Enter a sorted array and a target value into the binary search calculator to find the index of the target value.

What is Binary Search?

Binary search is an efficient algorithm for finding a target value within a sorted array. It works by repeatedly dividing the search interval in half. If the target value is less than the item in the middle of the interval, the search continues in the lower half, or if it is greater, it continues in the upper half. This process repeats until the target value is found or the interval is empty.

How Does Binary Search Work?

The binary search algorithm begins by determining the middle element of the sorted array. If the middle element is equal to the target value, the search is complete. If the target value is less than the middle element, the search continues in the left half of the array. Conversely, if the target value is greater, the search continues in the right half. This halving of the search space allows binary search to operate in logarithmic time, making it much faster than linear search for large datasets.

Binary Search Algorithm Steps

  1. Start with the entire array as the search interval.
  2. Find the middle element of the current interval.
  3. If the middle element is equal to the target, return the index.
  4. If the target is less than the middle element, narrow the interval to the left half.
  5. If the target is greater than the middle element, narrow the interval to the right half.
  6. Repeat the process until the target is found or the interval is empty.

Example of Binary Search

Consider a sorted array: [1, 3, 5, 7, 9, 11, 13, 15]. If we want to find the index of the target value 7, the binary search algorithm would proceed as follows:

  • Initial array: [1, 3, 5, 7, 9, 11, 13, 15], target = 7.
  • Middle element (index 3) is 7, which matches the target.
  • Return index 3 as the result.

Advantages of Binary Search

Binary search is significantly faster than linear search, especially for large datasets. Its time complexity is O(log n), which means that the time taken to search increases logarithmically as the size of the dataset increases. This efficiency makes binary search a preferred choice for searching in sorted arrays.

Limitations of Binary Search

Binary search can only be applied to sorted arrays. If the array is not sorted, the results will be incorrect. Additionally, binary search requires random access to elements, which is not possible in linked lists.

Conclusion

Binary search is a powerful algorithm for efficiently locating a target value in a sorted array. By understanding its mechanics and applying it correctly, you can significantly improve the performance of search operations in your applications.