Leetcode #1502: Can Make Arithmetic Progression From Sequence
In this guide, we solve Leetcode #1502 Can Make Arithmetic Progression From Sequence in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
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.
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Array, Sorting
Intuition
Sorting reveals structure that is hard to see in the original order.
Once sorted, a linear scan is usually enough to compute the answer.
Approach
Sort the data and sweep through it while maintaining a small state.
This keeps the logic straightforward and reliable.
Steps:
- Sort the data.
- Scan in order while maintaining state.
- Update the best answer.
Example
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.
Python Solution
class Solution:
def canMakeArithmeticProgression(self, arr: List[int]) -> bool:
arr.sort()
d = arr[1] - arr[0]
return all(b - a == d for a, b in pairwise(arr))
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.