Home Data Structures and Algorithms Working of Ternary Search

Working of Ternary Search

When to use Ternary Search:

Implementation:

The concept involves dividing the array into three equal segments and determining in which segment the key element is located. It works similarly to a binary search, with the distinction of reducing time complexity by dividing the array into three parts instead of two.

Below are the step-by-step explanation of working of Ternary Search:

  1. Initialization:
    • Set two pointers, left and right, initially pointing to the first and last elements of our search space.
  2. Divide the search space:
    • Calculate two midpoints, mid1 and mid2, dividing the current search space into three roughly equal parts:
    • mid1 = left + (right – left) / 3
    • mid2 = right – (right – left) / 3
    • The array is now effectively divided into [left, mid1], (mid1, mid2), and [mid2, right].
  3. Comparison with Target:.
    • If the target is equal to the element at mid1 or mid2, the search is successful, and the index is returned
    • If the target is less than the element at mid1, update the right pointer to mid1 – 1.
    • If the target is greater than the element at mid2, update the left pointer to mid2 + 1.
    • If the target is between the elements at mid1 and mid2, update the left pointer to mid1 + 1 and the right pointer to mid2 – 1.
  4. Repeat or Conclude:
    • Repeat the process with the reduced search space until the target is found or the search space becomes empty.
    • If the search space is empty and the target is not found, return a value indicating that the target is not present in the array.

Illustration:

Ternary Search

Ternary Search

Computer systems use different methods to find specific data. There are various search algorithms, each better suited for certain situations. For instance, a binary search divides information into two parts, while a ternary search does the same but into three equal parts. It’s worth noting that ternary search is only effective for sorted data. In this article, we’re going to uncover the secrets of Ternary Search – how it works, why it’s faster in some situations.

Table of Content

  • What is the Ternary Search?
  • When to use Ternary Search
  • Working of Ternary Search
  • Implementation of Ternary Search
  • Complexity Analysis of Ternary Search
  • Binary search Vs Ternary Search
  • Advantages
  • Disadvantages
  • Summary

Similar Reads

What is the Ternary Search?

Ternary search is a search algorithm that is used to find the position of a target value within a sorted array. It operates on the principle of dividing the array into three parts instead of two, as in binary search. The basic idea is to narrow down the search space by comparing the target value with elements at two points that divide the array into three equal parts....

When to use Ternary Search:

When you have a large ordered array or list and need to find the position of a specific value.When you need to find the maximum or minimum value of a function.When you need to find bitonic point in a bitonic sequence.When you have to evaluate a quadratic expression...

Working of Ternary Search:

The concept involves dividing the array into three equal segments and determining in which segment the key element is located. It works similarly to a binary search, with the distinction of reducing time complexity by dividing the array into three parts instead of two....

Implementation:

Below is the implementation of Ternary Search Approach:...

Complexity Analysis of Ternary Search:

Time Complexity:...

Binary search Vs Ternary Search:

The time complexity of the binary search is less than the ternary search as the number of comparisons in ternary search is much more than binary search. Binary Search is used to find the maxima/minima of monotonic functions where as Ternary Search is used to find the maxima/minima of unimodal functions....

Advantages:

Ternary search can find maxima/minima for unimodal functions, where binary search is not applicable.Ternary Search has a time complexity of O(2 * log3n), which is more efficient than linear search and comparable to binary search.Fits well with optimization problems....

Disadvantages:

Ternary Search is only applicable to ordered lists or arrays, and cannot be used on unordered or non-linear data sets.Ternary Search takes more time to find maxima/minima of monotonic functions as compared to Binary Search....

Summary:

Ternary Search is a divide-and-conquer algorithm that is used to find the position of a specific value in a given array or list.It works by dividing the array into three parts and recursively performing the search operation on the appropriate part until the desired element is found. The algorithm has a time complexity of O(2 * log3n) and is more efficient than a linear search, but less commonly used than other search algorithms like binary search. It’s important to note that the array to be searched must be sorted for Ternary Search to work correctly....

Tags:
#Algorithms #DSA #Searching #Sorting #Algorithms #Searching #Sorting

When to use Ternary Search:

Implementation:

Contact Us

Categories
Learn the most popular programming languages in the world.