Is Minimum Split Into Subarrays With GCD Greater Than One easy or hard?

The problem is rated Medium on LeetCode with around a 70% acceptance rate. The implementation is straightforward once you recognize the key observation that a running GCD cannot increase after reaching 1, enabling a greedy segmentation strategy.

Minimum Split Into Subarrays With GCD Greater Than One Python/Java solution

Implement a single pass through the array while tracking the current segment's GCD. Use the built-in gcd function (such as math.gcd in Python or Math.gcd equivalents in Java/C++ libraries). When the GCD becomes 1, increment the split counter and reset the running GCD to the current element.

What is the best approach for Minimum Split Into Subarrays With GCD Greater Than One?

The optimal approach is Greedy with running GCD computation. Traverse the array and maintain the GCD of the current segment. If the GCD becomes 1, split before the current element and start a new segment. This works because GCD is monotonic when adding elements and cannot increase once it reaches 1. The time complexity is O(n log A).

Is Minimum Split Into Subarrays With GCD Greater Than One asked at Google/Amazon/Meta?

Problems involving GCD properties, greedy segmentation, and number theory appear frequently in interviews at companies like Google, Amazon, and Meta. Variants that require maintaining a running GCD or splitting arrays based on mathematical constraints are common interview patterns.

What data structure is used in Minimum Split Into Subarrays With GCD Greater Than One?

The greedy solution mainly relies on simple array traversal and repeated GCD calculations using the Euclidean algorithm. No advanced data structures are required, which keeps the space complexity constant at O(1).

What is the time complexity of Minimum Split Into Subarrays With GCD Greater Than One?

The optimal greedy solution runs in O(n log A) time where n is the array length and A is the maximum value in the array. Each step performs a constant number of GCD computations, and the Euclidean algorithm takes O(log A). Space complexity is O(1).

2436. Minimum Split Into Subarrays With GCD Greater Than One - Practice Online

Q: How to solve Minimum Split Into Subarrays With GCD Greater Than One in O(n)?

A near-linear solution uses a greedy scan with a running GCD. Keep extending the current subarray while the GCD stays greater than 1. When the GCD becomes 1, increment the split count and restart the segment from the current element. The algorithm performs one pass over the array with GCD updates, giving O(n log A) complexity in practice.

You are given an array nums consisting of positive integers.

Split the array into one or more disjoint subarrays such that:

Each element of the array belongs to exactly one subarray, and
The GCD of the elements of each subarray is strictly greater than 1.

Return the minimum number of subarrays that can be obtained after the split.

Note that:

The GCD of a subarray is the largest positive integer that evenly divides all the elements of the subarray.
A subarray is a contiguous part of the array.

Example 1:

Input: nums = [12,6,3,14,8]
Output: 2
Explanation: We can split the array into the subarrays: [12,6,3] and [14,8].
- The GCD of 12, 6 and 3 is 3, which is strictly greater than 1.
- The GCD of 14 and 8 is 2, which is strictly greater than 1.
It can be shown that splitting the array into one subarray will make the GCD = 1.

Example 2:

Input: nums = [4,12,6,14]
Output: 1
Explanation: We can split the array into only one subarray, which is the whole array.

Constraints:

1 <= nums.length <= 2000
2 <= nums[i] <= 10⁹