> For the complete documentation index, see [llms.txt](https://aaronice.gitbook.io/lintcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://aaronice.gitbook.io/lintcode/high_frequency/4-sum-ii.md).

# 4 Sum II

Medium

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 -2^28 to 2^28- 1 and the result is guaranteed to be at most 2^31- 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
```

## Solution

**HashMap**

虽然是KSum系列，但是因为有4个数组，所以做法可以跟KSum很不一样，这里用HashMap记录两个数组中的数之和的计数，再遍历另两个数组，看HashMap中是否存在`-sum`。

[@fabrizio3](https://leetcode.com/problems/4sum-ii/discuss/93946/Simple-Java-Solution-with-Explanation):

> Take the arrays A and B, and compute all the possible sums of two elements. Put the sum in the Hash map, and increase the hash map value if more than 1 pair sums to the same value.
>
> Compute all the possible sums of the arrays C and D. If the hash map contains the opposite value of the current sum, increase the count of four elements sum to 0 by the counter in the map.

```java
class Solution {
    public int fourSumCount(int[] A, int[] B, int[] C, int[] D) {
        HashMap<Integer, Integer> map = new HashMap<>();
        int count = 0;
        for (int i = 0; i < A.length; i++) {
            for (int j = 0; j < B.length; j++) {
                int sum = A[i] + B[j];
                map.put(sum, map.getOrDefault(sum, 0) + 1);
            }
        }

        for (int k = 0; k < C.length; k++) {
            for (int l = 0; l < D.length; l++) {
                int sum = (C[k] + D[l]);
                count += map.getOrDefault(-sum, 0);
            }
        }

        return count;
    }
}

// Time complexity:  O(n^2)
// Space complexity: O(n^2)
```

## Reference

[https://leetcode.com/problems/4sum-ii/discuss/93920/Clean-java-solution-O(n2\\](https://leetcode.com/problems/4sum-ii/discuss/93920/Clean-java-solution-O%28n2%29\\)


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://aaronice.gitbook.io/lintcode/high_frequency/4-sum-ii.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.