Three Sum Problem All Unique Triplets in DSA C - Build from Scratch

Three Sum Problem All Unique Triplets

📖 Scenario: You are working on a financial app that analyzes daily stock price changes. You want to find all unique sets of three days where the total change sums to zero, indicating a balanced period.

🎯 Goal: Build a program that finds all unique triplets in an integer array that sum to zero.

📋 What You'll Learn

Create an integer array called nums with the exact values: -1, 0, 1, 2, -1, -4

Create an integer variable called numsSize and set it to the size of nums

Implement a function threeSum that takes nums and numsSize and prints all unique triplets that sum to zero

Print each triplet in the format: [a, b, c] on its own line

💡 Why This Matters

🌍 Real World

Finding balanced periods in stock price changes or financial data helps analysts detect stability or reversal points.

💼 Career

This problem is common in technical interviews and helps develop skills in sorting, two-pointer technique, and handling duplicates.

1

Create the input array

Create an integer array called nums with these exact values: -1, 0, 1, 2, -1, -4.

DSA C

# Your code here

Hint

Use curly braces to list the values inside the array.

2

Set the array size

Create an integer variable called numsSize and set it to the size of the nums array (6).

DSA C

int nums[] = {-1, 0, 1, 2, -1, -4};
# Your code here

Hint

Count the number of elements in nums and assign it to numsSize.

3

Implement the threeSum function

Implement a function called threeSum that takes nums and numsSize as parameters and prints all unique triplets that sum to zero. Use sorting and two-pointer technique inside the function.

DSA C

int nums[] = {-1, 0, 1, 2, -1, -4};
int numsSize = 6;

// Your code here

Hint

Sort the array first. Then use a for loop with two pointers to find triplets summing to zero. Skip duplicates.

4

Call threeSum and print results

Call the threeSum function with nums and numsSize to print all unique triplets that sum to zero.

DSA C

#include 
#include 

int compare(const void *a, const void *b) {
    return (*(int*)a - *(int*)b);
}

void threeSum(int* nums, int numsSize) {
    qsort(nums, numsSize, sizeof(int), compare);
    for (int i = 0; i  0 && nums[i] == nums[i - 1]) continue;
        int left = i + 1;
        int right = numsSize - 1;
        while (left < right) {
            int sum = nums[i] + nums[left] + nums[right];
            if (sum == 0) {
                printf("[%d, %d, %d]\n", nums[i], nums[left], nums[right]);
                while (left < right && nums[left] == nums[left + 1]) left++;
                while (left < right && nums[right] == nums[right - 1]) right--;
                left++;
                right--;
            } else if (sum < 0) {
                left++;
            } else {
                right--;
            }
        }
    }
}

int main() {
    int nums[] = {-1, 0, 1, 2, -1, -4};
    int numsSize = 6;
    // Your code here
}

Hint

Call threeSum(nums, numsSize); inside main to print the 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