added linear search using recursion - #9

Description
Implemented linear search algorithm using recursion in Java. This provides an alternative recursive approach to the classic linear search problem.

Type of Change
New algorithm implementation

Language
Java

Problem Details

• Problem Name: Linear Search
• Difficulty: Easy
• File Added/Modified: LinearSearchUsingRecursion.java

Time/Space Complexity

• Time Complexity: O(n)
• Space Complexity: O(n)

Approach
The implementation uses recursion to traverse through the array elements:

• Base Case 1: If we reach the end of the array, return -1 (element not found)
• Base Case 2: If current element matches the key, return the current index
• Recursive Case: Otherwise, recursively call the function with the next index
  The public search() method serves as a clean interface that initializes the recursive process starting from index 0.

Testing

• I have tested my solution locally
• I have included test cases in my implementation
• My solution handles edge cases appropriately
• I have verified the solution works with the provided examples

Additional Notes

• While iterative linear search has O(1) space complexity, this recursive version demonstrates how recursion can be applied to simple search problems.
• The implementation handles edge cases including empty arrays and elements not found in the array.
• This serves as a good educational example for understanding recursion in the context of search algorithms.