Four Sum Problem All Unique Quadruplets in DSA Python - 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 Python program that finds all unique quadruplets in a list of integers that sum up to a given target value.

📋 What You'll Learn

Create a list 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 function called four_sum that takes nums and target as parameters and returns a list of unique quadruplets that sum to target

Print the result of calling four_sum(nums, target)

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

1

Create the list of numbers

Create a list called nums with these exact values: [1, 0, -1, 0, -2, 2]

DSA Python

# Create the list nums with the given values
# Your code here

Hint

Use square brackets to create the list and separate numbers with commas.

2

Set the target sum

Create an integer variable called target and set it to 0

DSA Python

nums = [1, 0, -1, 0, -2, 2]
# Create the integer variable target and set it to 0
# Your code here

Hint

Use a simple assignment to create the variable.

3

Write the function to find unique quadruplets

Write a function called four_sum that takes nums and 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 Python

nums = [1, 0, -1, 0, -2, 2]
target = 0
# Define the function four_sum(nums, target) below
# Your code here

Hint

Sort the list first. Use two nested loops for the first two numbers, then use two pointers to find the other two numbers. Skip duplicates to avoid repeated quadruplets.

4

Print the result of the function

Print the result of calling four_sum(nums, target)

DSA Python

nums = [1, 0, -1, 0, -2, 2]
target = 0

def four_sum(nums, target):
    nums.sort()
    quadruplets = []
    n = len(nums)
    for i in range(n - 3):
        if i > 0 and nums[i] == nums[i - 1]:
            continue
        for j in range(i + 1, n - 2):
            if j > i + 1 and nums[j] == nums[j - 1]:
                continue
            left = j + 1
            right = n - 1
            while left < right:
                total = nums[i] + nums[j] + nums[left] + nums[right]
                if total == target:
                    quadruplets.append([nums[i], nums[j], nums[left], nums[right]])
                    left += 1
                    right -= 1
                    while left < right and nums[left] == nums[left - 1]:
                        left += 1
                    while left < right and nums[right] == nums[right + 1]:
                        right -= 1
                elif total < target:
                    left += 1
                else:
                    right -= 1
    return quadruplets

# Print the result of four_sum(nums, target)
# Your code here

Hint

Use print(four_sum(nums, target)) to show the result.

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 all unique sets of four numbers (quadruplets) in an array that add up to a given target sum.

2. Step 2: Identify the goal

   The goal is not sorting or counting pairs but to find quadruplets with a specific sum 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 = unique quadruplets summing to target [OK]

Hint: Look for four numbers adding to target, no duplicates [OK]

Common Mistakes:

• Confusing Four Sum with Two Sum or Three Sum problems
• Thinking the problem is about sorting or counting pairs
• Ignoring the uniqueness of quadruplets

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

easy

A. quadruplets = ()

B. quadruplets = []

C. quadruplets = {}

D. quadruplets = set()

Solution

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

   Quadruplets are multiple groups of four numbers, so a list is suitable to store them.

2. Step 2: Check the initialization syntax

   Using [] initializes an empty list, which is correct. Curly braces {} create a dictionary, parentheses () create a tuple, and set() creates a set which is unordered and not ideal here.

3. Final Answer:

   quadruplets = [] -> Option B

4. Quick Check:

   Empty list for quadruplets = [] [OK]

Hint: Use [] to store multiple quadruplets in a list [OK]

Common Mistakes:

• Using {} which creates a dictionary, not a list
• Using () which creates an immutable tuple
• Using set() which is unordered and may lose duplicates

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

nums = [1, 0, -1, 0, -2, 2]
target = 0
# After sorting
nums.sort()
quadruplets = []
for i in range(len(nums)-3):
    for j in range(i+1, len(nums)-2):
        left, right = j+1, len(nums)-1
        while left < right:
            total = nums[i] + nums[j] + nums[left] + nums[right]
            if total == target:
                quadruplets.append([nums[i], nums[j], nums[left], nums[right]])
                left += 1
                right -= 1
            elif total < target:
                left += 1
            else:
                right -= 1
print(quadruplets)

medium

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

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

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

D. []

Solution

1. Step 1: Sort the array and understand the loops

   Sorted nums = [-2, -1, 0, 0, 1, 2]. The nested loops and two-pointer approach check all quadruplets summing to target 0.

2. Step 2: Identify quadruplets that sum to zero

   Valid quadruplets are [-2, -1, 1, 2], [-2, 0, 0, 2], and [-1, 0, 0, 1]. These are appended to quadruplets list.

3. Final Answer:

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

4. Quick Check:

   Sum quadruplets = 0 matches output [OK]

Hint: Sort array, use two pointers inside nested loops [OK]

Common Mistakes:

• Not sorting the array before processing
• Missing some quadruplets due to pointer errors
• Appending duplicates without checks

4. Identify the bug in the following code snippet for the Four Sum problem and select the correct fix.

nums = [2, 2, 2, 2, 2]
target = 8
nums.sort()
quadruplets = []
for i in range(len(nums)-3):
    for j in range(i+1, len(nums)-2):
        left, right = j+1, len(nums)-1
        while left < right:
            total = nums[i] + nums[j] + nums[left] + nums[right]
            if total == target:
                quadruplets.append([nums[i], nums[j], nums[left], nums[right]])
                left += 1
                right -= 1
            elif total < target:
                left += 1
            else:
                right -= 1
print(quadruplets)

medium

A. Add checks to skip duplicates for i, j, left, and right indices

B. Change quadruplets to a set to avoid duplicates

C. Remove sorting to improve performance

D. Replace while loop with a for loop

Solution

1. Step 1: Identify the problem with duplicates

   The code appends quadruplets but does not skip duplicates, so it will add the same quadruplet multiple times.

2. Step 2: Fix by skipping duplicates

   Adding checks to skip duplicate values for i, j, left, and right indices after finding a quadruplet prevents repeated quadruplets.

3. Final Answer:

   Add checks to skip duplicates for i, j, left, and right indices -> Option A

4. Quick Check:

   Skipping duplicates avoids repeated quadruplets [OK]

Hint: Skip duplicates after finding quadruplets to avoid repeats [OK]

Common Mistakes:

• Not skipping duplicates causing repeated quadruplets
• Using set without sorting can cause unordered results
• Removing sorting breaks two-pointer logic

5. Given the array nums = [1, 0, -1, 0, -2, 2, 2] and target 2, which of the following lists contains all unique quadruplets that sum to the target?

hard

A. [[-2, -1, 2, 3], [0, 0, 1, 1]]

B. [[-2, 0, 1, 3], [-1, 0, 0, 3]]

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

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

Solution

1. Step 1: Sort the array and find quadruplets summing to 2

   Sorted nums = [-2, -1, 0, 0, 1, 2, 2]. We look for quadruplets where sum equals 2.

2. Step 2: Identify valid quadruplets

   Valid quadruplets are [-2, 0, 2, 2] (sum = 2) and [-1, 0, 1, 2] (sum = 2). Other options contain invalid or impossible sums.

3. Final Answer:

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

4. Quick Check:

   Sum quadruplets = 2 matches output [OK]

Hint: Sort and check quadruplets summing exactly to target [OK]

Common Mistakes:

• Including quadruplets with wrong sums
• Ignoring duplicates or invalid numbers
• Not sorting before searching quadruplets