Summary - Binary Search

Types of Binary Search

Finding an exact target

loop condition: while left <= right

update pointers: left = mid + 1 and right = mid - 1

def binary_search(array, target):
    left, right = 0, len(array) - 1 # Intial right is a possible value
    while left <= right:
        mid = (left + right) // 2
        if array[mid] == target:
            return mid # There is an additional if condition compared to other cases.
        elif array[mid] < target:
            left = mid + 1
        else:
            right = mid - 1
    return -1  # Target not found

Example: Leetcode 374 Guess Number

Finding the lower bound

loop condition: while left < right

update pointers: left = mid + 1 and right = mid

def lower_bound(array, target):
    left, right = 0, len(array) # Intial right is not a possible value
    while left < right:
        mid = (left + right) // 2
        if array[mid] < target:
            left = mid + 1
        else:
            right = mid
    return left  # This is the first of lower bound

Example: Leetcode 2300

Finding the upper bound

loop condition: while left < right

update pointers: left = mid + 1 and right = mid

def upper_bound(array, target):
    left, right = 0, len(array) # Intial right is not a possible value
    while left < right:
        mid = (left + right) // 2
        if array[mid] > target:
            right = mid
        else:
            left = mid + 1
    return left - 1  # This is the last of upper bound