5 Best Ways to Check if Subarrays Can Be Rearranged into Arithmetic Sequences in Python

💡 Problem Formulation: The task at hand involves examining subarrays within a larger array to determine whether they can be rearranged to form an arithmetic sequence. This is a common problem in algorithm and data structure challenges, with applications in pattern recognition and mathematical analysis. For example, given an input array [3, 8, 5, 1, 7], we aim to find if there exists a subarray, like [8, 5, 7], which can be rearranged to an arithmetic sequence such as [5, 7, 8] with a common difference of 1.

Method 1: Brute Force Approach

This method involves checking every possible subarray and attempting to rearrange them to find an arithmetic sequence. The functionality of this method ensures that we do not miss any subarray but can be computationally expensive for large arrays or numerous subarrays.

Here’s an example:

def can_rearrange_to_arithmetic_sequence(arr):
    for start in range(len(arr)):
        for end in range(start + 1, len(arr) + 1):
            subarr = sorted(arr[start:end])
            if len(subarr) > 1 and all(subarr[i] - subarr[i-1] == subarr[1] - subarr[0] for i in range(2, len(subarr))):
                return True
    return False

print(can_rearrange_to_arithmetic_sequence([3, 8, 5, 1, 7]))

Output: True

This code snippet defines a function that iterates through all possible subarrays within the given array, sorts each subarray, and checks whether they form an arithmetic sequence. The rationality behind sorting each subarray is to reorder the elements in a way that could reveal an arithmetic progression if one exists.

Method 2: Utilizing Hash Maps

…