Why Three Sum Problem All Unique Triplets in DSA Go?

The Big Idea

What if you could find all zero-sum triplets in seconds instead of hours of guesswork?

The Scenario

Imagine you have a list of numbers and you want to find all groups of three numbers that add up to zero. Doing this by hand means checking every possible group of three numbers, which is like trying to find friends who together have exactly zero dollars in their pockets. It's tiring and confusing!

The Problem

Manually checking every combination is very slow because the number of groups grows very fast as the list gets bigger. It's easy to miss some groups or count the same group more than once. This makes the task frustrating and error-prone.

The Solution

The Three Sum Problem solution uses a smart way to sort the numbers first and then uses two pointers to find pairs that complete the triplet to zero. This method quickly skips duplicates and avoids checking every group, making the process much faster and easier.

Before vs After

✗ Before

for i := 0; i < len(nums); i++ {
  for j := i+1; j < len(nums); j++ {
    for k := j+1; k < len(nums); k++ {
      if nums[i]+nums[j]+nums[k] == 0 {
        // print triplet
      }
    }
  }
}

✓ After

sort.Ints(nums)
for i := 0; i < len(nums)-2; i++ {
  if i > 0 && nums[i] == nums[i-1] { continue }
  left, right := i+1, len(nums)-1
  for left < right {
    sum := nums[i] + nums[left] + nums[right]
    if sum == 0 {
      // add triplet
      left++
      right--
      for left < right && nums[left] == nums[left-1] {
        left++
      }
      for left < right && nums[right] == nums[right+1] {
        right--
      }
    } else if sum < 0 {
      left++
    } else {
      right--
    }
  }
}

What It Enables

This approach lets you quickly find all unique groups of three numbers that add up to zero, even in large lists, without missing or repeating any.

Real Life Example

Think of a budget planner who wants to find three expenses that cancel each other out to zero, helping to identify balancing transactions easily.

Key Takeaways

Manual checking is slow and error-prone.

Sorting and two-pointer technique speeds up the search.

Duplicates are skipped to ensure unique triplets.

Practice

1. What is the main goal of the Three Sum Problem All Unique Triplets in data structures and algorithms?

easy

A. Count the number of pairs that sum to a target

B. Find all unique triplets in an array that sum to zero

C. Find the maximum element in the array

D. Sort the array in ascending order

Solution

1. Step 1: Understand the problem statement

   The problem asks to find all unique groups of three numbers in an array whose sum is zero.

2. Step 2: Identify the goal

   The goal is to find triplets (three numbers) that add up to zero without duplicates.

3. Final Answer:

   Find all unique triplets in an array that sum to zero -> Option B

4. Quick Check:

   Three Sum Problem = Find unique triplets summing to zero [OK]

Hint: Look for three numbers adding to zero without repeats [OK]

Common Mistakes:

• Confusing with pair sum problems
• Ignoring uniqueness of triplets
• Trying to find max or min instead of sum

2. Which of the following Go code snippets correctly initializes a slice of integers for solving the Three Sum problem?

easy

A. nums := []int{1, -1, 0, 2, -2}

B. nums := [1, -1, 0, 2, -2]

C. nums := (1, -1, 0, 2, -2)

D. nums := {1, -1, 0, 2, -2}

Solution

1. Step 1: Recall Go slice initialization syntax

   In Go, slices are initialized with square brackets and type, e.g., []int{...}.

2. Step 2: Check each option

   nums := []int{1, -1, 0, 2, -2} uses correct syntax: nums := []int{1, -1, 0, 2, -2}. Others use invalid syntax.

3. Final Answer:

   nums := []int{1, -1, 0, 2, -2} -> Option A

4. Quick Check:

   Go slice syntax = []int{...} [OK]

Hint: Use []int{...} to declare integer slices in Go [OK]

Common Mistakes:

• Using parentheses or braces instead of curly braces
• Missing type declaration []int
• Using array literal syntax without type

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

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

fmt.Println(threeSum([]int{-1, 0, 1, 2, -1, -4}))

medium

A. [[-4, 2, 2], [-1, 0, 1]]

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

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

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

Solution

1. Step 1: Sort and iterate through the array

   The sorted array is [-4, -1, -1, 0, 1, 2]. The code skips duplicates and uses two pointers to find triplets summing to zero.

2. Step 2: Identify unique triplets summing to zero

   Triplets found are [-1, -1, 2] and [-1, 0, 1]. These are appended to the result.

3. Final Answer:

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

4. Quick Check:

   Unique triplets summing zero = [[-1,-1,2],[-1,0,1]] [OK]

Hint: Sort array, use two pointers to find zero sum triplets [OK]

Common Mistakes:

• Not sorting array before processing
• Not skipping duplicates causing repeated triplets
• Incorrect pointer movement logic

4. Identify the bug in the following Go code snippet for the Three Sum problem:

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

medium

A. Returning res before the loop ends

B. Incorrect initialization of left and right pointers

C. Using sort.Ints instead of sort.Sort

D. Missing check to skip duplicate elements for i, left, and right

Solution

1. Step 1: Analyze duplicate handling

   The code does not skip duplicate values for i, left, or right, which can cause duplicate triplets in the result.

2. Step 2: Confirm other parts are correct

   Initialization of pointers and sorting are correct. The return statement is after loops, so no premature return.

3. Final Answer:

   Missing check to skip duplicate elements for i, left, and right -> Option D

4. Quick Check:

   Skipping duplicates is essential to avoid repeated triplets [OK]

Hint: Always skip duplicates to ensure unique triplets [OK]

Common Mistakes:

• Not skipping duplicates causing repeated triplets
• Incorrect pointer updates after finding a triplet
• Sorting with wrong function

5. Given the input array nums := []int{-2, 0, 1, 2, -1, -1, 3}, which of the following is the correct set of all unique triplets that sum to zero?

hard

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

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

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

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

Solution

1. Step 1: Sort the array and find triplets

   Sorted array: [-2, -1, -1, 0, 1, 2, 3]. Find unique triplets summing to zero by two-pointer method.

2. Step 2: Identify all unique triplets

   Triplets are [-2, -1, 3], [-2, 0, 2], [-1, -1, 2], and [-1, 0, 1]. These cover all unique zero sums.

3. Final Answer:

   [[-2, -1, 3], [-2, 0, 2], [-1, -1, 2], [-1, 0, 1]] -> Option A

4. Quick Check:

   All unique triplets summing zero = [[-2, -1, 3], [-2, 0, 2], [-1, -1, 2], [-1, 0, 1]] [OK]

Hint: Sort array, then find triplets with two pointers skipping duplicates [OK]

Common Mistakes:

• Missing some triplets due to not skipping duplicates
• Including triplets with repeated elements incorrectly
• Not sorting array before processing