Tuple with Same Product - Video Solutions

Problem Overview: You receive an array of distinct integers. The task is to count the number of tuples (a, b, c, d) such that a * b = c * d and all four elements come from different indices. Order matters, so each valid pair combination generates multiple permutations of tuples.

Approach 1: Hashmap Based Approach (O(n^2) time, O(n^2) space)

The key observation: if two different pairs of numbers produce the same product, they can form valid tuples. Iterate through all pairs (i, j) with i < j and compute their product. Store the frequency of each product in a hash map. If a product appears k times, it means there are k pairs producing that product. Any two of these pairs can combine to form tuples. The number of pair combinations is k choose 2, and each pair combination generates 8 valid permutations of (a, b, c, d). This approach relies on fast hash lookups and pair enumeration, making it the optimal method using a hash table and counting technique.

Approach 2: Two Pointers Approach (O(n^3) time, O(1) space)

Sort the array first. Then iterate through every pair (i, j) to form a target product. For the remaining elements, attempt to find another pair whose product matches the target using a two‑pointer scan from both ends of the remaining subarray. Each time a matching pair is found, count the valid tuple permutations. This method avoids additional memory but repeatedly scans the array for matching products, which increases the runtime significantly compared to the hashing approach.

Recommended for interviews: The hashmap approach is what interviewers expect. It demonstrates recognition of pair-product collisions and reduces the search space from brute-force tuple enumeration to pair counting. Brute-force or pointer-based exploration shows understanding of the problem structure, but the O(n^2) hash map solution highlights strong pattern recognition and efficient use of data structures.