Python Program for Binary Search

In this article, we will learn about the solution and approach to solve the given problem statement.

Problem statement − We will be given a sorted list and we need to find an element with the help of a binary search.

Algorithm

• Compare x with the middle element.

• If x matches with the middle element, we return the mid index.

• Else If x is greater than the mid element, then x can only lie in right half subarray after the mid element. So we recur for the right half.

• Else (x is smaller) recur for the left half

Recursive Algorithm

Example

def binarySearchAppr (arr, start, end, x):
# check condition
if end >= start:
   mid = start + (end- start)//2
   # If element is present at the middle
   if arr[mid] == x:
      return mid
   # If element is smaller than mid
   elif arr[mid] > x:
      return binarySearchAppr(arr, start, mid-1, x)
   # Else the element greator than mid
   else:
      return binarySearchAppr(arr, mid+1, end, x)
   else:
   # Element is not found in the array
      return -1
arr = sorted(['t','u','t','o','r','i','a','l'])
x ='r'
result = binarySearchAppr(arr, 0, len(arr)-1, x)
if result != -1:
   print ("Element is present at index "+str(result))
else:
print ("Element is not present in array")

Iterative Algorithm

Example

 Live Demo

def binarySearchAppr (arr, start, end, x):
# check condition
   if end >= start:
      mid = start + (end- start)//2
      # If element is present at the middle
      if arr[mid] == x:
      return mid
      # If element is smaller than mid
      elif arr[mid] > x:
      return binarySearchAppr(arr, start, mid-1, x)
      # Else the element greator than mid
      else:
      return binarySearchAppr(arr, mid+1, end, x)
   else:
      # Element is not found in the array
      return -1
arr = sorted(['t','u','t','o','r','i','a','l'])
   x ='r'
   result = binarySearchAppr(arr, 0, len(arr)-1, x)
if result != -1:
   print ("Element is present at index "+str(result))
else:
   print ("Element is not present in array")

Element is present at index 4

Conclusion

In this article, we learned about the approach to apply Binary Search.