Why Three Sum Problem All Unique Triplets in DSA Rust?

The Big Idea

What if you could find all special groups of three numbers in a huge list without checking every single combination?

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 checking every possible group by hand would take forever, especially if the list is long.

The Problem

Manually checking every combination means trying many groups again and again. This is slow and easy to make mistakes, like missing some groups or counting the same group twice.

The Solution

The Three Sum problem solution uses a smart way to sort the list and then move through it with two pointers. This method quickly finds all unique groups of three numbers that add up to zero without repeating or missing any.

Before vs After

✗ Before

for i in 0..n {
  for j in (i + 1usize)..n {
    for k in (j + 1usize)..n {
      if nums[i] + nums[j] + nums[k] == 0 {
        print_triplet(nums[i], nums[j], nums[k]);
      }
    }
  }
}

✓ After

nums.sort();
for i in 0..(n - 2usize) {
  if i > 0usize && nums[i] == nums[i - 1usize] {
    continue;
  }
  let mut left = i + 1usize;
  let mut right = n - 1usize;
  while left < right {
    let sum = nums[i] + nums[left] + nums[right];
    if sum == 0 {
      print_triplet(nums[i], nums[left], nums[right]);
      left += 1usize;
      right -= 1usize;
      while left < right && nums[left] == nums[left - 1usize] {
        left += 1usize;
      }
      while left < right && nums[right] == nums[right + 1usize] {
        right -= 1usize;
      }
    } else if sum < 0 {
      left += 1usize;
    } else {
      right -= 1usize;
    }
  }
}

What It Enables

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

Real Life Example

Think about finding three friends whose combined ages add up to a special number, like zero difference from a target age. This method helps find all such groups fast without checking every possible trio.

Key Takeaways

Manual checking of all triplets is slow and error-prone.

Sorting and two-pointer technique speeds up finding unique triplets.

This method avoids duplicates and works well on large lists.

Practice

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

easy

A. Find the maximum element in the array

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

C. Sort the array in ascending order

D. Count the number of pairs that sum to zero

Solution

1. Step 1: Understand the problem statement

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

2. Step 2: Clarify the output

   The output should be a list of triplets with no duplicates, each summing to zero.

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 duplicates [OK]

Common Mistakes:

• Confusing with pair sum problems
• Ignoring uniqueness of triplets
• Only finding one triplet instead of all

2. Which Rust code snippet correctly initializes a vector to solve the Three Sum problem?

easy

A. let nums = [1, -1, 0, 2, -2];

B. let nums = {1, -1, 0, 2, -2};

C. let nums = (1, -1, 0, 2, -2);

D. let nums = vec![1, -1, 0, 2, -2];

Solution

1. Step 1: Identify Rust vector syntax

   In Rust, vectors are created using vec![elements] syntax.

2. Step 2: Check each option

   let nums = vec![1, -1, 0, 2, -2]; uses vec![], which is correct. let nums = [1, -1, 0, 2, -2]; is an array, not a vector. let nums = (1, -1, 0, 2, -2); is a tuple. let nums = {1, -1, 0, 2, -2}; is invalid syntax.

3. Final Answer:

   let nums = vec![1, -1, 0, 2, -2]; -> Option D

4. Quick Check:

   Vector initialization uses vec! macro [OK]

Hint: Use vec![] to create vectors in Rust [OK]

Common Mistakes:

• Using array syntax instead of vector
• Using tuple instead of vector
• Invalid braces for initialization

3. What is the output of the following Rust code snippet that finds unique triplets summing to zero?

fn main() {
    let mut nums = vec![-1, 0, 1, 2, -1, -4];
    nums.sort();
    let mut result = Vec::new();
    for i in 0..nums.len() - 2 {
        if i > 0 && nums[i] == nums[i - 1] { continue; }
        let (mut left, mut right) = (i + 1, nums.len() - 1);
        while left < right {
            let sum = nums[i] + nums[left] + nums[right];
            if sum == 0 {
                result.push(vec![nums[i], nums[left], nums[right]]);
                while left < right && nums[left] == nums[left + 1] { left += 1; }
                while left < right && nums[right] == nums[right - 1] { right -= 1; }
                left += 1;
                right -= 1;
            } else if sum < 0 {
                left += 1;
            } else {
                right -= 1;
            }
        }
    }
    println!("{:?}", result);
}

medium

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

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

C. [[0, 0, 0]]

D. []

Solution

1. Step 1: Sort the array

   Sorted array is [-4, -1, -1, 0, 1, 2].

2. Step 2: Find triplets summing to zero

   Triplets found are [-1, -1, 2] and [-1, 0, 1].

3. Final Answer:

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

4. Quick Check:

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

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

Common Mistakes:

• Not sorting before two-pointer approach
• Including duplicate triplets
• Incorrect pointer movement

4. Identify the bug in this Rust code snippet for the Three Sum problem:

fn three_sum(nums: &mut Vec<i32>) -> Vec {
    nums.sort();
    let mut res = Vec::new();
    for i in 0..nums.len() {
        if i > 0 && nums[i] == nums[i - 1] { continue; }
        let (mut left, mut right) = (i + 1, nums.len() - 1);
        while left < right {
            let sum = nums[i] + nums[left] + nums[right];
            if sum == 0 {
                res.push(vec![nums[i], nums[left], nums[right]]);
                left += 1;
                right -= 1;
            } else if sum < 0 {
                left += 1;
            } else {
                right -= 1;
            }
        }
    }
    res
}

medium

A. Loop runs beyond valid range causing panic

B. Sorting is done after the loop

C. Missing duplicate skipping after finding a triplet

D. Using immutable vector instead of mutable

Solution

1. Step 1: Check duplicate handling after triplet found

   The code does not skip duplicates for left and right pointers after pushing a triplet.

2. Step 2: Understand impact

   Without skipping duplicates, duplicate triplets may be added to the result.

3. Final Answer:

   Missing duplicate skipping after finding a triplet -> Option C

4. Quick Check:

   Duplicate skipping after triplet push is required [OK]

Hint: Skip duplicates after adding triplet to avoid repeats [OK]

Common Mistakes:

• Not skipping duplicates for left and right pointers
• Incorrect loop range causing panic
• Sorting after loop instead of before

5. Given the input vector vec![0, 0, 0, 0], what is the correct output of a properly implemented Three Sum solution that finds all unique triplets summing to zero?

hard

A. [[0, 0, 0]]

B. [[0, 0, 0], [0, 0, 0]]

C. []

D. [[0, 0]]

Solution

1. Step 1: Analyze input with duplicates

   Input has four zeros, so multiple triplets of zeros exist but are duplicates.

2. Step 2: Unique triplets only

   The solution must return only one unique triplet [0, 0, 0].

3. Final Answer:

   [[0, 0, 0]] -> Option A

4. Quick Check:

   Only one unique zero triplet exists [OK]

Hint: Return unique triplets only, even if duplicates exist [OK]

Common Mistakes:

• Returning duplicate triplets multiple times
• Returning empty list incorrectly
• Returning pairs instead of triplets