - arr[0];
        // check the rest of the differences
        // if there is a new difference, then it is false
        // else it is true
        for (int i = 2; i < arr.size(); i++) {
            if (arr[i] - arr[i - 1] != d) {
                return false;
            }
        }
        return true;
    }
};

Rust

Written by @wkw

impl Solution {
    pub fn can_make_arithmetic_progression(mut arr: Vec<i32>) -> bool {
		// sort the arr first
        arr.sort();
		// then we focus on a window of size of 3
        for w in arr.windows(3) {
			// check if the difference between w[0] and w[1] and that between w[1] and w[2]  is same
			// if not, then we cannot make an AP
            if w[2] - w[1] != w[1] - w[0] {
                return false;
            }
        }
        true
    }
}