Four Sum Problem All Unique Quadruplets in DSA Java - Build from Scratch

Four Sum Problem All Unique Quadruplets

📖 Scenario: You are working on a shopping app that suggests combinations of four products whose prices add up to a customer's gift card value. You want to find all unique sets of four product prices that exactly match the gift card amount.

🎯 Goal: Build a Java program that finds all unique quadruplets in an integer array that sum up to a given target value.

📋 What You'll Learn

Create an integer array called nums with the exact values: 1, 0, -1, 0, -2, 2

Create an integer variable called target and set it to 0

Write a method called fourSum that takes nums and target as parameters and returns a list of lists of integers representing all unique quadruplets that sum to target

Print the list of quadruplets returned by fourSum

💡 Why This Matters

🌍 Real World

Finding combinations of products or items that match a specific budget or target sum is common in shopping apps, budgeting tools, and financial planning software.

💼 Career

Understanding how to find unique combinations in arrays is useful for software engineers working on recommendation systems, data analysis, and algorithm optimization.

1

Create the input array nums

Create an integer array called nums with these exact values: 1, 0, -1, 0, -2, 2

DSA Java

// Create the integer array nums with the given values
// Your code here

Hint

Use int[] nums = {1, 0, -1, 0, -2, 2}; to create the array.

2

Create the target sum variable target

Create an integer variable called target and set it to 0

DSA Java

int[] nums = {1, 0, -1, 0, -2, 2};
// Create the integer variable target and set it to 0
// Your code here

Hint

Use int target = 0; to create the target variable.

3

Write the fourSum method to find unique quadruplets

Write a method called fourSum that takes int[] nums and int target as parameters and returns a List> of all unique quadruplets that sum to target. Use sorting and two pointers inside nested loops to find quadruplets. The method signature must be public static List> fourSum(int[] nums, int target).

DSA Java

int[] nums = {1, 0, -1, 0, -2, 2};
int target = 0;

// Write the fourSum method below
// Your code here

Hint

Sort the array first. Use two nested loops for the first two numbers, then use two pointers to find the other two numbers. Skip duplicates to ensure unique quadruplets.

4

Print the result of fourSum(nums, target)

Call the fourSum method with nums and target and print the returned list of quadruplets.

DSA Java

import java.util.*;

int[] nums = {1, 0, -1, 0, -2, 2};
int target = 0;

public static List> fourSum(int[] nums, int target) {
    // method code here
}

// Call fourSum and print the result below
// Your code here

Hint

Call fourSum(nums, target) and print the result using System.out.println.

Practice

1. What is the main goal of the Four Sum Problem in data structures and algorithms?

easy

A. Find all unique quadruplets in an array that sum up to a target value

B. Sort the array in ascending order

C. Find the maximum element in the array

D. Count the number of pairs that sum to a target

Solution

1. Step 1: Understand the problem statement

   The Four Sum Problem asks to find sets of four numbers in an array that add up to a given target.

2. Step 2: Identify the expected output

   We want all unique quadruplets, meaning no repeated sets, that sum exactly to the target.

3. Final Answer:

   Find all unique quadruplets in an array that sum up to a target value -> Option A

4. Quick Check:

   Four Sum = unique quadruplets summing to target [OK]

Hint: Look for four numbers adding to target without duplicates [OK]

Common Mistakes:

• Confusing Four Sum with Two Sum or Three Sum problems
• Ignoring uniqueness of quadruplets
• Trying to find maximum or minimum instead of sum

2. Which of the following Java code snippets correctly initializes an empty list to store quadruplets for the Four Sum problem?

easy

A. List quadruplets = new List<>();

B. List quadruplets = new ArrayList<>();

C. ArrayList<int> quadruplets = new ArrayList<>();

D. List<List> quadruplets = new ArrayList();

Solution

1. Step 1: Check Java syntax for list initialization

   Correct generic syntax for a list of lists of integers is List quadruplets = new ArrayList<>();

2. Step 2: Identify errors in other options

   List quadruplets = new List<>(); uses raw List without generics and wrong constructor; ArrayList<int> quadruplets = new ArrayList<>(); uses primitive int which is invalid; List<List> quadruplets = new ArrayList(); mixes generics incorrectly.

3. Final Answer:

   List quadruplets = new ArrayList<>(); -> Option B

4. Quick Check:

   Correct generic list initialization = List quadruplets = new ArrayList<>(); [OK]

Hint: Use List with ArrayList constructor [OK]

Common Mistakes:

• Using raw types without generics
• Trying to use primitive types in generics
• Incorrect constructor calls for List

3. What will be the output of the following Java code snippet for the Four Sum problem?

int[] nums = {1, 0, -1, 0, -2, 2};
int target = 0;
List result = fourSum(nums, target);
System.out.println(result);

Assuming fourSum correctly finds all unique quadruplets summing to target.

medium

A. [[-2, -1, 0, 1], [0, 0, 0, 0]]

B. [[1, 0, -1, 0]]

C. [[-2, -1, 1, 2], [-2, 0, 0, 2], [-1, 0, 0, 1]]

D. []

Solution

1. Step 1: Sort and find quadruplets summing to zero

   Sorted array: [-2, -1, 0, 0, 1, 2]. Quadruplets summing to 0 are [-2,-1,1,2], [-2,0,0,2], and [-1,0,0,1].

2. Step 2: Verify uniqueness and completeness

   All quadruplets are unique and sum exactly to target 0. No other quadruplets exist.

3. Final Answer:

   [[-2, -1, 1, 2], [-2, 0, 0, 2], [-1, 0, 0, 1]] -> Option C

4. Quick Check:

   Unique quadruplets sum to 0 = [[-2, -1, 1, 2], [-2, 0, 0, 2], [-1, 0, 0, 1]] [OK]

Hint: Sort array first, then find quadruplets with two pointers [OK]

Common Mistakes:

• Not sorting array before processing
• Including duplicate quadruplets
• Missing some valid quadruplets

4. Identify the bug in this Java snippet for the Four Sum problem:

for (int i = 0; i < nums.length - 3; i++) {
  for (int j = i + 1; j < nums.length - 2; j++) {
    int left = j + 1, right = nums.length - 1;
    while (left < right) {
      int sum = nums[i] + nums[j] + nums[left] + nums[right];
      if (sum == target) {
        result.add(Arrays.asList(nums[i], nums[j], nums[left], nums[right]));
        left++;
        right--;
      } else if (sum < target) {
        left++;
      } else {
        right--;
      }
    }
  }
}

medium

A. Sum calculation uses wrong indices

B. Incorrect initialization of left and right pointers

C. Wrong loop conditions for i and j

D. Missing checks to skip duplicate elements for i, j, left, and right

Solution

1. Step 1: Analyze loop and pointer usage

   Loops and pointers are correctly set to find quadruplets, and sum calculation is correct.

2. Step 2: Identify missing duplicate skipping

   Code lacks checks to skip duplicate values for i, j, left, and right after finding a quadruplet, which can cause duplicate quadruplets in result.

3. Final Answer:

   Missing checks to skip duplicate elements for i, j, left, and right -> Option D

4. Quick Check:

   Duplicate skipping missing = Missing checks to skip duplicate elements for i, j, left, and right [OK]

Hint: Always skip duplicates after adding quadruplet to avoid repeats [OK]

Common Mistakes:

• Not skipping duplicates causing repeated quadruplets
• Changing pointers incorrectly inside loops
• Incorrect loop boundaries causing index errors

5. Given the array nums = {2, 2, 2, 2, 2} and target 8, what is the correct output of the Four Sum problem solution that finds all unique quadruplets?

hard

A. [[2, 2, 2, 2]]

B. [[2, 2, 2, 2], [2, 2, 2, 2]]

C. []

D. [[2, 2, 2]]

Solution

1. Step 1: Check if quadruplets sum to target

   All elements are 2, so quadruplet [2, 2, 2, 2] sums to 8.

2. Step 2: Ensure uniqueness of quadruplets

   Even though elements repeat, only one unique quadruplet exists. Duplicates must be avoided.

3. Final Answer:

   [[2, 2, 2, 2]] -> Option A

4. Quick Check:

   Unique quadruplet summing to 8 = [[2, 2, 2, 2]] [OK]

Hint: Same numbers can form one unique quadruplet if sum matches target [OK]

Common Mistakes:

• Returning duplicate quadruplets multiple times
• Returning empty list when quadruplet exists
• Confusing triple with quadruplet