Ternary search is a decrease(by constant) and conquer algorithm that can be used to find an element in an array. It is similar to binary search where we divide the array into two parts but in this algorithm, we divide the given array into three parts and determine which has the key (searched element). We can divide the array into three parts by taking mid1 and mid2 which can be calculated as shown below. Initially, l and r will be equal to 0 and n-1 respectively, where n is the length of the array.

It is same as the binary search. The only difference is that, it reduces the time complexity a bit more. Its time complexity is O(log n base 3) and that of binary search is O(log n base 2).

mid1 = l + (r-l)/3 mid2 = r – (r-l)/3

Note: Array needs to be sorted to perform ternary search on it.

Steps to perform Ternary Search:

First, we compare the key with the element at mid1. If found equal, we return mid1. If not, then we compare the key with the element at mid2. If found equal, we return mid2. If not, then we check whether the key is less than the element at mid1. If yes, then recur to the first part. If not, then we check whether the key is greater than the element at mid2. If yes, then recur to the third part. If not, then we recur to the second (middle) part.

Recursive Approach of Ternary Search

Ternary Search Recursive - Java Implementation

Ternary Search Recursive - Python Implementation

Time Complexity: O(log3n) Auxiliary Space: O(log3n)

Iterative Approach of Ternary Search

Ternary Search Iterative - Java Implementation

Ternary Search Iterative - Python Implementation

Time Complexity: O(log3n), where n is the size of the array.

Auxiliary Space: O(1)

Binary search Vs Ternary Search

The time complexity of the binary search is more than the ternary search but it does not mean that ternary search is better. In reality, the number of comparisons in ternary search much more which makes it slower than binary search.