C Program For Sentinel Linear Search

Sentinel Linear Search is basically a variation of the traditional linear search algorithm. It is designed to reduce the number of comparisons required to find a specific target value within an array or list. In this article, we will learn how to implement Sentinal Linear Search in C, see how it works, and compare its performance with traditional linear search.

What is Sentinel Linear Search?

In a typical linear search, you would check each element of an array one by one until you find the target value or reach the end. This means that in the worst-case scenario, you would make N comparisons, where N is the number of elements in the array.

However, Sentinel Linear Search uses an extra value to make the process faster. Instead of just searching through the array, it adds a special "sentinel" value at the end of the array. This sentinel value is set to be equal to the target value you're looking for.

It eliminates the need to check for boundary conditions during each iteration of the search loop in the traditional linear search as you would have to ensure that you don't go beyond the array's bounds when checking elements. With the sentinel in place, you're guaranteed that the index you're checking will always fall within the array's boundaries because the sentinel value is a valid element.

So, this sentinel value acts as a marker, thus making the search process more efficient. It doesn't change the worst-case time complexity, which is still O(n) like the regular linear search, but it significantly reduces the actual number of comparisons made in practice. This reduction in comparisons leads to improved performance, especially when dealing with large datasets.

Prerequisites: Before implementing Sentinel Linear Search in C, you should have a basic understanding of:

• C programming language fundamentals.
• Arrays in C.
• Basic knowledge of loops and conditionals.

Working of Sentinal Linear Search in C

Here's a step-by-step example to understand the working of Sentinel Linear Search.

Input

Array[] = [3, 5, 1, 8, 2]
Target =  8

Steps

1. Append the target element (8) at the end of the array as a sentinel. Array becomes: [3, 5, 1, 8, 2, 8]
2. Initialize a loop variable i to 0, representing the current index.
3. Compare the element at index 0 with the target element (8). No match (3 ≠ 8).
4. Increment the loop variable i to 1 and compare the element at index 1 with the target element (8). No match (5 ≠ 8).
5. Increment the loop variable i to 2 and compare the element at index 2 with the target element (8). No match (1 ≠ 8).
6. Increment the loop variable i to 3 and compare the element at index 3 with the target element (8). A match is found (8 = 8).
7. The search is successful, and the index (3) where the match was found is returned.

Output

The target element 8 is found at index 3 in the original array.

C Program for Sentinel Linear Search

Below is the implementation of the above approach:

// C program to implement sentinal linear search
#include <stdio.h>

int sentinelLinearSearch(int arr[], int size, int target)
{
    // Storing the last element in temporary variable
    int last = arr[size - 1];
    // Setting the sentinel to the target
    arr[size - 1] = target;

    int i = 0;
    while (arr[i] != target) {
        i++;
    }

    // Restore the original value at the end
    arr[size - 1] = last;

    // checking if last element is target or not
    if (i < size - 1 || arr[size - 1] == target) {
        return i; // Element found at index i
    }
    else {
        return -1; // Element not found
    }
}

// driver code
int main()
{
    int arr[] = { 3, 5, 1, 8, 2 };
    int size = sizeof(arr) / sizeof(arr[0]);
    int target = 8;

    int result = sentinelLinearSearch(arr, size, target);

    // printing result based on the value returned by
    // sentinalLinearSearch
    if (result != -1) {
        printf("Element %d found at index %d\n", target,
               result);
    }
    else {
        printf("Element %d not found\n", target);
    }

    return 0;
}

Element 8 found at index 3

Complexity Analysis

Time Complexity: O(N)
Auxiliary Space: O(1)

Sentinel Linear Search Vs Traditional Linear Search

The below table lists the major differences between Sentinel Linear Search and Traditional Linear Search:

Performance Comparision between Sentinel Linear Search and Traditional Linear Search

Let's take an example of a traditional linear search that searches for an element in a large dataset and see the time needed for execution.

Traditional Linear Search:

// C program to find the execution time of traditional
// linear search
#include <stdio.h>
#include <time.h>

// array with large number of elements
#define ARRAY_SIZE 1000000
#define TARGET_VALUE 999999

// Traditional Linear Search
int linearSearch(int arr[], int size, int target)
{
    for (int i = 0; i < size; i++) {
        if (arr[i] == target) {
            return i; // Found the target value at index i
        }
    }

    // Target value not found in the array
    return -1;
}

// driver code
int main()
{
    int arr[ARRAY_SIZE];

    // Initialize the array with sorted values from 0 to
    // ARRAY_SIZE - 1
    for (int i = 0; i < ARRAY_SIZE; i++) {
        arr[i] = i;
    }

    // target is already the last value of array
    int target = TARGET_VALUE;

    // Measure the execution time
    clock_t start_time, end_time;
    start_time = clock();

    // Perform the sentinel search
    int result = linearSearch(arr, ARRAY_SIZE, target);

    end_time = clock();

    // Calculate the execution time in seconds
    double execution_time
        = ((double)(end_time - start_time))
          / CLOCKS_PER_SEC;

    // Print the execution time
    printf("Time taken by sentinel Search: %lf seconds\n",
           execution_time);

    return 0;
}

Output

Time taken by sentinel Search: 0.003044 seconds

Now, let's consider the same dataset and use a sentinel linear search instead and see the execution time.

Sentinel Linear Search:

// C program to find the execution time of sentinal linear
// search
#include <stdio.h>
#include <time.h>

#define ARRAY_SIZE 1000000
#define TARGET_VALUE 999999

// Sentinel Linear Search
int sentinelSearch(int arr[], int size, int target)
{
    int lastValue = arr[size - 1];
    arr[size - 1] = target;
    int i = 0;
    while (arr[i] != target) {
        i++;
    }
    arr[size - 1] = lastValue;
    if (i < size - 1 || arr[size - 1] == target) {
        return i; // Found the target value at index i
    }
    else {
        return -1; // Target value not found in the array
    }
}

// driver code
int main()
{
    int arr[ARRAY_SIZE];

    // Initialize the array with sorted values from 0 to
    // ARRAY_SIZE - 1
    for (int i = 0; i < ARRAY_SIZE; i++) {
        arr[i] = i;
    }

    // target is already the last value of array
    int target = TARGET_VALUE;

    // Measure the execution time
    clock_t start_time, end_time;
    start_time = clock();

    // Perform the sentinel search
    int result = sentinelSearch(arr, ARRAY_SIZE, target);

    end_time = clock();

    // Calculate the execution time in seconds
    double execution_time
        = ((double)(end_time - start_time))
          / CLOCKS_PER_SEC;

    // Print the execution time
    printf("Time taken by sentinel Search: %lf seconds\n",
           execution_time);

    return 0;
}

Output

Time taken by sentinel Search: 0.002660 seconds

As we can see, the time taken by sentinal linear search is less than the time taken by traditional linear search.

Why Traditional Linear Search is still preferred over Sentinal Linear Search?

The Traditional Linear Search is still preferred over Sentinal Linear Search even after being efficient in performance due to the following reasons:

1. Modification of data in a shared array or immutable data is not possible or may result in errors.
2. Brach Prediction due to which some loop conditions are faster to evaluate than others.

For more details about Sentinel Linear Search, refer www.geeksforgeeks.org/sentinel-linear-search/