DSA using Java - Binary Search


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Overview

Binary search is a very fast search algorithm. This search algorithm works on the principle of divide and conquer. For this algorithm to work properly the data collection should be in sorted form.

Binary search search a particular item by comparing the middle most item of the collection. If match occurs then index of item is returned. If middle item is greater than item then item is searched in sub-array to the right of the middle item other wise item is search in sub-array to the left of the middle item. This process continues on sub-array as well until the size of subarray reduces to zero.

Binary search halves the searchable items and thus reduces the count of comparisons to be made to very less numbers.

Algorithm

Binary Search ( A: array of item, n: total no. of items ,x: item to be searched)
Step 1: Set lowerBound = 1
Step 2: Set upperBound = n 
Step 3: if upperBound < lowerBound go to step 12
Step 4: set midPoint = ( lowerBound + upperBound ) / 2
Step 5: if A[midPoint] < x
Step 6: set lowerBound = midPoint + 1
Step 7: if A[midPoint] > x
Step 8: set upperBound = midPoint - 1 
Step 9  if A[midPoint] = x go to step 11
Step 10: Go to Step 3
Step 11: Print Element x Found at index midPoint and go to step 13
Step 12: Print element not found
Step 13: Exit

Demo Program

package com.tutorialspoint.simplesearch;

import java.util.Arrays;

public class BinarySearchDemo {
    
   public static void main(String args[]){
      int[] sourceArray = {1,2,3,4,6,7,9,11,12,14,15,
      16,17,19,33,34,43,45,55,66,76,88};
      System.out.println("Input Array: " +Arrays.toString(sourceArray));
      printline(50);
      // find location of 55 
      int location = find(sourceArray, 55);
      if(location != -1){
         System.out.println("Element found at location: " +(location+1));
      }else {
         System.out.println("Element not found.");
      }    
   }

   public static int find(int[] intArray, int data){
      int lowerBound = 0;
      int upperBound = intArray.length -1;
      int midPoint = -1;
      int comparisons = 0;      
      int index = -1;
      while(lowerBound <= upperBound){
         System.out.println("Comparison " + (comparisons +1) ) ;
         System.out.println("lowerBound : "+lowerBound  
                           + " , intArray[" + lowerBound+"] = " 
                           + intArray[lowerBound]) ;
         System.out.println("upperBound : "+upperBound  
                           + " , intArray[" + upperBound+"] = " 
                           + intArray[upperBound]) ;
         comparisons++;
         // compute the mid point 
         midPoint = (lowerBound + upperBound) / 2;
         // data found
         if(intArray[midPoint] == data){
		    index = midPoint;
            break;
         }
         else {
            // if data is larger 
            if(intArray[midPoint] < data){
               // data is in upper half
               lowerBound = midPoint + 1;
            }
            // data is smaller 
            else{           
               // data is in lower half 
               upperBound = midPoint -1;
            }
         }               
      }
      System.out.println("Total comparisons made: " + comparisons);
      return index;
   }
   
   public static void printline(int count){
      for(int i=0;i <count-1;i++){
         System.out.print("=");
      }
      System.out.println("=");
   }
}

If we compile and run the above program then it would produce following result:

Input Array: [1, 2, 3, 4, 6, 7, 9, 11, 12, 14, 15, 16, 17, 19, 33, 34, 43, 45, 55, 66, 76, 88]
==================================================
Comparison 1
lowerBound : 0 , intArray[0] = 1
upperBound : 21 , intArray[21] = 88
Comparison 2
lowerBound : 11 , intArray[11] = 16
upperBound : 21 , intArray[21] = 88
Comparison 3
lowerBound : 17 , intArray[17] = 45
upperBound : 21 , intArray[21] = 88
Comparison 4
lowerBound : 17 , intArray[17] = 45
upperBound : 18 , intArray[18] = 55
Comparison 5
lowerBound : 18 , intArray[18] = 55
upperBound : 18 , intArray[18] = 55
Total comparisons made: 5
Element found at location: 19
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