Recursive Binary Search
by Isai Damier

/***********************************************************************
 * Author: Isai Damier
 * Title: Recursive Binary Search
 * Project: geekviewpoint
 * Package: algorithms
 *
 * Statement:
 *   Given a sorted array and an element, find the index of the element.
 *   Return -1 otherwise.
 *
 *  Time Complexity: O(lg n)
 *    where n is the size of the array
 * 
 * Sample Input: {1,2,3,5,7,8,11,13,17,19,21}; 11
 * Sample Output: 6
 * 
 * Technical Details: This is among the most intuitive algorithms in
 *   the world. And yet many experts have historically gotten it
 *   wrong (i.e. your nearest textbook may have it wrong). The idea
 *   is to continuously split the array until the element is found
 *   (or not).
 *   
 *   Because binary search is a tail-recursive algorithm (i.e.
 *   recursion is the last line in the method), we could also solve
 *   the problem using iteration as in 
 * http://www.geekviewpoint.com/java/search/binary_search_iterative
 * 
 **********************************************************************/ 
 public int binarySearchRecursive(int[] A, int el) {
  return binarySearchRecursive(A, 0, A.length - 1, el);
}

private int binarySearchRecursive(int[] A, int min, int max, int el) {
  if (min <= max) {
    int mid = min + (max - min) / 2;
    if (el == A[mid]) {
      return mid;
    } else if (el > A[mid]) {
      return binarySearchRecursive(A, mid + 1, max, el);
    } else {
      return binarySearchRecursive(A, min, mid - 1, el);
    }
  }
  return -1;
}
package algorithms;

import java.util.List;
import org.junit.Test;
import static org.junit.Assert.*;

public class SearchAlgorithmsTest {
  
  /**
   * Test of binarySearchRecursive method, of class SearchAlgorithms.
   */
  @Test
  public void testBinarySearchRecursive() {
    System.out.println("binarySearchRecursive");
    int[] A = {1,2,3,5,7,8,11,13,17,19,21};
    
    int el = 11;
    SearchAlgorithms instance = new SearchAlgorithms();
    int expResult = 6;
    int result = instance.binarySearchRecursive(A, el);
    assertEquals(expResult, result);
    
    el=21;
    expResult = 10;
    result = instance.binarySearchRecursive(A, el);
    assertEquals(expResult, result);
    
    el=1;
    expResult = 0;
    result = instance.binarySearchRecursive(A, el);
    assertEquals(expResult, result);
    
    el=19;
    expResult = 9;
    result = instance.binarySearchRecursive(A, el);
    assertEquals(expResult, result);
    
    el=55;
    expResult = -1;
    result = instance.binarySearchIterative(A, el);
    assertEquals(expResult, result);
  }
}