The Off-by-One Bug in Binary Search

Binary search looks simple, but a subtle bug hid in production libraries for years: computing the midpoint with (low + high) / 2 can overflow when the array is large enough.

The buggy version

int mid = (low + high) / 2; // overflows when low + high > Integer.MAX_VALUE

The fix

Compute the midpoint from the difference instead of the sum:

int mid = low + (high - low) / 2;

In languages with arbitrary-precision integers, like Python, this particular bug can't happen — but it's a good reminder that even "textbook" algorithms deserve careful testing:

def binary_search(items, target):
    low, high = 0, len(items) - 1
    while low <= high:
        mid = (low + high) // 2  # safe in Python
        if items[mid] == target:
            return mid
        if items[mid] < target:
            low = mid + 1
        else:
            high = mid - 1
    return -1

Small details matter — especially the ones that only fail at scale.