coderz.py

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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