Four Sum Problem All Unique Quadruplets in DSA C++ - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main goal of the Four Sum problem?

To find all unique sets of four numbers in an array that add up to a given target sum.

beginner

Why do we sort the array before solving the Four Sum problem?

Sorting helps to efficiently skip duplicates and use two-pointer technique to find pairs that sum to a target.

intermediate

In the Four Sum problem, after fixing two numbers, how do we find the other two numbers?

We use two pointers starting from the ends of the remaining array segment and move them inward to find pairs that sum to the remaining target.

intermediate

How do we ensure the quadruplets are unique in the Four Sum problem?

By skipping duplicate values for each fixed number and for the two pointers during the search.

intermediate

What is the time complexity of the Four Sum problem solution using sorting and two pointers?

O(n^3), where n is the number of elements in the array.

What is the first step in solving the Four Sum problem efficiently?

A Use a hash map

B Sort the array

C Reverse the array

D Remove duplicates first

Sorting the array helps to skip duplicates and use two pointers effectively.

After fixing two numbers, which technique is used to find the remaining two numbers in Four Sum?

A Brute force

B Binary search

C Recursion

D Two pointers

Two pointers are used to find pairs that sum to the remaining target efficiently.

How do we avoid counting the same quadruplet multiple times?

A By sorting and skipping duplicates

B By using a hash set only

C By sorting only

D By using recursion

Sorting combined with skipping duplicates ensures unique quadruplets.

What is the overall time complexity of the Four Sum solution using sorting and two pointers?

A O(n^4)

B O(n^2)

C O(n^3)

D O(n log n)

The solution fixes two numbers and uses two pointers for the rest, resulting in O(n^3) complexity.

Which of these is NOT a step in the Four Sum algorithm?

A Use dynamic programming to store quadruplets

B Fix two numbers with loops

C Use two pointers for the remaining two numbers

D Sort the array

Dynamic programming is not used in the standard Four Sum solution.

Explain the step-by-step approach to solve the Four Sum problem with unique quadruplets.

Think about how sorting and two pointers help reduce complexity.

How does sorting help in avoiding duplicate quadruplets in the Four Sum problem?

Consider how sorted order groups duplicates together.

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