Question

Problem 1:

- Write a java method to search for an element in an array using a linear search. Many list processing tasks, including searching, can be done recursively. The base case typically involves doing something with a limited number of elements in the list (say the first element), then the recursive step involves doing the task on the rest of the list.
- Think about how linear search can be viewed recursively; if you are looking for an item in a list starting at index i :
If i exceeds the last index in the list, the item is not found (return -1).
If the item is at list [i], return i.
If the is not at list [i], do a linear search starting at index i+1.
- Analyze the running time of your algorithm.

Answer 1

A Java method for performing a recursive linear search returns the index of an element in an array, with a worst-case running time of O(n). The recursion continues until the element is found or the end of the array is reached.

Step-by-step explanation:

Java Method for Recursive Linear Search

In Java, a method for performing a linear search on an array can be implemented recursively. Recursive algorithms often consist of a base case that stops the recursion and a recursive step that continues the search. For a recursive linear search, the base case checks if the index, i, has exceeded the bounds of the array, in which case the element is not found, and the method returns -1. If the element is found at the current index in the array, the index is returned. Otherwise, the recursion continues by calling the method again with the next index, i+1.

The running time of this recursive linear search algorithm is O(n) in the worst case, where n is the number of elements in the array. This is because, in the worst-case scenario, each element will be compared exactly once until the desired element is found, or the end of the array is reached without finding the element.

Here is a sample Java method for a recursive linear search:

public int recursiveLinearSearch(int[] array, int i, int key) {
if (i >= array.length) {
return -1; // Base case: not found
} else if (array[i] == key) {
return i; // Element found
} else {
return recursiveLinearSearch(array, i + 1, key); // Recursive step
}
}