Four Sum Problem All Unique Quadruplets in DSA Go - 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 groups of four product prices that sum to the gift card amount.

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

📋 What You'll Learn

Create a slice 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

Write a function called fourSum that takes nums and target as parameters and returns a slice of slices of integers containing all unique quadruplets that sum to target

Print the result of calling fourSum(nums, target)

💡 Why This Matters

🌍 Real World

Finding combinations of items that meet a specific sum is useful in shopping apps, budgeting tools, and financial planning software.

💼 Career

This problem teaches skills in array manipulation, sorting, and two-pointer techniques, which are common in coding interviews and real-world software development.

1

Create the initial slice of integers

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

DSA Go

nums := []int{1, 0, -1, 0, -2, 2} // Your code here

Hint

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

2

Set the target sum value

Create an integer variable called target and set it to 0

DSA Go

package main

func main() {
    nums := []int{1, 0, -1, 0, -2, 2}
    target := 0 // Your code here
}

Hint

Use target := 0 to set the target sum.

3

Implement the fourSum function

Write a function called fourSum that takes nums []int and target int as parameters and returns [][]int. The function should find all unique quadruplets in nums that sum to target. Use sorting and two-pointer technique inside nested loops to find quadruplets without duplicates.

DSA Go

package main

import "fmt"
import "sort"

func main() {
    nums := []int{1, 0, -1, 0, -2, 2}
    target := 0
}

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

Hint

Sort the slice 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 fourSum

Print the result of calling fourSum(nums, target) using fmt.Println

DSA Go

package main

import (
    "fmt"
    "sort"
)

func fourSum(nums []int, target int) [][]int {
    sort.Ints(nums)
    var result [][]int
    n := len(nums)
    for i := 0; i  0 && nums[i] == nums[i-1] {
            continue
        }
        for j := i + 1; j  i+1 && nums[j] == nums[j-1] {
                continue
            }
            left, right := j+1, n-1
            for left < right {
                sum := nums[i] + nums[j] + nums[left] + nums[right]
                if sum == target {
                    quadruplet := []int{nums[i], nums[j], nums[left], nums[right]}
                    result = append(result, quadruplet)
                    left++
                    right--
                    for left < right && nums[left] == nums[left-1] {
                        left++
                    }
                    for left < right && nums[right] == nums[right+1] {
                        right--
                    }
                } else if sum < target {
                    left++
                } else {
                    right--
                }
            }
        }
    }
    return result
}

func main() {
    nums := []int{1, 0, -1, 0, -2, 2}
    target := 0
    fmt.Println(fourSum(nums, target)) // Your code here
}

Hint

Use fmt.Println(fourSum(nums, target)) to print the result.

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: Identify the goal

   The goal is not sorting or counting pairs but to find quadruplets that sum to the target without duplicates.

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 summing to target [OK]

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

Common Mistakes:

• Confusing with two or three sum problems
• Trying to sort only without finding quadruplets
• Counting pairs instead of quadruplets

2. Which of the following Go code snippets correctly initializes a slice to store quadruplets for the Four Sum problem?

easy

A. quadruplets := [][]int{}

B. quadruplets := [4]int{}

C. quadruplets := make([]int, 4)

D. quadruplets := map[int]int{}

Solution

1. Step 1: Understand data structure for quadruplets

   We need a slice of slices of integers to store multiple quadruplets, each quadruplet is a slice of 4 ints.

2. Step 2: Choose correct initialization

   quadruplets := [][]int{} initializes an empty slice of int slices, suitable for storing multiple quadruplets. quadruplets := [4]int{} is a fixed array of 4 ints, not multiple quadruplets. quadruplets := make([]int, 4) is a slice of 4 ints, not a slice of quadruplets. quadruplets := map[int]int{} is a map, not suitable here.

3. Final Answer:

   quadruplets := [][]int{} -> Option A

4. Quick Check:

   Slice of int slices = [][]int{} [OK]

Hint: Use [][]int{} for list of quadruplets [OK]

Common Mistakes:

• Using fixed arrays instead of slices
• Using map instead of slice
• Initializing slice with wrong dimensions

3. What will be the output of the following Go code snippet that finds unique quadruplets summing to 0?

nums := []int{1, 0, -1, 0, -2, 2}
target := 0
result := fourSum(nums, target)
fmt.Println(result)

// Assume fourSum is correctly implemented

medium

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

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

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

D. []

Solution

1. Step 1: Understand input and target

   The input array is [1, 0, -1, 0, -2, 2] and target sum is 0.

2. Step 2: Identify unique quadruplets summing to 0

   Possible unique quadruplets are [-2, -1, 1, 2], [-2, 0, 0, 2], and [-1, 0, 0, 1]. These sum exactly to 0 and are unique.

3. Final Answer:

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

4. Quick Check:

   Sum quadruplets = 0 [OK]

Hint: Sort array and find quadruplets summing to target [OK]

Common Mistakes:

• Including duplicate quadruplets
• Incorrect sums in quadruplets
• Missing some valid quadruplets

4. Given the following Go code snippet for the Four Sum problem, what is the main bug causing incorrect results?

func fourSum(nums []int, target int) [][]int {
    sort.Ints(nums)
    var res [][]int
    for i := 0; i < len(nums)-3; i++ {
        for j := i + 1; j < len(nums)-2; j++ {
            left, right := j+1, len(nums)-1
            for left < right {
                sum := nums[i] + nums[j] + nums[left] + nums[right]
                if sum == target {
                    res = append(res, []int{nums[i], nums[j], nums[left], nums[right]})
                    left++
                    right--
                } else if sum < target {
                    left++
                } else {
                    right--
                }
            }
        }
    }
    return res
}

medium

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

B. Incorrect sorting of the input array

C. Wrong initialization of left and right pointers

D. Using append incorrectly causing runtime error

Solution

1. Step 1: Analyze duplicate handling

   The code finds quadruplets but does not skip duplicates after finding a valid quadruplet, so duplicates appear in the result.

2. Step 2: Check other parts

   Sorting is correct, pointers are correctly initialized, and append usage is valid.

3. Final Answer:

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

4. Quick Check:

   Missing duplicate skip = duplicates in output [OK]

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

Common Mistakes:

• Not skipping duplicates for i, j, left, right
• Incorrect pointer updates after finding quadruplet
• Assuming sorting alone removes duplicates

5. You want to optimize the Four Sum solution to avoid unnecessary computations. Which approach best reduces the search space while ensuring all unique quadruplets are found?

hard

A. Sort the array and use two nested loops with two pointers, skipping duplicates at each step

B. Use four nested loops to check all quadruplets without sorting

C. Sort the array and use a hash map to store sums of pairs, then find complements

D. Use recursion without sorting or duplicate checks

Solution

1. Step 1: Understand optimization goals

   We want to reduce time complexity and avoid duplicates efficiently.

2. Step 2: Evaluate approaches

   Sort the array and use two nested loops with two pointers, skipping duplicates at each step is common but still O(n^3). Use four nested loops to check all quadruplets without sorting is brute force O(n^4). Sort the array and use a hash map to store sums of pairs, then find complements uses a hash map to store pair sums and find complements, reducing complexity and handling duplicates well. Use recursion without sorting or duplicate checks is inefficient without sorting or duplicate checks.

3. Final Answer:

   Sort the array and use a hash map to store sums of pairs, then find complements -> Option C

4. Quick Check:

   Hash map pairs + complements = optimized search [OK]

Hint: Use hash map of pair sums to find quadruplets faster [OK]

Common Mistakes:

• Using brute force four loops
• Ignoring duplicate skipping
• Not sorting before processing