Introduction to Binary Search in Ruby

Welcome to today's lesson! We're diving into Binary Search, a clever technique for locating specific elements within a sorted list. By repeatedly dividing the search interval in half, we can efficiently find the targeted item. Think of it as flipping through a dictionary — rather than going page by page, you'd start in the middle, then narrow down the section in half until you find your desired word.

Binary Search begins at the midpoint of a sorted list, halving the search area at each step until it locates the target. For example, if you are looking for the number 8 in a sorted list ranging from 1 to 10, you would start at 5. Since 8 is larger than the midpoint, you narrow the search to the second half of the list, leaving you with numbers 6 to 10. In this new sublist, the middle number is 8, and thus, you've found your target. This efficient approach significantly reduces the number of comparisons needed compared to a linear search.

Let's see how Binary Search can be implemented in Ruby, taking a recursive approach. This process involves a function calling itself — with a base case in place to prevent infinite loops — and a recursive case to solve smaller parts of the problem.

def binary_search(arr, start, end_index, target)
  return -1 if start > end_index # Base case
  
  mid = start + (end_index - start) / 2 # Find the midpoint
  
  return mid if arr[mid] == target # Target found
  
  if arr[mid] > target # If the target is less than the midpoint
    binary_search(arr, start, mid - 1, target) # Search the left half
  else
    binary_search(arr, mid + 1, end_index, target) # Search the right half
  end
end

In this Ruby code, the base case is defined first. If the start index is greater than the end_index, it indicates the search area is exhausted, resulting in a -1 return. The code then locates the midpoint. If the midpoint equals our target, it’s returned. Depending on whether the target is less or more than the midpoint, the search continues within the left or right half, respectively.