# Binary Search

In this tutorial, you will learn how the Binary Search sort works. Likewise, you will discover working instances of Binary Search in C, C++, Java, and Python.

## What is Binary Search?

A Binary search is an advanced type of search algorithm that finds and fetches data from a sorted list of items. Its center working rule includes dividing the data in the list in half until the necessary value is found and shown to the user in the search result. A binarysearch is normally known as a half-interval search or a logarithmic search.

BinarySearch is a searching algorithm for finding an element’s situation in a sorted array.

In this methodology, the element is constantly searched in a part of an array.

Binarysearch can be actualized distinctly on a sorted list of items. In the event that the elements are not sorted as of now, we need to sort them first.

## Binary Search Working

BinarySearch Algorithm can be actualized in two different ways which are talked about underneath.

1. Iterative Method
2. Recursive Method

The recursive strategy follows the divide and conquer approach.

The general steps for the two techniques are examined underneath.

1. The array in which searching is to be performed is:

Let x = 4 be the element to be searched.

2. Set two pointers low and high at the lowest and the highest positions respectively.

3. Locate the middle element mid of the array ie. (arr[low + high])/2 = 6.

4. On the off chance that x == mid, return mid. Else, compare the element with be searched with m.

5. On the off chance that x > mid, compare x and the middle element of the elements on the right side of mid. This is finished by setting low to low = mid + 1.

6. Else, compare x and the middle element of the elements on the left side of mid. This is finished by setting high to high = mid – 1.

7. Repeat steps 3 to 6 until low meets high.

8. x = 4 is found.

## Binary Search Algorithm

### Iteration Method

```do until the pointers low and high meet each other.
mid = (low + high)/2
if (x == arr[mid])
return mid
else if (x > A[mid]) // x is on the right side
low = mid + 1
else                       // x is on the left side
high = mid - 1```

### Recursive Method

```binarySearch(arr, x, low, high)
if low > high
return False
else
mid = (low + high) / 2
if x == arr[mid]
return mid
else if x < data[mid]        // x is on the right side
return binarySearch(arr, x, mid + 1, high)
else                               // x is on the right side
return binarySearch(arr, x, low, mid - 1)
```

## Python, Java, C/C++ Examples (Iterative Method)

Python

```# Binary Search in python

def binarySearch(array, x, low, high):

# Repeat until the pointers low and high meet each other
while low <= high:

mid = low + (high - low)//2

if array[mid] == x:
return mid

elif array[mid] < x:
low = mid + 1

else:
high = mid - 1

return -1

array = [3, 4, 5, 6, 7, 8, 9]
x = 4

result = binarySearch(array, x, 0, len(array)-1)

if result != -1:
print("Element is present at index " + str(result))
else:

Java

```// Binary Search in Java

class BinarySearch {
int binarySearch(int array[], int x, int low, int high) {

// Repeat until the pointers low and high meet each other
while (low <= high) {
int mid = low + (high - low) / 2;

if (array[mid] == x)
return mid;

if (array[mid] < x)
low = mid + 1;

else
high = mid - 1;
}

return -1;
}

public static void main(String args[]) {
BinarySearch ob = new BinarySearch();
int array[] = { 3, 4, 5, 6, 7, 8, 9 };
int n = array.length;
int x = 4;
int result = ob.binarySearch(array, x, 0, n - 1);
if (result == -1)
else
System.out.println("Element found at index " + result);
}
}```

C

```// Binary Search in C

#include <stdio.h>

int binarySearch(int array[], int x, int low, int high) {
// Repeat until the pointers low and high meet each other
while (low <= high) {
int mid = low + (high - low) / 2;

if (array[mid] == x)
return mid;

if (array[mid] < x)
low = mid + 1;

else
high = mid - 1;
}

return -1;
}

int main(void) {
int array[] = {3, 4, 5, 6, 7, 8, 9};
int n = sizeof(array) / sizeof(array[0]);
int x = 4;
int result = binarySearch(array, x, 0, n - 1);
if (result == -1)
else
printf("Element is found at index %d", result);
return 0;
}```

C++

```// Binary Search in C++

#include <iostream>
using namespace std;

int binarySearch(int array[], int x, int low, int high) {

// Repeat until the pointers low and high meet each other
while (low <= high) {
int mid = low + (high - low) / 2;

if (array[mid] == x)
return mid;

if (array[mid] < x)
low = mid + 1;

else
high = mid - 1;
}

return -1;
}

int main(void) {
int array[] = {3, 4, 5, 6, 7, 8, 9};
int x = 4;
int n = sizeof(array) / sizeof(array[0]);
int result = binarySearch(array, x, 0, n - 1);
if (result == -1)
else
printf("Element is found at index %d", result);
}```

## Python, Java, C/C++ Examples (Recursive Method)

Python

```# Binary Search in python

def binarySearch(array, x, low, high):

if high >= low:

mid = low + (high - low)//2

# If found at mid, then return it
if array[mid] == x:
return mid

# Search the left half
elif array[mid] > x:
return binarySearch(array, x, low, mid-1)

# Search the right half
else:
return binarySearch(array, x, mid + 1, high)

else:
return -1

array = [3, 4, 5, 6, 7, 8, 9]
x = 4

result = binarySearch(array, x, 0, len(array)-1)

if result != -1:
print("Element is present at index " + str(result))
else:

Java

```// Binary Search in Java

class BinarySearch {
int binarySearch(int array[], int x, int low, int high) {

if (high >= low) {
int mid = low + (high - low) / 2;

// If found at mid, then return it
if (array[mid] == x)
return mid;

// Search the left half
if (array[mid] > x)
return binarySearch(array, x, low, mid - 1);

// Search the right half
return binarySearch(array, x, mid + 1, high);
}

return -1;
}

public static void main(String args[]) {
BinarySearch ob = new BinarySearch();
int array[] = { 3, 4, 5, 6, 7, 8, 9 };
int n = array.length;
int x = 4;
int result = ob.binarySearch(array, x, 0, n - 1);
if (result == -1)
else
System.out.println("Element found at index " + result);
}
}```

C

```// Binary Search in C

#include <stdio.h>

int binarySearch(int array[], int x, int low, int high) {
if (high >= low) {
int mid = low + (high - low) / 2;

// If found at mid, then return it
if (array[mid] == x)
return mid;

// Search the left half
if (array[mid] > x)
return binarySearch(array, x, low, mid - 1);

// Search the right half
return binarySearch(array, x, mid + 1, high);
}

return -1;
}

int main(void) {
int array[] = {3, 4, 5, 6, 7, 8, 9};
int n = sizeof(array) / sizeof(array[0]);
int x = 4;
int result = binarySearch(array, x, 0, n - 1);
if (result == -1)
else
printf("Element is found at index %d", result);
}```

C++

```// Binary Search in C++

#include <iostream>
using namespace std;

int binarySearch(int array[], int x, int low, int high) {
if (high >= low) {
int mid = low + (high - low) / 2;

// If found at mid, then return it
if (array[mid] == x)
return mid;

// Search the left half
if (array[mid] > x)
return binarySearch(array, x, low, mid - 1);

// Search the right half
return binarySearch(array, x, mid + 1, high);
}

return -1;
}

int main(void) {
int array[] = {3, 4, 5, 6, 7, 8, 9};
int x = 4;
int n = sizeof(array) / sizeof(array[0]);
int result = binarySearch(array, x, 0, n - 1);
if (result == -1)
else
printf("Element is found at index %d", result);
}```

## Binary Search Complexity

Time Complexities

• Best case complexity: O(1)
• Average case complexity: O(log n)
• Worst case complexity: O(log n)

Space Complexity

The space complexity of the binary search is O(n).

## Binary Search Applications

• In libraries of Java, .Net, C++ STL
• While debugging, the binarysearch is used to pinpoint where the mistake occurs.

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