题目描述：

LeetCode 454. 4Sum II

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

题目大意：

给定4个整数列表A, B, C, D，计算有多少个元组 (i, j, k, l) 满足 A[i] + B[j] + C[k] + D[l] = 0。

为了使问题简化，A, B, C, D相等都是N， 0 ≤ N ≤ 500。所有整数在范围 [-2^28 , 2^28 - 1] 之内，并且结果确保至多为 2^31 - 1。

解题思路：

利用字典cnt，将A，B中各元素（笛卡尔积）的和进行分类计数。

将C，D中各元素（笛卡尔积）和的相反数在cnt中的值进行累加，即为答案。

Python代码：

class Solution(object):
    def fourSumCount(self, A, B, C, D):
        """
        :type A: List[int]
        :type B: List[int]
        :type C: List[int]
        :type D: List[int]
        :rtype: int
        """
        ans = 0
        cnt = collections.defaultdict(int)
        for a in A:
            for b in B:
                cnt[a + b] += 1
        for c in C:
            for d in D:
                ans += cnt[-(c + d)]
        return ans

 

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