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 amount. You want to find all unique sets of four product prices that sum exactly to the gift card value.

🎯 Goal: Build a C++ program that finds all unique quadruplets in a list of integers that sum to a target value.

📋 What You'll Learn

Create a vector of integers called nums with the exact values: {1, 0, -1, 0, -2, 2}

Create an integer variable called target and set it to 0

Implement a function called fourSum that takes nums and target and returns a vector of vectors of integers containing all unique quadruplets that sum to target

Print the resulting quadruplets in the format: [a, b, c, d] one per line

💡 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 in arrays is useful for software engineers working on recommendation systems, data analysis, and algorithm optimization.

1

Create the input vector nums

Create a vector of integers called nums with these exact values: {1, 0, -1, 0, -2, 2}

DSA C++

#include 
#include 

int main() {
    // Create vector nums with values {1, 0, -1, 0, -2, 2}
    // Your code here
}

Hint

Use std::vector<int> and initialize it with the given values inside curly braces.

2

Create the target integer variable target

Create an integer variable called target and set it to 0

DSA C++

#include 
#include 

int main() {
    std::vector nums = {1, 0, -1, 0, -2, 2};
    // Create int variable target and set it to 0
    // Your code here
}

Hint

Declare int target = 0; inside main().

3

Implement the fourSum function

Implement a function called fourSum that takes std::vector<int>& nums and int target and returns a std::vector<std::vector<int>> containing all unique quadruplets that sum to target. Use sorting and two-pointer technique inside nested loops.

DSA C++

#include 
#include 
#include 

std::vector> fourSum(std::vector& nums, int target) {
    // Implement fourSum function to find unique quadruplets
    // Your code here
}

int main() {
    std::vector nums = {1, 0, -1, 0, -2, 2};
    int target = 0;
}

Hint

Sort the vector 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 all unique quadruplets

Call the fourSum function with nums and target. Then print each quadruplet in the format [a, b, c, d] on its own line.

DSA C++

#include 
#include 
#include 

std::vector> fourSum(std::vector& nums, int target) {
    std::vector> result;
    int n = nums.size();
    if (n  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 = {1, 0, -1, 0, -2, 2};
    int target = 0;
    // Call fourSum and print results
    // Your code here
}

Hint

Call fourSum(nums, target) and store the result. Then use a for loop to print each quadruplet in the format [a, b, c, d].

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 with a given sum

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: Identify the goal

   The goal is to find quadruplets (groups of four numbers) that sum exactly to the target, without duplicates.

3. Final Answer:

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

4. Quick Check:

   Four Sum Problem = Find quadruplets summing to target [OK]

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

Common Mistakes:

• Confusing with pair or triplet sum problems
• Ignoring uniqueness of quadruplets
• Trying to sort only without finding quadruplets

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

easy

A. std::vector<int> quadruplets(4);

B. std::vector quadruplets;

C. std::vector<int> quadruplets = {4};

D. std::vector> quadruplets;

Solution

1. Step 1: Understand the data structure needed

   We need to store multiple quadruplets, each is a vector of 4 integers, so a vector of vector<int> is suitable.

2. Step 2: Check each option

   std::vector quadruplets; declares a vector of vector<int>, perfect for storing multiple quadruplets. std::vector<int> quadruplets(4); creates a single vector of size 4, not multiple quadruplets. std::vector<int> quadruplets = {4}; initializes a vector with one element 4, incorrect. std::vector> quadruplets; uses pairs, which store only two integers, not four.

3. Final Answer:

   std::vector quadruplets; -> Option B

4. Quick Check:

   Use vector of vector<int> for quadruplets [OK]

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

Common Mistakes:

• Using vector<int> for multiple quadruplets
• Using pairs instead of quadruplets
• Initializing vector with wrong size or values

3. What will be the output of the following C++ code snippet for input array {1, 0, -1, 0, -2, 2} and target 0?

std::vector<int> nums = {1, 0, -1, 0, -2, 2};
int target = 0;
// Assume fourSum function returns all unique quadruplets
auto result = fourSum(nums, target);
for (auto &quad : result) {
    for (int num : quad) std::cout << num << " ";
    std::cout << std::endl;
}

medium

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

B. [-2 -1 0 1]
[-1 0 0 2]

C. [-2 -2 1 3]
[-1 0 0 1]

D. No quadruplets found

Solution

1. Step 1: Sort the array and find quadruplets summing to target 0

   Sorted array: [-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 output matches quadruplets

   [-2 -1 1 2] [-2 0 0 2] [-1 0 0 1] lists exactly these three quadruplets. Options A, C, and D have incorrect quadruplets or sums.

3. Final Answer:

   [-2 -1 1 2] [-2 0 0 2] [-1 0 0 1] -> Option A

4. Quick Check:

   Unique quadruplets summing to 0 = [-2 -1 1 2] [-2 0 0 2] [-1 0 0 1] [OK]

Hint: Sort array first, then find quadruplets summing to target [OK]

Common Mistakes:

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

4. Identify the bug in the following C++ code snippet for the Four Sum Problem:

std::vector fourSum(std::vector<int>& nums, int target) {
    std::vector result;
    std::sort(nums.begin(), nums.end());
    for (int i = 0; i < nums.size(); ++i) {
        for (int j = i + 1; j < nums.size(); ++j) {
            int left = j + 1, right = nums.size() - 1;
            while (left < right) {
                int sum = nums[i] + nums[j] + nums[left] + nums[right];
                if (sum == target) {
                    result.push_back({nums[i], nums[j], nums[left], nums[right]});
                    ++left; --right;
                } else if (sum < target) {
                    ++left;
                } else {
                    --right;
                }
            }
        }
    }
    return result;
}

medium

A. Returns result before completing loops

B. Incorrect sorting of the input array

C. Wrong initialization of left and right pointers

D. Does not skip duplicate quadruplets, causing repeated results

Solution

1. Step 1: Analyze duplicate handling in loops

   The code does not skip duplicates for i, j, left, or right indices, so it can add the same quadruplet multiple times.

2. Step 2: Check other parts for errors

   Sorting is correct, left and right pointers are initialized properly, and return is after loops. So these are not bugs.

3. Final Answer:

   Does not skip duplicate quadruplets, causing repeated results -> Option D

4. Quick Check:

   Missing duplicate checks = Does not skip duplicate quadruplets, causing repeated results [OK]

Hint: Always skip duplicates after finding quadruplets [OK]

Common Mistakes:

• Not skipping duplicates for i, j, left, right
• Returning result too early
• Incorrect pointer initialization

5. Given an array nums = {2, 2, 2, 2, 2} and target 8, how many unique quadruplets does the Four Sum algorithm find, and what are they?

hard

A. 10 quadruplets: including duplicates

B. 5 quadruplets: all combinations of 2s

C. 1 quadruplet: [2, 2, 2, 2]

D. 0 quadruplets: no quadruplets sum to 8

Solution

1. Step 1: Understand the input and target

   All elements are 2, and target is 8. Sum of four 2s is 8, so quadruplet [2, 2, 2, 2] is valid.

2. Step 2: Consider uniqueness

   Even though multiple combinations exist, they are duplicates. The algorithm returns only one unique quadruplet.

3. Final Answer:

   1 quadruplet: [2, 2, 2, 2] -> Option C

4. Quick Check:

   All 2s sum to 8 once uniquely [OK]

Hint: Duplicates count as one unique quadruplet [OK]

Common Mistakes:

• Counting duplicate quadruplets multiple times
• Assuming no quadruplets because of repeated numbers
• Confusing number of combinations with unique quadruplets