Is Number of Subarrays With GCD Equal to K easy or hard?

The problem is rated Medium because the brute force solution is straightforward but inefficient. Recognizing that subarrays share intermediate GCD values and compressing those states into a smaller set requires deeper understanding of GCD properties and optimization techniques.

Number of Subarrays With GCD Equal to K Python/Java solution

Both Python and Java implementations rely on the Euclidean algorithm to compute GCD values while iterating through the array. The optimized version stores previous GCD results and updates them for each new element, producing an O(n log V) solution suitable for large inputs.

How to solve Number of Subarrays With GCD Equal to K in O(n)?

A near-linear solution uses incremental GCD tracking. Maintain all distinct GCDs for subarrays ending at the current index and update them when a new element is processed. Because the number of distinct GCD values remains small, the effective complexity becomes O(n log V), which is close to linear in practice.

What is the best approach for Number of Subarrays With GCD Equal to K?

The most efficient approach maintains distinct GCD values for subarrays ending at each index and compresses identical results. Instead of recalculating every subarray independently, it reuses previously computed GCDs and updates them with the current element. This reduces the complexity to about O(n log V), where V is the maximum array value.

Is Number of Subarrays With GCD Equal to K asked at Google/Amazon/Meta?

GCD-based subarray problems frequently appear in interviews at companies like Google, Amazon, and other large tech firms because they test number theory fundamentals and array optimization techniques. Variations involving subarray GCD, LCM, or divisibility are common in coding rounds.

What data structure is used in Number of Subarrays With GCD Equal to K?

The optimized solution typically uses a map or list of pairs to store distinct GCD values and their frequencies for subarrays ending at the current index. This structure allows quick updates when computing new GCDs with the incoming element.

What is the time complexity of Number of Subarrays With GCD Equal to K?

The brute force approach runs in O(n^2 log V) because every subarray is explored and each extension requires a GCD computation. The optimized approach reduces this to roughly O(n log V) by tracking only distinct GCD values for subarrays ending at each position.

Description Hints 2 Solution Video 6:30

2447. Number of Subarrays With GCD Equal to K

Medium53.9% acceptance

Given an integer array nums and an integer k, return the number of subarrays of nums where the greatest common divisor of the subarray's elements is k.

A subarray is a contiguous non-empty sequence of elements within an array.

The greatest common divisor of an array is the largest integer that evenly divides all the array elements.

Example 1:

Input: nums = [9,3,1,2,6,3], k = 3
Output: 4
Explanation: The subarrays of nums where 3 is the greatest common divisor of all the subarray's elements are:
- [9,3,1,2,6,3]
- [9,3,1,2,6,3]
- [9,3,1,2,6,3]
- [9,3,1,2,6,3]

Example 2:

Input: nums = [4], k = 7
Output: 0
Explanation: There are no subarrays of nums where 7 is the greatest common divisor of all the subarray's elements.

Constraints:

1 <= nums.length <= 1000
1 <= nums[i], k <= 10⁹

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Hint 1

The constraints on nums.length are small. It is possible to check every subarray.

Hint 2

To calculate GCD, you can use a built-in function or the Euclidean Algorithm.

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2447. Number of Subarrays With GCD Equal to K

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