DSA using C - Binary Search

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

Example

#include <stdio.h>
#define MAX 20

// array of items on which linear search will be conducted. 
int intArray[MAX] = {1,2,3,4,6,7,9,11,12,14,15,16,17,19,33,34,43,45,55,66};

void printline(int count){
   int i;
   for(i=0;i <count-1;i++){
      printf("=");
   }
   printf("=\n");
}
int find(int data){
   int lowerBound = 0;
   int upperBound = MAX -1;
   int midPoint = -1;
   int comparisons = 0;      
   int index = -1;
   while(lowerBound <= upperBound){
      printf("Comparison %d\n" , (comparisons +1) );
      printf("lowerBound : %d, intArray[%d] = %d\n", 
         lowerBound,lowerBound,intArray[lowerBound]);
      printf("upperBound : %d, intArray[%d] = %d\n",
         upperBound,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;
         }
      }             
   }
   printf("Total comparisons made: %d" , comparisons);
   return index;
}
void display(){
   int i;
   printf("[");
   // navigate through all items 
   for(i=0;i<MAX;i++){
		printf("%d ",intArray[i]);
	}
	printf("]\n");
}
main(){
   printf("Input Array: ");
   display();
   printline(50);
   //find location of 1
   int location = find(55);

   // if element was found 
   if(location != -1)
      printf("\nElement found at location: %d" ,(location+1));
   else
      printf("\nElement not found.");
}

Output

If we compile and run the above program then it would produce following output −

Input Array: [1 2 3 4 6 7 9 11 12 14 15 16 17 19 33 34 43 45 55 66 ]
==================================================
Comparison 1
lowerBound : 0, intArray[0] = 1
upperBound : 19, intArray[19] = 66
Comparison 2
lowerBound : 10, intArray[10] = 15
upperBound : 19, intArray[19] = 66
Comparison 3
lowerBound : 15, intArray[15] = 34
upperBound : 19, intArray[19] = 66
Comparison 4
lowerBound : 18, intArray[18] = 55
upperBound : 19, intArray[19] = 66
Total comparisons made: 4
Element found at location: 19