4Sum II

Problem Description

Given four integer arrays nums1, nums2, nums3, and nums4 all of length n, return the number of tuples (i, j, k, l) such that:

• 0 <= i, j, k, l < n
• nums1[i] + nums2[j] + nums3[k] + nums4[l] == 0

Key Insights

• The problem requires finding combinations of four indices from four arrays that sum to zero.
• A brute-force approach would involve four nested loops, leading to O(n^4) time complexity, which is inefficient for the upper limit of n (200).
• Instead, we can utilize hashing to optimize the solution by breaking the problem into two parts.
• Count the sums of all pairs from the first two arrays and use a hash table to store the frequency of these sums.
• For each pair from the last two arrays, check if the negation of their sum exists in the hash table.

Space and Time Complexity

Time Complexity: O(n^2)
Space Complexity: O(n)

Solution

To solve this problem, we can use a hash table to store the sum of pairs from the first two arrays (nums1 and nums2). We then iterate through pairs from the last two arrays (nums3 and nums4) and check how many times the negation of their sum appears in the hash table. This method significantly reduces the time complexity to O(n^2).

Code Solutions