A Lesson from a Naive Binary Search

A Lesson from a Naive Binary Search

I’ve been grinding hard every day, solving coding problems to get better at algorithms. Recently, I came across something interesting—a naive implementation of binary search can actually cause a bug. It’s a small detail, but it matters.

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

It works fine in Python—but I recently learned that the way I calculate mid can cause problems in some cases.

The issue is with this line:

mid = (left + right) // 2

If left and right are very large, their sum might be too big in some languages, causing an overflow.

A safer way to write it is:

mid = left + (right - left) // 2

This version avoids adding two potentially large numbers.

Even something as simple as binary search deserves careful thought. It reminded me that writing correct code isn’t just about making it work—it’s about making it right.