What is the Binary Search Algorithm?
The binary search algorithm is an efficient method for finding a target value in a sorted array or list. It works by repeatedly dividing the search interval in half, eliminating portions that cannot contain the target. This divide-and-conquer strategy makes it much faster than linear search for large datasets, requiring the array to be sorted beforehand.
How Does Binary Search Work? Key Steps
Start with the sorted array and define low and high pointers at the beginning and end. Calculate the midpoint and compare it to the target: if equal, return the index; if the target is smaller, search the left half by setting high to mid-1; if larger, search the right half by setting low to mid+1. Repeat until the target is found or the interval is empty, indicating not found.
Practical Example of Binary Search
Consider a sorted array [1, 3, 5, 7, 9, 11] searching for 7. Initial low=0, high=5, mid=2 (value 5). Since 7 > 5, set low=3. New mid=4 (value 9). Since 7 < 9, set high=3. New mid=3 (value 7), found at index 3. This process took just 3 steps for 6 elements.
Time Complexity and Real-World Applications
Binary search has a time complexity of O(log n) in the average and worst cases, where n is the number of elements, making it ideal for large-scale data like dictionary lookups or database indexing. It's crucial in applications such as search engines, file systems, and any scenario involving sorted data, though it requires preprocessing for sorting which adds O(n log n) if unsorted.