C Program for Linear Search

Linear Search is a sequential searching algorithm in C that is used to find an element in a list. Linear Search compares each element of the list with the key till the element is found or we reach the end of the list.

Example

Input: arr = {10, 50, 30, 70, 80, 60, 20, 90, 40}, key: 30
Output: Key Found at Index: 2
Explanation: Start from index 0, compare each element with the key (30). When index 2 is reached, the element (30) matches the target value.

Linear Search Algorithm

To search for the given element using linear search, follow the below approach:

• Start traversing from the start of the dataset.
• Compare the current element with the key (element to be searched).
• If the element is equal to the key, return index.
• Else, increment the index and repeat the step 2 and 3.
• If we reach the end of the list without finding the element equal to the key, return some value to represent that the element is not found.

C Program to Implement Linear Search

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

int linearSearch(int* arr, int n, int key) {
  
    // Starting the loop and looking for the key in arr
    for (int i = 0; i < n; i++) {

        // If key is found, return key
        if (arr[i] == key) {
            return i;
        }
    }

    // If key is not found, return some value to indicate
    // end
    return -1;
}

int main() {
    int arr[] = { 10, 50, 30, 70, 80, 60, 20, 90, 40 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int key = 30;

    // Calling linearSearch() for arr with key = 43
    int i = linearSearch(arr, n, key);

    // printing result based on value returned by
    // linearSearch()
    if (i == -1)
        printf("Key Not Found");
    else
        printf("Key Found at Index: %d", i);

    return 0;
}

Key Found at Index: 2

Complexity Analysis of Linear Search

• Time Complexity: O(n), where n is the number of elements in the list.
• Auxiliary Space: O(1)

How Linear Search Works?

The working of linear search is very simple. Let's take an array arr = {10, 50, 30, 70, 80, 60, 20, 90, 40} and the key as 30.

Recursive Implementation of Linear Search

Just like most of the algorithms, linear search can also be implemented using recursion:

• Define the recursive function that takes an array, its size, and the key as parameters.
• Check if the current last element of the array is equal to the key.
  • If it is equal, return the index of it.
  • Otherwise, recursively call the linearSearch() with same array but with size decreased by one.
• If the size reaches is 0, return -1 indicating the element is not found.

C Program to Implement Recursive Linear Search

// C Program to implement linear search using recursion
#include <stdio.h>

int linearSearch(int* arr, int n, int key) {
  
    // Base Case: if there are no elements, return -1
    if (n == 0)
        return -1;

    // If the element at (n - 1) index is equal to key,
    // return (n - 1)
    if (arr[n - 1] == key) {
        return n - 1;
    }

    // If element is not at n - 1, call linear search for
    // same array arr but reducing the size by a single
    // element
    return linearSearch(arr, n - 1, key);
}

int main() {
    int arr[] = { 10, 50, 30, 70, 80, 60, 20, 90, 40 };
    int n = sizeof(arr) / sizeof(int);
    int key = 30;

    // Calling linearSearch function
    int i = linearSearch(arr, n, key);

    if (i == -1)
        printf("Key Not Found");
    else
        printf("Key Found at Index: %d", i);

    return 0;
}

Key Found at Index: 2

Time Complexity: O(n), where n is the number of elements in the list.
Auxiliary Space: O(n)

Note: If the compiler performs tail call optimization, then Auxiliary Space for recursive approach can be reduced to O(1).