Searching

Binary Search (Recursive)

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

Algorithm

execution replay The checked-in replay follows the language-neutral state table for `search-binary-recursive`.
cross-language comparison This Swift DSA version keeps the same data and final output as every other DSA book in this wave.

Basic Implementation

basic.swift
Replay: real traced execution (multi-file project)
func search(_ arr: [Int], _ target: Int, _ lo: Int, _ hi: Int) -> Int {
	if lo > hi { return -1 }
	let mid = lo + (hi - lo) / 2
	if arr[mid] == target { return mid }
	if arr[mid] < target { return search(arr, target, mid + 1, hi) }
	return search(arr, target, lo, mid - 1)
}

let arr = [1, 3, 5, 7, 9, 11, 13]
let target = 11
print(search(arr, target, 0, arr.count - 1))

  1. lo ← 0, hi ← 6, target ← 11

    1func search(_ arr: [Int], _ target: Int, _ lo: Int, _ hi: Int) -> Int {2	if lo > hi { return -1 }
    values this step0lo6hi11target

  2. mid ← 3, arr[mid] ← 7, next call ← (4, 6)

    2if lo > hi { return -1 }3let mid = lo + (hi - lo) / 24if arr[mid] == target { return mid }
    values this step3mid7arr[mid](4, 6)next call0lo6hi

  3. mid ← 5, arr[mid] ← 11, result ← 5

    2if lo > hi { return -1 }3let mid = lo + (hi - lo) / 24if arr[mid] == target { return mid }
    values this step5mid11arr[mid]5result4lo6hi

  4. stdout ← 5

    10let target = 1111print(search(arr, target, 0, arr.count - 1))
    values this step5stdout5result

Complexity

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

Implementation notes

  • search(_ arr: [Int], _ target: Int, _ lo: Int, _ hi: Int) -> Int receives the Swift array and scalar bounds as immutable parameters on each recursive call.
  • The base case if lo > hi { return -1 } is the not-found sentinel path; this trace does not take it because the target is present.
  • let mid = lo + (hi - lo) / 2 computes the current Int index with integer division before reading arr[mid].
  • A match returns mid immediately. If arr[mid] < target, the recursive call is search(arr, target, mid + 1, hi); otherwise it is search(arr, target, lo, mid - 1).
  • The top-level bindings are let arr = [1, 3, 5, 7, 9, 11, 13] and let target = 11, then print(search(arr, target, 0, arr.count - 1)).
  • The trace records the first call (lo=0, hi=6), mid=3 with value 7, and the right-side call (4, 6).
  • The second call computes mid=5, reads arr[mid]=11, returns result 5, and print writes the Swift integer output 5.