Interview Question 4Sum

By Fatih KABAKCI

The problem is to find out all unique quadruplets in the array which the sum of any 4 elements is a specified target. The solution of the problem is almost same with the solution of the problem 3Sum. The only difference between them is number of the elements in the list which have been gathered, and the target does not have to be zero as 3Sum does. However, by this way, it is similar to solution of the problem 3Sum Closest..

So, in order to understand this problem, it is better idea to understand 3Sum Problem.

Problem #18 - 4Sum

Description: 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.

Difficulty: Medium

Solution in Java

package com.fatihkabakci.Medium._4Sum;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Iterator;
import java.util.LinkedHashSet;
import java.util.List;
import java.util.Set;

/**
 * @author fkabakci
 * 
 * Problem Description: 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: 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]
 * 	    ]
 * 
 * Solution:
 * 
 * The main idea of the solution is as same as the solution of the problem 3Sum.
 * 
 * 1. Sort the input array.
 * 2. Start with getting first, second, third and last element.
 * 3. Add up them.
 * 4. If sum equals to target,
 * 		 then add them into the list, and pass to fourth one, and previous one element of the last one.
 * 	  If sum is less than zero,
 * 	     then close to higher one. (Pass to fourth one by increasing loop variable k)
 * 	  If sum is greater than zero,
 * 		 then close to lower one. (Pass to previous one of the last one by decreasing loop variable m)
 * 5. Lastly, get rid of duplicated elements by using Collection Set.
 */

public class _4Sum {
	public List<List<Integer>> fourSum(int[] nums, int target) {
		if (nums.length < 4)
			return new ArrayList<List<Integer>>();
		
		Arrays.sort(nums);
		List<List<Integer>> list = new ArrayList<List<Integer>>();
		
		int i = 0, j = 0, k = 1, m;
		while (i < nums.length - 1 && j < k) {
			if(++j == nums.length) {
				j = (++i) + 1;
			}
			k = j + 1;
 			m = nums.length - 1;
			while (k < m) {
				int sum = nums[i] + nums[j] + nums[k] + nums[m];
				if (sum == target) {
					List<Integer> tsum = new ArrayList<Integer>();
					tsum.add(nums[i]);
					tsum.add(nums[j]);
					tsum.add(nums[k]);
					tsum.add(nums[m]);
					list.add(tsum);
					k++;
					m--;
				} else if (sum < target)
					k++;
				else
					m--;
			}
		}
		Set<List<Integer>> set = new LinkedHashSet<List<Integer>>(list);
		return new ArrayList<List<Integer>>(set);
	}

	public static void main(String[] args) {
		_4Sum i = new _4Sum();
		List<List<Integer>> l = i.fourSum(new int[] {1, 0, -1, 0, -2, 2}, 0);
		Iterator<List<Integer>> it = l.iterator();
		while(it.hasNext()) {
			System.out.println(it.next());
		}
	}
}

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