Complexity Analysis of Ternary Search

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....