Linear Search Algorithm

Last Updated : 27 Mar, 2025

Given an array, arr of n integers, and an integer element x, find whether element x is present in the array. Return the index of the first occurrence of x in the array, or -1 if it doesn't exist.

Input: arr[] = [1, 2, 3, 4], x = 3
Output: 2
Explanation: There is one test case with array as [1, 2, 3 4] and element to be searched as 3. Since 3 is present at index 2, the output is 2.
Input: arr[] = [10, 8, 30, 4, 5], x = 5
Output: 4
Explanation: For array [10, 8, 30, 4, 5], the element to be searched is 5 and it is at index 4. So, the output is 4.
Input: arr[] = [10, 8, 30], x = 6
Output: -1
Explanation: The element to be searched is 6 and its not present, so we return -1.

In Linear Search, we iterate over all the elements of the array and check if it the current element is equal to the target element. If we find any element to be equal to the target element, then return the index of the current element. Otherwise, if no element is equal to the target element, then return -1 as the element is not found. Linear search is also known as sequential search.

For example: Consider the array arr[] = {10, 50, 30, 70, 80, 20, 90, 40} and key = 30

Below is the implementation of the linear search algorithm:

C++

#include <iostream>
#include <vector>
using namespace std;

int search(vector<int>& arr, int x) {
    for (int i = 0; i < arr.size(); i++)
        if (arr[i] == x)
            return i;
    return -1;
}

int main() {
    vector<int> arr = {2, 3, 4, 10, 40};
    int x = 10;
    int res = search(arr, x);
    if (res == -1)
       cout << "Not Present";
    else
       cout << "Present at Index " << res;
    return 0;
}

// C code to linearly search x in arr[].

#include <stdio.h>

int search(int arr[], int N, int x)
{
    for (int i = 0; i < N; i++)
        if (arr[i] == x)
            return i;
    return -1;
}

// Driver code
int main(void)
{
    int arr[] = { 2, 3, 4, 10, 40 };
    int x = 10;
    int N = sizeof(arr) / sizeof(arr[0]);

    // Function call
    int result = search(arr, N, x);
    (result == -1)
        ? printf("Element is not present in array")
        : printf("Element is present at index %d", result);
    return 0;
}

Java

// Java code for linearly searching x in arr[]. 

import java.io.*;

class GFG {
    public static int search(int arr[], int N, int x)
    {
        for (int i = 0; i < N; i++) {
            if (arr[i] == x)
                return i;
        }
        return -1;
    }

    // Driver code
    public static void main(String args[])
    {
        int arr[] = { 2, 3, 4, 10, 40 };
        int x = 10;

        // Function call
        int result = search(arr, arr.length, x);
        if (result == -1)
            System.out.print(
                "Element is not present in array");
        else
            System.out.print("Element is present at index "
                             + result);
    }
}

Python

# Python3 code to linearly search x in arr[].


def search(arr, N, x):

    for i in range(0, N):
        if (arr[i] == x):
            return i
    return -1


# Driver Code
if __name__ == "__main__":
    arr = [2, 3, 4, 10, 40]
    x = 10
    N = len(arr)

    # Function call
    result = search(arr, N, x)
    if(result == -1):
        print("Element is not present in array")
    else:
        print("Element is present at index", result)

// C# code to linearly search x in arr[].

using System;

class GFG {
    public static int search(int[] arr, int N, int x)
    {
        for (int i = 0; i < N; i++) {
            if (arr[i] == x)
                return i;
        }
        return -1;
    }

    // Driver's code
    public static void Main()
    {
        int[] arr = { 2, 3, 4, 10, 40 };
        int x = 10;

        // Function call
        int result = search(arr, arr.Length, x);
        if (result == -1)
            Console.WriteLine(
                "Element is not present in array");
        else
            Console.WriteLine("Element is present at index "
                              + result);
    }
}

// This code is contributed by DrRoot_

JavaScript

// Javascript code to linearly search x in arr[].

function search(arr, n, x)
{
    for (let i = 0; i < n; i++)
        if (arr[i] == x)
            return i;
    return -1;
}

// Driver code

    let arr = [ 2, 3, 4, 10, 40 ];
    let x = 10;
    let n = arr.length;

    // Function call
    let result = search(arr, n, x);
    (result == -1)
        ? console.log("Element is not present in array")
        : console.log("Element is present at index " + result);

// This code is contributed by Manoj

PHP

<?php
// PHP code for linearly search x in arr[].

function search($arr, $n, $x)
{
    for($i = 0; $i < $n; $i++) {
        if($arr[$i] == $x)
            return $i;
    }
    return -1;
}

// Driver Code
$arr = array(2, 3, 4, 10, 40); 
$x = 10;

// Function call
$result = search($arr, sizeof($arr), $x);
if($result == -1)
    echo "Element is not present in array";
else
    echo "Element is present at index " ,
                                 $result;

// This code is contributed
// by jit_t
?>

Output

Present at Index 3

Time and Space Complexity of Linear Search Algorithm:

Time Complexity:

Best Case: In the best case, the key might be present at the first index. So the best case complexity is O(1)
Worst Case: In the worst case, the key might be present at the last index i.e., opposite to the end from which the search has started in the list. So the worst-case complexity is O(N) where N is the size of the list.
Average Case: O(N)

Auxiliary Space: O(1) as except for the variable to iterate through the list, no other variable is used.

Applications of Linear Search Algorithm:

Unsorted Lists: When we have an unsorted array or list, linear search is most commonly used to find any element in the collection.
Small Data Sets: Linear Search is preferred over binary search when we have small data sets with
Searching Linked Lists: In linked list implementations, linear search is commonly used to find elements within the list. Each node is checked sequentially until the desired element is found.
Simple Implementation: Linear Search is much easier to understand and implement as compared to Binary Search or Ternary Search.

Advantages of Linear Search Algorithm:

Linear search can be used irrespective of whether the array is sorted or not. It can be used on arrays of any data type.
Does not require any additional memory.
It is a well-suited algorithm for small datasets.