Searching

Binary Search (Recursive)

Use the same binary-search window as the iterative lesson, but pass lo and hi through recursive calls.

Algorithm

Basic Implementation

basic.rb 
arr = [1, 3, 5, 7, 9, 11, 13]
target = 11

def search(arr, target, lo, hi)
	return -1 if lo > hi
	mid = lo + (hi - lo) / 2
	return mid if arr[mid] == target
	return search(arr, target, mid + 1, hi) if arr[mid] < target
	search(arr, target, lo, mid - 1)
end

puts search(arr, target, 0, arr.length - 1)

Complexity

  • Time: O(log n)
  • Space: O(log n) call stack

Implementation notes

  • search(arr, target, lo, hi) is a Ruby method that returns an integer index or -1; it does not mutate the array.
  • The base case is return -1 if lo > hi, so an empty search window returns the miss sentinel immediately.
  • mid = lo + (hi - lo) / 2 uses Ruby integer division to produce an array index.
  • The method reads arr[mid] directly for the equality check and then for the branch comparison.
  • On a match, return mid sends the found index back through the recursive call chain.
  • If arr[mid] < target, the next call is search(arr, target, mid + 1, hi); otherwise it searches lo through mid - 1.
  • The trace starts with bounds (0, 6), sees arr[3] = 7, recurses right to (4, 6), then finds arr[5] = 11.
  • puts search(arr, target, 0, arr.length - 1) prints the returned index 5.
execution replay The checked-in replay follows the language-neutral state table for `search-binary-recursive`.
cross-language comparison This Ruby DSA version keeps the same data and final output as every other DSA book in this wave.