LeetCode 15 Solution: 3Sum

The “3Sum” problem, also known as LeetCode 15, is one of the most popular coding challenges in technical interviews. This problem requires finding unique triplets in an integer array where the sum of the three numbers is zero. While the concept may seem simple, achieving an efficient solution can be tricky, especially when working with larger arrays. In this post, we’ll dive deep into understanding the problem and provide a clear, efficient LeetCode 15 solution that can handle a wide range of inputs.

Problem Overview: What is the 3Sum Problem?

The 3Sum problem asks us to find all unique triplets in a given array, nums, where the sum of the three numbers is zero. For instance, given an array like [-1, 0, 1, 2, -1, -4], the output should be two triplets: [-1, -1, 2] and [-1, 0, 1].

It’s important to note that:

• We must avoid duplicate triplets. That means if the input contains repeated numbers, the output should not have duplicate results.
• The array may contain positive, negative, or zero values, and the solution must consider all possible triplet combinations.

Key Challenges and Constraints

The biggest challenge in solving the 3Sum problem is doing so efficiently. A naive approach would be to check every possible combination of triplets in the array, which would result in a time complexity of O(n³). This approach is too slow, especially given that the input array can have up to 3000 elements.

So, how can we solve this problem faster? By using a combination of sorting and a two-pointer technique, we can reduce the time complexity to O(n²), making the solution fast enough even for larger inputs.

Understanding the Efficient LeetCode 15 Solution

The trick to solving the 3Sum problem efficiently lies in using two main techniques: sorting the array and using two pointers to search for pairs of numbers. Let’s break down how this works.

1. Sorting the Array: First, we sort the array in non-decreasing order. Sorting helps us efficiently skip over duplicate numbers and use two pointers to search for pairs.

2. Using a Two-pointer Approach: For each number in the array, we treat it as the first element of the triplet and then use two pointers to find the other two numbers that sum to zero. One pointer starts just after the current number, and the other starts at the end of the array. By moving these pointers, we can quickly find pairs that sum up to the target value (zero minus the current number).

3. Handling Duplicates:After sorting the array, duplicate numbers can be skipped easily by comparing the current number with the previous one. This ensures that we don’t add the same triplet multiple times to the result.

   
   

The Python Code Implementation

Now, let’s look at the Python code that implements this approach for the LeetCode 15 solution:

def threeSum(nums):
    # Sort the array first
    nums.sort()
    result = []

    # Loop through the array, treating nums[i] as the target
    for i in range(len(nums) - 2):
        # Skip duplicate values for the target
        if i > 0 and nums[i] == nums[i - 1]:
            continue

        # Two-pointer approach to find the other two numbers
        left, right = i + 1, len(nums) - 1

        while left < right:
            current_sum = nums[i] + nums[left] + nums[right]

            if current_sum == 0:
                result.append([nums[i], nums[left], nums[right]])

                # Move both pointers and skip duplicates
                while left < right and nums[left] == nums[left + 1]:
                    left += 1
                while left < right and nums[right] == nums[right - 1]:
                    right -= 1

                left += 1
                right -= 1
            elif current_sum < 0:
                left += 1
            else:
                right -= 1

    return result

This code efficiently finds all unique triplets in the array that sum to zero. The two-pointer technique helps reduce unnecessary computations, and sorting helps handle duplicates gracefully.

Example Walkthrough

Let’s walk through an example to understand how the LeetCode 15 solution works:

Consider the input array: [-1, 0, 1, 2, -1, -4]. After sorting, the array becomes [-4, -1, -1, 0, 1, 2].

We then start looping through each element:

• For the first element, -4, we use two pointers: one at -1 (second element) and the other at 2 (last element). The sum of -4, -1, and 2 is -3, which is less than zero, so we move the left pointer to the next position.
• We repeat this process until we find a triplet that sums to zero. Eventually, we identify the valid triplets [-1, 0, 1] and [-1, -1, 2].

Handling Edge Cases in the 3Sum Problem

There are several important edge cases to consider when solving the 3Sum problem:

1. No triplets found: If the array contains no triplets that sum to zero, the result should be an empty list. For example, nums = [1, 2, 3] would return [].
2. Arrays containing zeros: If the array contains multiple zeros, the result may contain the triplet [0, 0, 0], as all three numbers sum to zero. For example, nums = [0, 0, 0] would return [[0, 0, 0]].
3. Duplicate numbers: To avoid duplicate triplets in the result, we carefully skip over repeated numbers both for the target number and in the two-pointer search.

Time and Space Complexity

The time complexity of the LeetCode 15 solution is O(n²), where n is the length of the input array. This is because we sort the array in O(n log n) time, and then for each element, we use the two-pointer approach which runs in O(n) time. Given that n can go up to 3000, this is a very efficient solution.

The space complexity is O(n) due to the space required for the result list and the sorting process.

Conclusion

In this post, we explored the 3Sum problem and how to efficiently solve it using sorting and a two-pointer technique. By understanding the problem’s constraints and avoiding duplicates, we can significantly improve the performance of our solution. The LeetCode 15 solution we’ve discussed runs in O(n²) time, making it a solid approach for larger input arrays.

If you’re preparing for coding interviews, mastering the 3Sum problem is a great way to sharpen your problem-solving skills, especially when it comes to array manipulation and efficient searching techniques.

Happy Coding!

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Looking for more LeetCode solutions? Stay tuned for upcoming guides on tackling other LeetCode challenges in Python. Whether you’re preparing for technical interviews or aiming to improve your coding skills, exploring a variety of problems will enhance your understanding and proficiency.

You can find this problem on LeedCode, click here.