Recursive Linear Search Algorithm

Last Updated : 25 Jul, 2024

Linear Search is defined as a sequential search algorithm that starts at one end and goes through each element of a list until the desired element is found, otherwise the search continues till the end of the data set.

How Linear Search Works?

Linear search works by comparing each element of the data structure with the key to be found. To learn the working of linear search in detail, refer to this post.

Pseudocode for Recursive Linear Search:

LinearSearch (array, index, key):
if index < 0:
return -1;
if item = key:
return index
return LinearSearch (array, index-1, key)

Implementation of Recursive Linear Search:

Below is the recursive implementation of linear search:

C++14

// C++ Recursive Code For Linear Search #include <bits/stdc++.h> using namespace std;  int linearsearch(int arr[], int size, int key) {     if (size == 0) {         return -1;     }     else if (arr[size - 1] == key) {                  // Return the index of found key.         return size - 1;     }     return linearsearch(arr, size - 1, key); }  // Driver Code int main() {     int arr[] = { 5, 15, 6, 9, 4 };     int key = 4;      // Function call     int ans = linearsearch(arr, 5, key);     if (ans == -1) {         cout << "The element " << key << " is not found."              << endl;     }     else {         cout << "The element " << key << " is found at "              << ans << " index of the given array." << endl;     }     return 0; }

#include <stdio.h>  // Define a function to perform the linear search int linearSearch(int arr[], int size, int key) {     // If the size of the array is zero, return -1     if (size == 0) {         return -1;     }      // Check if the element at the current index     // is equal to the key     if (arr[size - 1] == key) {                  // If equal, return the index         return size - 1;     }     // If not equal, call the function again     // with the size reduced by 1     return linearSearch(arr, size - 1, key); }  // Driver code int main() {     int arr[] = { 5, 15, 6, 9, 4 };     int key = 4;     int index         = linearSearch(arr, sizeof(arr) / sizeof(int), key);     if (index == -1) {         printf("Key not found in the array.\n");     }     else {         printf("The element %d is found at %d index of the "                "given array \n",                key, index);     }     return 0; }

Java

// Java Recursive Code For Linear Search import java.io.*;  class Test {      // Recursive Method to search key in the array     static int linearsearch(int arr[], int size, int key)     {         if (size == 0) {             return -1;         }         else if (arr[size - 1] == key) {              // Return the index of found key.             return size - 1;         }         return linearsearch(arr, size - 1, key);     }      // Driver method     public static void main(String[] args)     {         int arr[] = { 5, 15, 6, 9, 4 };         int key = 4;          // Function call to find key         int index = linearsearch(arr, arr.length, key);         if (index != -1)             System.out.println(                 "The element " + key + " is found at "                 + index + " index of the given array.");          else             System.out.println("The element " + key                                + " is not found.");     } }

Python

# Python Program to Implement Linear Search Recursively   def linear_search(arr, size, key):      # If the array is empty we will return -1     if (size == 0):         return -1      elif (arr[size - 1] == key):          # Return the index of found key.         return size - 1          return linear_search(arr, size - 1, key)   # Driver code if __name__ == "__main__":     arr = [5, 15, 6, 9, 4]     key = 4     size = len(arr)      # Calling the Function     ans = linear_search(arr, size, key)     if ans != -1:         print("The element", key, "is found at",               ans, "index of the given array.")     else:         print("The element", key, "is not found.")  # Code Contributed By - DwaipayanBandyopadhyay # Code is modified by Susobhan Akhuli

// C# Recursive Code For Linear Search using System;  static class Test {      // Recursive Method to search key in the array     static int linearsearch(int[] arr, int size, int key)     {         if (size == 0) {             return -1;         }         else if (arr[size - 1] == key) {              // Return the index of found key.             return size - 1;         }         return linearsearch(arr, size - 1, key);     }      // Driver method     public static void Main(String[] args)     {         int[] arr = { 5, 15, 6, 9, 4 };         int key = 4;          // Method call to find key         int index = linearsearch(arr, arr.Length, key);          if (index != -1)             Console.Write("The element " + key                           + " is found at " + index                           + " index of the given array.");         else             Console.Write("The element " + key                           + " is not found.");     } }  // This Code is submitted by Susobhan Akhuli

JavaScript

// JavaScript Recursive Code For Linear Search  let linearsearch = (arr, size, key) => {   if (size == 0) {     return -1;   }   else if (arr[size - 1] == key)   {        // Return the index of found key.     return size - 1;   }   return linearsearch(arr, size - 1, key); };  // Driver Code let main = () => {   let arr = [5, 15, 6, 9, 4];   let key = 4;   let ans = linearsearch(arr, 5, key);   if (ans == -1) {     console.log(`The element ${key} is not found.`);   } else {     console.log(       `The element ${key} is found at ${ans} index of the given array.`     );   }   return 0; };  main();  // This code is contributed by Aman Singla...

PHP

<?php // PHP Recursive Code For Linear Search  // Recursive function to search key in the array function linearsearch($arr, int $size, int $key) {     if ($size == 0)         return -1;     else if ($arr[$size - 1] == $key)                  // Return index         return $size - 1;          return linearsearch($arr, $size - 1, $key); }  // Driver Code $arr = array(5, 15, 6, 9, 4); $i; $size = count($arr); $key = 4; $ans = linearsearch($arr, $size, $key); if ($ans != -1)     echo "The element ", $key, " is found at ", $ans,         " index of the given array."; else     echo "The element ", $key, " is not found."; // This code is submitted by Susobhan Akhuli ?>

Output

The element 4 is found at 4 index of the given array.

Complexity Analysis:

Time Complexity:

Best Case: In the best case, the key might be present at the last index. So the best case complexity is O(1)
Worst Case: In the worst case, the key might be present at the first 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 this is a tail recursion, so no recursion stack space is utilized.

Sentinel Linear Search

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Recursive Linear Search Algorithm

How Linear Search Works?

Pseudocode for Recursive Linear Search:

Implementation of Recursive Linear Search:

Complexity Analysis:

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