Why Four Sum Problem All Unique Quadruplets in DSA Rust?

The Big Idea

What if you could find all groups of four numbers adding to a target without checking every single combination by hand?

The Scenario

Imagine you have a big box of numbered cards and you want to find all groups of four cards that add up to a special number. Doing this by checking every possible group by hand would take forever!

The Problem

Manually checking every group of four cards means trying many combinations, which is very slow and easy to mess up. It's like trying to find four friends in a crowd who together have a certain total height by guessing every possible group.

The Solution

The Four Sum problem uses a smart way to quickly find all unique groups of four numbers that add up to the target. It avoids repeating groups and skips unnecessary checks, saving a lot of time and effort.

Before vs After

✗ Before

for i in 0..n {
  for j in i+1..n {
    for k in j+1..n {
      for l in k+1..n {
        if nums[i] + nums[j] + nums[k] + nums[l] == target {
          print quadruplet
        }
      }
    }
  }
}

✓ After

nums.sort();
for i in 0..n {
  if i > 0 && nums[i] == nums[i-1] { continue; }
  for j in i+1..n {
    if j > i+1 && nums[j] == nums[j-1] { continue; }
    let mut left = j+1;
    let mut right = n-1;
    while left < right {
      let sum = nums[i] + nums[j] + nums[left] + nums[right];
      if sum == target {
        print quadruplet;
        // skip duplicates
        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 < target {
        left += 1;
      } else {
        right -= 1;
      }
    }
  }
}

What It Enables

This method lets you quickly find all unique sets of four numbers that add up to a target, even in large lists, without wasting time on repeated or impossible groups.

Real Life Example

Suppose you want to find four ingredients from a list that together reach a specific calorie count for a recipe. This approach helps find all such combinations efficiently.

Key Takeaways

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

Sorting and using two pointers speeds up the search and avoids duplicates.

This technique finds all unique quadruplets summing to the target efficiently.

Practice

1. What is the main goal of the Four Sum Problem in data structures and algorithms?

easy

A. Count the number of pairs with a given sum

B. Find all unique quadruplets in an array that sum up to a target value

C. Find the maximum element in the array

D. Sort the array in ascending order

Solution

1. Step 1: Understand the problem statement

   The Four Sum Problem asks to find all unique groups of four numbers (quadruplets) 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 specifically finding quadruplets whose sum equals the target.

3. Final Answer:

   Find all unique quadruplets in an array that sum up to a target value -> Option B

4. Quick Check:

   Four Sum Problem = Find quadruplets with target sum [OK]

Hint: Look for four numbers adding to target, not sorting or counting [OK]

Common Mistakes:

• Confusing Four Sum with sorting problems
• Looking for pairs instead of quadruplets
• Ignoring uniqueness of quadruplets

2. Which Rust syntax correctly declares a vector of integers named nums?

easy

A. let nums = {1, 2, 3, 4};

B. let nums = [1, 2, 3, 4];

C. let nums = (1, 2, 3, 4);

D. let nums = vec![1, 2, 3, 4];

Solution

1. Step 1: Identify Rust vector syntax

   In Rust, vectors are created using vec![elements] macro, which creates a growable array.

2. Step 2: Check each option

   let nums = vec![1, 2, 3, 4]; uses vec![1, 2, 3, 4] which is correct. let nums = [1, 2, 3, 4]; is an array, not a vector. let nums = (1, 2, 3, 4); is a tuple. let nums = {1, 2, 3, 4}; is invalid syntax.

3. Final Answer:

   let nums = vec![1, 2, 3, 4]; -> Option D

4. Quick Check:

   Vector syntax = vec![...] [OK]

Hint: Use vec! macro for vectors, arrays use brackets only [OK]

Common Mistakes:

• Using array syntax when vector is needed
• Confusing tuples with vectors
• Using curly braces which are invalid here

3. What is the output of the following Rust code snippet that finds quadruplets summing to 0?

let nums = vec![1, 0, -1, 0, -2, 2];
let target = 0;
// Assume function four_sum returns Vec of quadruplets
let result = four_sum(nums, target);
println!("{:?}", result);

Assuming four_sum is correctly implemented, what is the printed output?

medium

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

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

C. [[0, 0, 0, 0]]

D. []

Solution

1. Step 1: Understand the input and target

   The input array is [1, 0, -1, 0, -2, 2] and target sum is 0. We want all unique quadruplets that sum to 0.

2. Step 2: Identify all quadruplets summing to 0

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

3. Final Answer:

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

4. Quick Check:

   Quadruplets sum to 0 = [[-2, -1, 1, 2], [-2, 0, 0, 2], [-1, 0, 0, 1]] [OK]

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

Common Mistakes:

• Returning incomplete quadruplets
• Ignoring duplicates
• Returning empty list incorrectly

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

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

What is the main issue causing duplicate quadruplets in the result?

medium

A. The vector nums is not sorted before processing

B. The while loop condition left < right is incorrect and should be left <= right

C. The code does not skip duplicate values for i, j, left, and right indices after finding a quadruplet

D. The function does not return the result vector

Solution

1. Step 1: Analyze duplicate handling in loops

   The code finds quadruplets but does not skip over duplicate values for indices i, j, left, and right after adding a quadruplet, causing duplicates in the result.

2. Step 2: Check other options

   The vector is sorted correctly, the while loop condition is correct, and the function returns the result vector properly.

3. Final Answer:

   The code does not skip duplicate values for i, j, left, and right indices after finding a quadruplet -> Option C

4. Quick Check:

   Skipping duplicates needed to avoid repeated quadruplets [OK]

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

Common Mistakes:

• Not skipping duplicates for all pointers
• Changing loop conditions incorrectly
• Forgetting to sort the array

5. Given the array nums = [2, 2, 2, 2, 2] and target 8, what is the correct output of a Four Sum function that returns all unique quadruplets summing to the target?

hard

A. [[2, 2, 2, 2]]

B. [[2, 2, 2, 2], [2, 2, 2, 2]]

C. []

D. [[2, 2, 2]]

Solution

1. Step 1: Understand the input and target

   The array contains five 2's and the target sum is 8. We need quadruplets of four numbers summing to 8.

2. Step 2: Identify unique quadruplets

   Only one unique quadruplet exists: [2, 2, 2, 2]. Although multiple combinations exist, duplicates must be avoided.

3. Final Answer:

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

4. Quick Check:

   Unique quadruplet summing to 8 = [[2, 2, 2, 2]] [OK]

Hint: Avoid duplicates; only one quadruplet of identical numbers [OK]

Common Mistakes:

• Returning duplicate quadruplets multiple times
• Returning empty list incorrectly
• Returning triples instead of quadruplets