> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/hashmap-and-hashset-and-sliding-window/4-sum.md).

# 4 Sum

Given an array `S` of `n` integers, are there elements `a, b, c, and d` in `S` such that `a + b + c + d = target`? Find all unique quadruplets in the array which gives the sum of target.

> **Note:**
>
> * Elements in a quadruplet (a,b,c,d) must be in non-descending order. (ie, a ≤ b ≤ c ≤ d)
> * The solution set must not contain duplicate quadruplets.

**Example :**\
Given array `S = {1 0 -1 0 -2 2}`, and `target = 0`\
A solution set is:

```
    (-2, -1, 1, 2)
    (-2,  0, 0, 2)
    (-1,  0, 0, 1)
```

Also make sure that the solution set is lexicographically sorted.\
`Solution[i] < Solution[j] iff Solution[i][0] < Solution[j][0] OR (Solution[i][0] == Solution[j][0] AND ... Solution[i][k] < Solution[j][k])`

```java
public class Solution {
    public ArrayList<ArrayList<Integer>> fourSum(ArrayList<Integer> A, int target) {
        Collections.sort(A);
        // changing ArrayList to Integer array
        Integer[] num = new Integer[A.size()];
        num = A.toArray(num);
        HashSet<String> hashSet = new HashSet<>();
        ArrayList<ArrayList<Integer>> result = new ArrayList<ArrayList<Integer>>();
        for (int i = 0; i + 3 < num.length; i++) {
            for (int j = i + 1; j + 2 < num.length; j++) {
                int k = j + 1;
                int l = num.length - 1;
                while (k < l) {
                    int sum = num[i] + num[j] + num[k] + num[l];
                    if (sum > target)
                        l--;
                    else if (sum < target)
                        k++;
                    else if (sum == target) {
                        ArrayList<Integer> temp = new ArrayList<Integer>();
                        temp.add(num[i]);
                        temp.add(num[j]);
                        temp.add(num[k]);
                        temp.add(num[l]);
                        String str = Integer.toString(num[i]) + " " + Integer.toString(num[j]) + " "
                                + Integer.toString(num[k]) + " " + Integer.toString(num[l]);
                        if (!hashSet.contains(str)) {
                            hashSet.add(str);
                            result.add(temp);
                        }
                        k++;
                        l--;
                    }
                }
            }
        }
        return result;
    }
}
```


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