Binary Search Tips and Tricks

Mastering binary search involves understanding its nuances and common patterns. Here are some tips and tricks to help you solve a wide range of problems.

Tip 1: Identifying a Binary Search Problem

Binary search isn't just for finding elements in a sorted array. It can be applied to any problem where you can make a "yes" or "no" decision to discard half of the search space. Look for problems with a monotonic (consistently increasing or decreasing) property. If you can guess an answer and then determine if the real answer is higher or lower, it's likely a binary search problem.

Tip 2: Choosing the Right Template

There are several templates for binary search. A robust template helps avoid off-by-one errors and infinite loops. Here is a standard implementation:

def binary_search(arr, target):
    left, right = 0, len(arr) - 1
    while left <= right:
        mid = (left + right) // 2
        if arr[mid] == target:
            return mid
        elif arr[mid] < target:
            left = mid + 1
        else:
            right = mid - 1
    return -1

This template is effective for finding the first or last occurrence of a value that satisfies a condition.

Tip 3: Handling Search Space Boundaries

Be careful with left and right boundaries. If you are searching for a real number, you might need to run the loop for a fixed number of iterations or until the interval (right - left) is smaller than a certain precision (epsilon). For integer searches, left <= right is usually safe.

Tip 4: Avoiding Integer Overflow

When calculating the middle index, mid = left + (right - left) / 2 is preferred over mid = (left + right) / 2. The latter can cause an integer overflow if left and right are very large positive numbers.