Problem Description
Given a 0-indexed integer array nums of length n and an integer k, return the number of pairs (i, j) where 0 <= i < j < n, such that nums[i] == nums[j] and (i * j) is divisible by k.
Key Insights
- The problem requires counting pairs of indices in an array that have equal values.
- The indices of these pairs must also satisfy the condition that their product is divisible by a given integer
k. - A brute-force approach would involve checking all pairs, but optimizations can be made using counting techniques.
Space and Time Complexity
Time Complexity: O(n^2)
Space Complexity: O(1)
Solution
To solve this problem, we can use a brute-force approach where we iterate through all possible pairs of indices (i, j) in the array. For each pair, we check if the values at those indices are equal and if their product (i * j) is divisible by k. If both conditions are satisfied, we increment our count.
This approach utilizes a nested loop to generate all pairs, leading to a quadratic time complexity. However, since the maximum length of the array is 100, this is acceptable within the given constraints.