Real-World Examples of Binary Search: Applications in Computer Science

📚 Quick Study Guide

• 🍎 Definition: Binary search is a search algorithm that finds the position of a target value within a sorted array.
• ⏱️ Efficiency: It works by repeatedly dividing the search interval in half. Its time complexity is $O(\log n)$, making it very efficient for large datasets.
• 🔢 Prerequisites: Binary search requires the input data to be sorted.
• ➗ Core Idea: At each step, the algorithm compares the input element to the middle element of the array. If the values match, the location has been found. Otherwise, the algorithm repeats its action on the sub-array to the left or right, depending on the value of the middle element.
• 💡 Common Use Cases: Searching in sorted arrays, finding the square root of a number, and locating elements in data structures like binary search trees.
• 📐 Formula (Midpoint Calculation): $\text{mid} = \lfloor(\text{low} + \text{high}) / 2\rfloor$, where low and high are the boundaries of the search space.

🧪 Practice Quiz

1. Which of the following is a prerequisite for using binary search?
   1. The data must be unsorted.
   2. The data must be stored in a linked list.
   3. The data must be sorted.
   4. The data must be numeric.
2. What is the time complexity of binary search?
   1. O(n)
   2. O(n^2)
   3. O(log n)
   4. O(1)
3. In binary search, if the target value is less than the middle element, which part of the array is searched next?
   1. The right half
   2. The middle element only
   3. The left half
   4. The entire array again
4. Which of the following is NOT a typical application of binary search?
   1. Searching for a word in a dictionary.
   2. Finding the largest element in an unsorted array.
   3. Finding the square root of a number.
   4. Searching for a specific record in a sorted database index.
5. What is the formula to calculate the midpoint in binary search, where 'low' and 'high' are the boundaries?
   1. mid = (low + high) * 2
   2. mid = (low - high) / 2
   3. mid = (low + high) / 2
   4. mid = (low * high) / 2
6. You have a sorted array: [2, 5, 7, 8, 11, 12]. You are searching for the number 13. How many iterations will binary search take before determining 13 is not in the array?
   1. 2
   2. 3
   3. 4
   4. 5
7. In what scenario would a linear search be faster than a binary search?
   1. When the array is very large.
   2. When the target element is the first element in the sorted array.
   3. When the array is unsorted.
   4. Linear search is never faster than binary search.