What is the 3Sum Closest Problem in Tech Interviews?

The 3Sum Closest problem is a classic algorithmic question frequently encountered in technical interviews for software engineering positions. It challenges candidates to find a triplet of numbers within an array that is closest to a given target sum, and it has gained popularity due to its mathematical and coding implications.

The problem can be formally stated as follows: Given an array of integers nums and an integer target, you are tasked with finding three integers from nums such that the sum of these three integers is as close as possible to target. The output should be the sum of these three integers.

Understanding the Approach

A naive approach to solving this would involve using three nested loops to explore every possible triplet in the array, resulting in a time complexity of O(n^3). This method is inefficient, especially for large arrays.

A more efficient solution employs a combination of sorting and the two-pointer technique, bringing the time complexity down to O(n^2). Here's a breakdown of the approach:

1. Sort the Array: Start by sorting the input array. This will allow us to use the two-pointer technique effectively.
2. Iterate with a Fixed Point: For each number in the array (let's call it current), use it as the first number of the triplet.
3. Two-Pointer Technique: Set two pointers, one starting just after current (let's call it left) and the other at the end of the array (right).
4. Calculate and Compare Sums: Calculate the sum of the triplet (current, nums[left], nums[right]) and compare it with the target. If this sum is closer to the target than the previously recorded closest sum, update your closest sum.
5. Adjust Pointers: If the current sum is less than the target, move the left pointer to the right; if it's greater, move the right pointer to the left. This process continues until the left pointer meets the right.

Code Example

Here is a Python implementation of the 3Sum Closest problem:

PythonCopy code

Explanation of the Code

• The three_sum_closest function takes in a list of integers and an integer target.
• First, it sorts the input array. The sorting allows us to use the two-pointer technique efficiently.
• A loop runs through each element, initializing the two pointers, and it continues to calculate the current sum while adjusting the pointers based on comparisons with the target.
• The absolute difference between the current sum and the target controls updates, pursuing the closest sum throughout the process.

This method balances efficiency with clarity, making it a great approach to tackle the 3Sum Closest problem effectively during technical interviews. Understanding this fundamental algorithm equips candidates with the skills to approach similar problems in future challenges.