Description

Given four lists A, B, C, D of integer values, compute how many tuples (i, j, k, l) there are such that A[i] + B[j] + C[k] + D[l] is zero.

To make problem a bit easier, all A, B, C, D have same length of N where 0 ≤ N ≤ 500. All integers are in the range of -228 to 228 - 1 and the result is guaranteed to be at most 231 - 1.

Example:

Input:
A = [ 1, 2]
B = [-2,-1]
C = [-1, 2]
D = [ 0, 2]

Output:
2

Explanation:
The two tuples are:
1. (0, 0, 0, 1) -> A[0] + B[0] + C[0] + D[1] = 1 + (-2) + (-1) + 2 = 0
2. (1, 1, 0, 0) -> A[1] + B[1] + C[0] + D[0] = 2 + (-1) + (-1) + 0 = 0

Solutions

1. Array

# Time: O(n^2)
# Space: O(n^2)
class Solution:
    def fourSumCount(self, A: List[int], B: List[int], C: List[int], D: List[int]) -> int:
        res = 0
        ab_hash = {}
        for a in A:
            for b in B:
                ab_hash[a + b] = ab_hash.get(a + b, 0) + 1
        for c in C:
            for d in D:
                if -c - d in ab_hash:
                    res += ab_hash[-c - d]
        return res
# 48/48 cases passed (636 ms)
# Your runtime beats 5.05 % of python3 submissions
# Your memory usage beats 100 % of python3 submissions (33.6 MB)

References

  1. 454. 4Sum II