Ternary Search in C

When searching for a specific element in a sorted dataset, many programmers are familiar with binary search. Binary search efficiently narrows down the search space by dividing it into two halves repeatedly. But there’s another search algorithm that can be even more efficient in certain scenarios.

Ternary search is a searching algorithm that efficiently locates an element in a sorted dataset by dividing it into three parts, rather than two, as in binary search. This additional partitioning can lead to a faster search in some cases. While binary search reduces the search space by half in each iteration, ternary search narrows it down to two-thirds.

Prerequisites: C Loops, Arrays, Binary Search and Recursion

Working of Ternary Search

Ternary search is based on the divide-and-conquer strategy. It works as follows:

1. Divide the dataset into three parts.
2. Compare the target element with the elements at the two division points.
3. Depending on the comparisons, you can eliminate one-third of the dataset.
4. Repeat the process until you find the target element or exhaust the search space.

Let’s illustrate this with a simple example.

Consider a sorted array ‘arr’:

arr = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}

Suppose we want to find the index of the element 13 using ternary search. The algorithm proceeds as follows:

1. In each step, we divide the array into three parts and compare the middle elements.
2. Based on the comparison, we eliminated one-third of the dataset.
3. This process continues until we find the target element or determine it doesn’t exist in the dataset.

C Program for Ternary Search

Here’s a simple C code example to perform ternary search:

C

// C Program to illustrate Ternary Search
#include <stdio.h>

// Ternary search function
int ternarySearch(int arr[], int left, int right,
                  int target)
{
    // Check if the left boundary is less than or equal to
    // the right boundary
    if (left <= right) {
        // Calculate two midpoints dividing the current
        // subarray into three equal parts
        int mid1 = left + (right - left) / 3;
        int mid2 = right - (right - left) / 3;

        // Check if the target is equal to either of the
        // midpoints
        if (arr[mid1] == target)
            return mid1;
        if (arr[mid2] == target)
            return mid2;

        // If the target is less than the element at mid1,
        // search in the left third of the subarray
        if (target < arr[mid1])
            return ternarySearch(arr, left, mid1 - 1,
                                 target);
        // If the target is greater than the element at
        // mid2, search in the right third of the subarray
        else if (target > arr[mid2])
            return ternarySearch(arr, mid2 + 1, right,
                                 target);
        // If the target is in between mid1 and mid2,
        // search in the middle third of the subarray
        else
            return ternarySearch(arr, mid1 + 1, mid2 - 1,
                                 target);
    }
    // Element not found, return -1
    return -1;
}

int main()
{
    int arr[] = { 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 };
    int target = 13;
    int n = sizeof(arr) / sizeof(arr[0]);

    // Call the ternarySearch function to find the target
    // element
    int result = ternarySearch(arr, 0, n - 1, target);

    // Check if the result is not -1 (element found) and
    // print the index
    if (result != -1)
        printf("Element %d found at index %d\n", target,
               result);
    // If result is -1, the element was not found in the
    // array
    else
        printf("Element %d not found in the array\n",
               target);

    return 0;
}

Output

Element 13 found at index 6

Application and Benefits

Ternary search is particularly useful in scenarios where you have a large, sorted dataset, and you want to find an element efficiently. Here are some key benefits:

• Efficiency: Ternary search reduces the search space by one-third in each iteration, making it faster than Linear search. In some cases, It is faster than binary search, especially when the target element is closer to the beginning of the dataset.
• Simplicity: The algorithm is easy to understand and implement, making it accessible to programmers of all levels.
• Guaranteed Success: Ternary search guarantees success if the target element is present in the dataset. It continues until the search space is empty.