Ternary search is a divide-and-conquer search algorithm that works on sorted arrays. It is similar to binary search, but it divides the array into three parts instead of two. This allows it to find the target element in O(log₃n) time, which is faster than binary search in some cases.

When to Use Ternary Search?

Ternary search is most useful when the array is sorted and the target element is likely to be near the middle of the array. This is because ternary search divides the array into three parts, so it can quickly narrow down the search to the part of the array where the target element is most likely to be found.

Here are some specific situations where ternary search can be used:

1. Finding the Peak or Valley in a Function

Ternary search is ideal for situations where we have a unimodal function and we need to find the highest or lowest point in that function. By repeatedly dividing the search space into three parts and discarding the unneeded parts based on the function values, ternary search efficiently converges to the maximum or minimum value.

2. Optimization Problems

In optimization problems where we need to find the maximum or minimum value of a function, ternary search can be a powerful tool. By applying ternary search on the function, we can quickly narrow down the search space to find the optimal solution.

3. Peak Finding in Arrays

Ternary search can also be used to find a peak element in an array. A peak element in an array is an element that is greater than or equal to its neighbors. By applying ternary search on the array, we can efficiently locate a peak element.

4. Finding a Threshold Value

In certain scenarios, we may need to find a threshold value in a dataset or a function. Ternary search can be employed to efficiently determine the threshold value by iteratively narrowing down the search space based on the threshold condition.

Advantages of Ternary Search:

The advantage of Ternary search are:

• Efficient for finding maximum or minimum in unimodal functions
• Useful for peak finding in arrays
• Effective in optimization problems
• Helps locate threshold values
• Provides a systematic way to narrow down search space

Disadvantages of Ternary Search:

Ternary search also has some disadvantages, including:

• Limited applicability to unimodal functions
• Slower convergence compared to binary search
• Increased complexity in implementation
• Not always guaranteeing the optimal solution
• Higher space complexity due to tracking three points