**Binary Search**, also known as **half-interval search**,** logarithmic search**, or **binary chop**, is a search algorithm that finds the position of a target value within a sorted array. Binary search compares the target value to the middle element of the array.

If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half, again taking the middle element to compare to the target value, and repeating this until the target value is found. If the search ends with the remaining half being empty, the target is not in the array.

Binary search runs in logarithmic time in the worst case, making comparisons, where is the number of elements in the array.

#### Solution

def binary_search(arr, ele): # First and last index values first = 0 last = len(arr) - 1 found = False while first <= last and not found: mid = (first+last)/2 # or // for Python 3 # Match found if arr[mid] == ele: found = True # Set new midpoints up or down depending on comparison else: # Set down if ele < arr[mid]: last = mid -1 # Set up else: first = mid + 1 return found

# list must already be sorted! arr = [1,2,3,4,5,6,7,8,9,10]

binary_search(arr,4)

True

binary_search(arr,2.2)

False

#### Binary Search using Recursive Method

def rec_bin_search(arr,ele): # Base Case! if len(arr) == 0: return False # Recursive Case else: mid = len(arr)/2 # If match found if arr[mid] == ele: return True else: # Call again on second half if ele < arr[mid]: return rec_bin_search(arr[:mid], ele) # Or call on first half else: return rec_bin_search(arr[mid+1:], ele)

rec_bin_search(arr,3)

True

rec_bin_search(arr,15)

False

**Recommended:** Introduction to Recursion

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