Given a sorted array arr[] of n elements, write a function to search a given element x in arr[].

A simple approach is to do **linear search.**The time complexity of above algorithm is O(n). Another approach to perform the same task is using Binary Search.

**Binary Search:** Search a sorted array by repeatedly dividing the search interval in half. Begin with an interval covering the whole array. If the value of the search key is less than the item in the middle of the interval, narrow the interval to the lower half. Otherwise narrow it to the upper half. Repeatedly check until the value is found or the interval is empty.

`// Java implementation of recursive Binary Search`

`class`

`BinarySearch`

`{`

` `

`// Returns index of x if it is present in arr[l..r], else`

` `

`// return -1`

` `

`int`

`binarySearch(`

`int`

`arr[], `

`int`

`l, `

`int`

`r, `

`int`

`x)`

` `

`{`

` `

`if`

`(r>=l)`

` `

`{`

` `

`int`

`mid = l + (r - l)/`

`2`

`;`

` `

`// If the element is present at the middle itself`

` `

`if`

`(arr[mid] == x)`

` `

`return`

`mid;`

` `

`// If element is smaller than mid, then it can only`

` `

`// be present in left subarray`

` `

`if`

`(arr[mid] > x)`

` `

`return`

`binarySearch(arr, l, mid-`

`1`

`, x);`

` `

`// Else the element can only be present in right`

` `

`// subarray`

` `

`return`

`binarySearch(arr, mid+`

`1`

`, r, x);`

` `

`}`

` `

`// We reach here when element is not present in array`

` `

`return`

`-`

`1`

`;`

` `

`}`

` `

`// Driver method to test above`

` `

`public`

`static`

`void`

`main(String args[])`

` `

`{`

` `

`BinarySearch ob = `

`new`

`BinarySearch();`

` `

`int`

`arr[] = {`

`2`

`,`

`3`

`,`

`4`

`,`

`10`

`,`

`40`

`};`

` `

`int`

`n = arr.length;`

` `

`int`

`x = `

`10`

`;`

` `

`int`

`result = ob.binarySearch(arr,`

`0`

`,n-`

`1`

`,x);`

` `

`if`

`(result == -`

`1`

`)`

` `

`System.out.println(`

`"Element not present"`

`);`

` `

`else`

` `

`System.out.println(`

`"Element found at index "`

`+result);`

` `

`}`

`}`

`/* This code is contributed by Rajat Mishra */`

Advertisements