Find a triplet that sum to a given value in an array

Introduction

A fundamental data structure in the world of programming and problem-solving are arrays. They enable us to sequentially store many elements of the same type. Finding a triplet within an array that adds up to a specific value is one of many intriguing array-related coding problems. We will examine various strategies to effectively address this issue in this article.

Problem Statement Definition

The goal is to identify a triplet of array elements whose sum is the specified target value given an array of integers and a target sum.

Naive Approach

Using three nested loops is the simplest way to solve this issue. The array contains all feasible triplets, and we can iterate through them all to see if their sums match the desired value. Although this method works, it is incredibly inefficient for large arrays due to its O(n3) time complexity.

Hashing-Optimized Approach

Hashing is a technique we can use to increase efficiency. The plan is to fix one element while using a two-pointer approach to locate the other two elements. The frequency of the array's elements will be recorded in a hash table, and we'll iterate through the array to locate the triplet that meets the requirement.

The following are the steps for the optimised approach:

To keep track of the frequency of the array's elements, create an empty hash table.

For each iteration, go through the array's element 'a':

• Determine the balance, sum (sum = Target Sum - a).

Repeat the iteration process for each element 'b' in the array (but not 'a'):

• Determine the third remaining amount (third = sum - b).
• Verify that 'third' is not the same element as 'a' or 'b' and that it is present in the hash table.
• If the target value is found, we have a triplet (a, b, third) that adds up to it.
• This method is much more effective than the naive method in terms of efficiency, having a time complexity of O(n2).

Two-Pointer Approach with Optimised Approach

Using the two-pointers technique is another effective strategy. The array must be sorted for this method to function.

The two-pointers approach involves the following steps:

• Non-decreasing orderly sorting of the supplied array.
• Create two pointers with initial values of "left" at the start and "right" at the end of the array.
• Go through the array iteratively while 'left' 'right'
• Add the elements at "left," "right," and the final "third" element to get their sum.
• We identified a triplet if the sum is equal to the desired value.
• Increase "left" to explore larger elements if the sum is below the desired value.
• Reduce the 'right' to explore smaller elements if the sum exceeds the desired value.
• This method doesn't need additional space, has a time complexity of O(n2), and is not a hashing method.

The Best Method Is Sorting

The goal of this method is to locate the triplet in an array without taking up extra space by hashing. It is predicated on the idea of sorting the array before applying the two-pointers method.

The following are the steps for the sorting approach:

Non-decreasing orderly sorting of the supplied array.

For each iteration, go through the array's element 'a':

• 'Left' and 'Right' are two pointers that should be initialised. 'Left' points to the element that follows 'a,' and 'Right' points to the last element.

While "right" > "left":

• Find the total of the elements at "a," "left," and "right."
• We identified a triplet if the sum is equal to the desired value.
• Increase "left" to explore larger elements if the sum is below the desired value.
• Reduce the 'right' to explore smaller elements if the sum exceeds the desired value.
• This method has an O(n2) time complexity and produces an optimal result without taking up more space.

Applications in the Real World

Finding triplets in an array that add up to a specific value is a common issue in many different fields. Real-world examples of applications include:

• Finding groups of transactions that result in a particular financial outcome is the goal of financial analysis.
• Playing video games, where players must find combinations that satisfy specific requirements in order to complete challenges and puzzles.
• Data analysis is the process of looking for particular relationships or patterns within datasets.

Python code:

Output:

```Triplet found: [2, 3, 5]
```

The provided code defines a Python function called find_triplet that searches for a triplet of elements in a given array. The triplet's elements sum up to a specified target sum. If a triplet meeting this condition exists, the function returns the triplet; otherwise, it returns None.

The function sorts the input array in ascending order and then utilizes two pointers to efficiently search for the triplet. It iterates through the array, considering each element as a potential starting point. Within the loop, two pointers, left and right, are used to explore elements that could complete the triplet to reach the target sum. The pointers are adjusted based on whether the current sum is less than or greater than the target.