[FEATURE REQUEST] <Recursive Binary Search> TheAlgorithms#4457

Author: Lahu19

src/main/java/com/thealgorithms/searches/RecursiveBinarySearch.java

@@ -0,0 +1,68 @@
+package com.thealgorithms.searches;
+
+import java.util.Scanner;
+
+/**
+ * @author: Lahu Shahadev Andhale
+ * @date: 1-10-2023(Sunday)
+ */
+/*
+ * Recursive Binary Search is an efficient algorithm for finding a search
+ * element within a sorted array of data. It works by repeatedly dividing the
+ * search
+ * space in half until the desired element is found or it is determined that the
+ * element
+ * is not present in the array.
+ */
+public class RecursiveBinarySearch {
+
+    public static int BinarySearchRecursively(int n, int arr[], int search, int firstIdx, int lastIdx) {
+        if (lastIdx >= firstIdx) {
+            //We are finding mid;
+            int mid = (firstIdx + lastIdx) / 2;
+            //Checking is value at mid is equal to the search ;
+            if (arr[mid] == search) {
+                return mid;
+            } else if (arr[mid] > search) {
+                //recursively call the binary search on the left half of the array
+                return BinarySearchRecursively(n, arr, search, firstIdx, mid - 1);
+            } else {
+                //recursively call the binary search on the right half of the array
+                return BinarySearchRecursively(n, arr, search, mid + 1, lastIdx);
+            }
+        }
+        return -1;
+    }
+
+    public static void main(String args[]) {
+        Scanner sc = new Scanner(System.in);
+        System.out.print("Enter the size of data set: ");
+        int n = sc.nextInt();
+        int arr[] = new int[n];
+        System.out.print("Enter the elements in sorted order: ");
+        for (int i = 0; i < n; i++) {
+            arr[i] = sc.nextInt();
+        }
+        System.out.print("Enter the element to be search over data set: ");
+        int search = sc.nextInt();
+        int idx = BinarySearchRecursively(n, arr, search, 0, n - 1);
+        if (idx == -1) {
+            System.out.println("Element is not present in the given data set");
+        } else {
+            System.out.println("The element is present at the index: " + idx + " value is " + arr[idx]);
+        }
+    }
+}
+/* input and Output:
+ * Enter the size of data set: 10
+ * Enter the elements in sorted order: 2 4 5 6 7 8 9 10 22 24
+ * Enter the element to be search over data set: 22
+ * The element is present at the index: 8 value is 22
+ */
+/*
+ * Complexity Analysis:
+ * Best Case: O(1) the element is found at mid int first iteration
+ * Average Case: T(N)=T(N/2)+c that is " O(log N) "
+ * Worst Case: T(N)=T(N/2)+c that is " O(log N) "
+ * Space Complexity: O(logN) that is size of recursion tree.
+ */