# C Program to Implement Binary Search

This is the C Program to Implement Binary Search

Binary Search can be implemented both recursively and non recursively

In computer science, a binary search or half-interval search algorithm finds the position of a specified input value (the search “key”) within an array sorted by key value.For binary search, the array should be arranged in ascending or descending order. In each step, the algorithm compares the search key value with the key value of the middle element of the array. If the keys match, then a matching element has been found and its index, or position, is returned. Otherwise, if the search key is less than the middle element’s key, then the algorithm repeats its action on the sub-array to the left of the middle element or, if the search key is greater, on the sub-array to the right. If the remaining array to be searched is empty, then the key cannot be found in the array and a special “not found” indication is returned.

A binary search halves the number of items to check with each iteration, so locating an item (or determining its absence) takes logarithmic time. A binary search is a dichotomic divide and conquer search algorithm.

Non Recursive Version:

```
#include<stdio.h>
int n,arr[100],x;
main()
{
int i;
printf("Enter the Items in the Arrayn");
scanf("%d",&n);
for(i=0;i<n;i++)
{
scanf("%d",&arr[i]);
}
printf("Enter the Element to be Searchedn");
scanf("%d",&x);
sort(n);
bsearch(0,n-1);
printf("nSorted Arrayn");
for(i=0;i<n;i++)
{
printf("%d -> ",arr[i]);
}
}
bsearch(int low,int high)
{
int mid,stop=0;
while(low<=high)
{
mid=(low+high)/2;
if(arr[mid]==x)
{
printf("Element Present at Position-%dn",mid);
stop=1;break;
}
else
{
if(arr[mid]<x)
{
low=mid+1;
}
else high=mid-1;
}
}
if(stop==0)
{
printf("Element is absentn");
}
}
sort(int n)
{
int temp,i,j;
for(i=0;i<n;i++)
{
for(j=0;j<n;j++)
{
if(arr[i]<arr[j])
{
temp=arr[i];
arr[i]=arr[j];
arr[j]=temp;
}
}
}
}
```

Recursive Version:

```
#include<stdio.h>
int arr[100];
int flag=-1;
main()
{
int mid,res,i,key,n;
printf("Enter the Size of the Arrayn");
scanf("%d",&n);
for(i=0;i<n;i++)
{ scanf("%d",&arr[i]);}
printf("Enter the Key to be Searchedn");
scanf("%d",&key);
sort(n);
mid=(n+1)/2;
bsearch(key,0,n,mid);
if(flag==-1){printf("Element is not present in Arrayn");}
else printf("Element present at %d Position of Arrayn",flag+1);
}
bsearch(int key,int lb,int ub,int mid)
{
if(key<arr[mid]){ return bsearch(key,lb,mid-1,(lb+(mid-1))/2); }
if(key>arr[mid]){ return bsearch(key,mid+1,ub,(lb+(mid+1))/2); }
if(key==arr[mid]){flag=mid;return mid;}
}
sort(int n)
{
int temp,i,j;
for(i=0;i<n;i++)
{
for(j=0;j<n-i;j++)
{
if(arr[i]>arr[j])
{
temp=arr[i];
arr[i]=arr[j];
arr[j]=temp;
}
}
}
}
```

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