Three Sum Problem All Unique Triplets in DSA C - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main goal of the Three Sum Problem?

To find all unique triplets in an array that sum up to zero.

beginner

Why do we sort the array before solving the Three Sum Problem?

Sorting helps to avoid duplicates easily and allows using two pointers to find pairs efficiently.

intermediate

Explain the two-pointer technique used in the Three Sum Problem.

After fixing one element, use two pointers starting from the next element and the end of the array to find pairs that sum with the fixed element to zero.

intermediate

How do you avoid duplicate triplets in the Three Sum Problem?

Skip duplicate elements when moving the fixed pointer and also skip duplicates when moving the two pointers.

intermediate

What is the time complexity of the optimal Three Sum solution?

O(n^2), where n is the number of elements in the array.

What is the first step in solving the Three Sum Problem?

A Use a hash map

B Reverse the array

C Sort the array

D Find the maximum element

Sorting the array helps in efficiently finding triplets and avoiding duplicates.

In the two-pointer approach, after fixing one element, where do the two pointers start?

A Both at the start of the array

B One just after the fixed element, one at the end of the array

C Both at the end of the array

D Random positions

One pointer starts just after the fixed element, and the other starts at the end to find pairs summing to the target.

How do you handle duplicates when the fixed element is the same as the previous one?

A Skip it to avoid duplicate triplets

B Include it anyway

C Double the count

D Remove all duplicates from the array

Skipping duplicates prevents repeated triplets in the result.

What is the sum target for the pairs when the fixed element is nums[i]?

A nums[i]

B 0

C nums[i] * 2

D -nums[i]

The pairs must sum to the negative of the fixed element to make the total zero.

What is the overall time complexity of the optimal Three Sum solution?

A O(n^2)

B O(n log n)

C O(n^3)

D O(n)

The solution uses sorting (O(n log n)) and a nested loop with two pointers (O(n^2)), so overall O(n^2).

Describe the step-by-step approach to solve the Three Sum Problem with unique triplets.

Think about sorting, fixing one number, and two-pointer search.

Explain how to avoid duplicate triplets in the Three Sum Problem solution.

Duplicates appear when same numbers are repeated; skipping them avoids repeated triplets.

Practice

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

easy

A. Find the maximum sum of any three elements

B. Sort the array in ascending order

C. Count the number of pairs that sum to zero

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

Solution

1. Step 1: Understand the problem statement

   The Three Sum Problem asks to find all unique sets of three numbers in an array whose sum is zero.

2. Step 2: Differentiate from other options

   Options A, B, and D describe different problems like maximum sum, sorting, or pairs, not triplets summing to zero.

3. Final Answer:

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

4. Quick Check:

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

Hint: Remember: Three Sum finds triplets with zero sum [OK]

Common Mistakes:

• Confusing with pair sum problems
• Thinking it finds maximum sums
• Assuming it sorts the array only

2. Which of the following code snippets correctly initializes the array for solving the Three Sum Problem in C?

easy

A. int nums[] = { -1, 0, 1, 2, -1, -4 }; int size = sizeof(nums) / sizeof(nums[0]);

B. int nums = { -1, 0, 1, 2, -1, -4 }; int size = 6;

C. int nums[] = (-1, 0, 1, 2, -1, -4); int size = 6;

D. int nums[] = [-1, 0, 1, 2, -1, -4]; int size = 6;

Solution

1. Step 1: Check array initialization syntax in C

   In C, arrays are initialized with curly braces {}, not parentheses or square brackets.

2. Step 2: Verify size calculation

   int nums[] = { -1, 0, 1, 2, -1, -4 }; int size = sizeof(nums) / sizeof(nums[0]); correctly calculates size using sizeof operator divided by element size.

3. Final Answer:

   int nums[] = { -1, 0, 1, 2, -1, -4 }; int size = sizeof(nums) / sizeof(nums[0]); -> Option A

4. Quick Check:

   C array init with {} and sizeof = int nums[] = { -1, 0, 1, 2, -1, -4 }; int size = sizeof(nums) / sizeof(nums[0]); [OK]

Hint: Use curly braces {} for arrays in C [OK]

Common Mistakes:

• Using parentheses () instead of braces {}
• Using square brackets [] for initialization
• Not calculating size correctly

3. What will be the output of the following C code snippet that attempts to find unique triplets summing to zero?

int nums[] = {-1, 0, 1, 2, -1, -4};
int size = 6;
// Assume function threeSum prints triplets
threeSum(nums, size);
// Output format: each triplet printed as (a, b, c)

medium

A. No triplets found

B. (-4, 2, 2)
(-1, 0, 1)

C. (-1, -1, 2)
(-1, 0, 1)

D. (0, 0, 0)
(-1, 1, 2)

Solution

1. Step 1: Identify triplets that sum to zero

   From the array {-1, 0, 1, 2, -1, -4}, the unique triplets summing to zero are (-1, -1, 2) and (-1, 0, 1).

2. Step 2: Verify output matches these triplets

   (-1, -1, 2) (-1, 0, 1) lists these exact triplets; other options include invalid or non-existent triplets.

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: Check sums of triplets carefully for zero [OK]

Common Mistakes:

• Including duplicates like (-4, 2, 2)
• Assuming zero triplets when some exist
• Mixing up triplet elements

4. Identify the bug in the following C code snippet for the Three Sum Problem:

void threeSum(int* nums, int size) {
    for (int i = 0; i < size - 2; i++) {
        for (int j = i + 1; j < size - 1; j++) {
            for (int k = j + 1; k < size; k++) {
                if (nums[i] + nums[j] + nums[k] == 0) {
                    printf("(%d, %d, %d)\n", nums[i], nums[j], nums[k]);
                }
            }
        }
    }
}

medium

A. Does not avoid printing duplicate triplets

B. Loops have incorrect ranges causing out-of-bounds access

C. Sum condition should be nums[i] * nums[j] * nums[k] == 0

D. Missing return statement in void function

Solution

1. Step 1: Analyze triplet printing logic

   The code prints any triplet summing to zero but does not check for duplicates, so duplicate triplets may print multiple times.

2. Step 2: Check loop ranges and conditions

   Loop ranges are correct and sum condition is correct; void functions do not require return statements.

3. Final Answer:

   Does not avoid printing duplicate triplets -> Option A

4. Quick Check:

   Duplicate triplets not filtered = Does not avoid printing duplicate triplets [OK]

Hint: Check if duplicates are filtered in nested loops [OK]

Common Mistakes:

• Confusing sum with product condition
• Thinking void needs return
• Assuming loops cause out-of-bounds

5. Given the array int nums[] = {0, 0, 0, 0}; and size 4, what is the correct output of a Three Sum solution that finds all unique triplets summing to zero?

hard

A. No triplets found

B. (0, 0, 0)

C. (0, 0, 0)
(0, 0, 0)

D. (0, 0, 0)
(0, 0, 0)
(0, 0, 0)

Solution

1. Step 1: Identify unique triplets summing to zero

   All elements are zero, so the only unique triplet is (0, 0, 0).

2. Step 2: Avoid duplicates in output

   Even though multiple combinations exist, only one unique triplet should be printed.

3. Final Answer:

   (0, 0, 0) -> Option B

4. Quick Check:

   Unique triplet from zeros = (0, 0, 0) [OK]

Hint: Only print unique triplets, even if duplicates exist [OK]

Common Mistakes:

• Printing duplicate triplets multiple times
• Assuming no triplets because all zeros
• Confusing triplet uniqueness