This code implements a **ternary search** algorithm to search for...

This code implements a ternary search algorithm to search for a given element x in a sorted array ar. Here's a step-by-step explanation of what this code does:

1. Input Parameters:

   • l: The starting index of the array subrange to search.
   • r: The ending index of the array subrange to search.
   • x: The value to search for in the array ar.

2. Base Case:

   • If r >= l, the function proceeds with the search.
   • If the base case fails (r < l), it means the value x is not found in the array, and the function returns -1.

3. Divide the Search Space:

   • The array segment [l, r] is divided into three parts using two middle indices:
     • mid1 = l + (r-l)/3: The first dividing point (approximately 1/3rd of the current range).
     • mid2 = r - (r-l)/3: The second dividing point (approximately 2/3rd of the current range).

4. Compare the Target Value x:

   • If ar[mid1] == x, return mid1 (found at the first third).
   • If ar[mid2] == x, return mid2 (found at the second third).

5. Recursive Search:

   • If x is smaller than ar[mid1], search in the leftmost third: [l, mid1-1].
   • If x is greater than ar[mid2], search in the rightmost third: [mid2+1, r].
   • Otherwise, search in the middle segment: [mid1+1, mid2-1].

6. Return -1 if x is Not Found:

   • If the range becomes invalid (when l > r), return -1, indicating that x does not exist in the array.

Summary:

• This function performs a ternary search, which is a divide-and-conquer algorithm similar to binary search.
• Unlike binary search, it divides the array into three parts instead of two, which may result in fewer recursive steps depending on the situation.
• The input array ar must be sorted for this algorithm to work correctly.
• If x is found, the function returns its index. If not, it returns -1.