Four Sum Problem All Unique Quadruplets in DSA C# - 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. To help the app, you need to find all unique sets of four product prices that sum to the gift card amount.

🎯 Goal: Build a program that finds all unique quadruplets in a list of integers that sum up to a 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 unique quadruplets that sum to target

Print the result of calling FourSum(nums, target) in the format: quadruplets separated by commas, each quadruplet as numbers separated by spaces

💡 Why This Matters

🌍 Real World

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

💼 Career

Understanding how to find unique combinations efficiently is important for software engineers working on recommendation systems, data analysis, and optimization problems.

1

Create the input array nums

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

DSA C#

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

Hint

Use int[] nums = { ... }; to create the array with the exact values.

2

Create the target sum variable target

Create an integer variable called target and set it to 0

DSA C#

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 unique quadruplets that sum to target. Use sorting and two pointers inside nested loops to find quadruplets without duplicates.

DSA C#

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 pairs that complete the quadruplet. Skip duplicates carefully.

4

Print the unique quadruplets found by FourSum

Print the result of calling FourSum(nums, target). For each quadruplet, print the four numbers separated by spaces. Separate quadruplets by commas on the same line.

DSA C#

using System;
using System.Collections.Generic;

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

List> FourSum(int[] nums, int target)
{
    Array.Sort(nums);
    List> result = new List>();
    int n = nums.Length;
    for (int i = 0; i  0 && nums[i] == nums[i - 1]) continue;
        for (int j = i + 1; j  i + 1 && nums[j] == nums[j - 1]) continue;
            int left = j + 1;
            int right = n - 1;
            while (left  { nums[i], nums[j], nums[left], nums[right] });
                    left++;
                    right--;
                    while (left < right && nums[left] == nums[left - 1]) left++;
                    while (left < right && nums[right] == nums[right + 1]) right--;
                }
                else if (sum < target)
                {
                    left++;
                }
                else
                {
                    right--;
                }
            }
        }
    }
    return result;
}

// Print the quadruplets found by FourSum
# Your code here

Hint

Call FourSum(nums, target) and print each quadruplet's numbers separated by spaces. Separate quadruplets by commas.

Practice

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

easy

A. Sort the array in ascending order

B. Count the number of pairs with a given sum

C. Find the maximum element in the array

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

Solution

1. Step 1: Understand the problem statement

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

2. Step 2: Differentiate from other problems

   Unlike sorting or finding maximum, this problem focuses on quadruplets and their sums, not individual elements or pairs.

3. Final Answer:

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

4. Quick Check:

   Four Sum Problem = Find quadruplets with target sum [OK]

Hint: Look for four numbers adding to target, not sorting or max [OK]

Common Mistakes:

• Confusing with sorting or max element problems
• Looking for pairs instead of quadruplets
• Ignoring uniqueness of quadruplets

2. Which of the following C# code snippets correctly initializes a list to store quadruplets for the Four Sum Problem?

easy

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

B. var quadruplets = new List<int>();

C. var quadruplets = new Dictionary<int, int>();

D. var quadruplets = new int[4];

Solution

1. Step 1: Identify the data structure for storing quadruplets

   Each quadruplet is a list of 4 integers, so a list of lists is needed to store multiple quadruplets.

2. Step 2: Match with C# syntax

   Using List<List<int>> correctly represents multiple quadruplets, unlike a single list or dictionary.

3. Final Answer:

   var quadruplets = new List<List<int>>(); -> Option A

4. Quick Check:

   Use List of List for quadruplets [OK]

Hint: Use List<List<int>> to store multiple quadruplets [OK]

Common Mistakes:

• Using List<int> for multiple quadruplets
• Using Dictionary instead of List
• Using fixed-size array for dynamic quadruplets

3. For the input array nums = [1, 0, -1, 0, -2, 2] and target 0, what does FourSum(nums, 0) return?
Assuming FourSum returns all unique quadruplets that sum to target.

medium

A. []

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

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

D. [[0, 0, 0, 0]]

Solution

1. Step 1: Sort and find quadruplets summing to 0

   Sorting nums gives [-2, -1, 0, 0, 1, 2]. The unique 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 0, matching the expected output.

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 C# 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(new List<int> { nums[i], nums[j], nums[left], nums[right] });
                left++;
                right--;
            } else if (sum < target) {
                left++;
            } else {
                right--;
            }
        }
    }
}

medium

A. No check to skip duplicate quadruplets causing duplicates in result

B. Incorrect initialization of left and right pointers

C. Wrong loop ranges for i and j causing index out of range

D. Missing sorting of the input array before processing

Solution

1. Step 1: Analyze duplicate handling

   The code adds quadruplets without skipping duplicates, so repeated quadruplets can appear in the result.

2. Step 2: Check other parts

   Left and right pointers are correctly initialized; loop ranges are valid; sorting is assumed done before this snippet.

3. Final Answer:

   No check to skip duplicate quadruplets causing duplicates in result -> Option A

4. Quick Check:

   Missing duplicate skip = No check to skip duplicate quadruplets causing duplicates in result [OK]

Hint: Always skip duplicates after finding quadruplets [OK]

Common Mistakes:

• Not skipping duplicates for i, j, left, right
• Assuming sorting is done inside the loop
• Incorrect pointer updates causing infinite loops

5. Given the array nums = [2, 2, 2, 2, 2] and target 8, what is the correct output of the Four Sum Problem algorithm that finds all unique quadruplets?

medium

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

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

C. []

D. [[2, 2, 2]]

Solution

1. Step 1: Understand the input and target

   All elements are 2, and target is 8, so quadruplets of four 2's sum to 8.

2. Step 2: Identify unique quadruplets

   Only one unique quadruplet [2, 2, 2, 2] exists despite duplicates in input.

3. Final Answer:

   [[2, 2, 2, 2]] -> Option B

4. Quick Check:

   Only one unique quadruplet sums to 8 [OK]

Hint: Duplicates form one unique quadruplet if sum matches target [OK]

Common Mistakes:

• Counting duplicate quadruplets multiple times
• Returning empty list when quadruplet exists
• Returning triplets instead of quadruplets