4Sum

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.

    For example, given array S = {1 0 -1 0 -2 2}, and target = 0.

    A solution set is:
    (-1,  0, 0, 1)
    (-2, -1, 1, 2)
    (-2,  0, 0, 2)

Solution1:
A typical k-sum problem. Time is N to the poser of (k-1).
Run time complexity is O(n^3), solution based on 3sum
the efficiency of the best solution for m sum is O(n^(m-1)) 

public class Solution {
    public ArrayList> fourSum(int[] num, int target) {
        ArrayList> result = new ArrayList>();
        HashSet> check = new HashSet>();
        Arrays.sort(num);
        
        if(num.length < 4)
            return result;
        
        for(int i = 0; i < num.length; i++) {
            //3 sum
            for(int j = i + 1; j < num.length; j++) {
                int start = j + 1;
                int end = num.length - 1;
                //2 sum
                while(start < end) {
                    int sum = num[i] + num[j] + num[start] + num[end];
                    ArrayList temp = new ArrayList();
                    if(sum == target) {
                        temp.add(num[i]);
                        temp.add(num[j]);
                        temp.add(num[start]);
                        temp.add(num[end]);
                        
                        if(!check.contains(temp)) {
                            result.add(temp);
                            check.add(temp);
                        }
                        start++;
                        end--;
                    }else if(sum < target) {
                        start++;
                    }else {
                        end--;
                    }
                }
            }
        }
        return result;
    }
}