Sorted GCD Pair Queries

Problem Description

You are given an integer array nums of length n and an integer array queries. Let gcdPairs denote an array obtained by calculating the GCD of all possible pairs (nums[i], nums[j]), where 0 <= i < j < n, and then sorting these values in ascending order. For each query queries[i], you need to find the element at index queries[i] in gcdPairs. Return an integer array answer, where answer[i] is the value at gcdPairs[queries[i]] for each query.

Key Insights

• Calculate the GCD for all unique pairs in the nums array.
• Store the GCD values in a list and sort them.
• Efficiently answer the queries by indexing into the sorted GCD list.
• The maximum number of GCD values is n * (n - 1) / 2 for n elements.

Space and Time Complexity

Time Complexity: O(n^2 log(n)) for GCD calculations and sorting. Space Complexity: O(n^2) to store the GCD pairs.

Solution

To solve the problem, we will:

1. Use a nested loop to compute the GCD of all possible pairs in the nums array.
2. Store these GCD values in a list called gcdPairs.
3. Sort the gcdPairs list in ascending order.
4. Use the indices provided in the queries array to retrieve the corresponding values from the sorted gcdPairs list.

This approach utilizes the GCD function, stored in a list, and sorting to efficiently respond to each query.

Code Solutions