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 Dart DSA version keeps the same data and final output as every other DSA book in this wave.

Basic Implementation

basic.dart
Replay: real traced execution (multi-file project)
int search(List<int> arr, int target, int lo, int hi) {
  if (lo > hi) return -1;
  final 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);
}

void main() {
  final arr = [1, 3, 5, 7, 9, 11, 13];
  const target = 11;
  print(search(arr, target, 0, arr.length - 1));
}

  1. lo ← 0, hi ← 6, target ← 11

    1int search(List<int> arr, int target, int lo, int hi) {2  if (lo > hi) return -1;
    values this step0lo6hi11target

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

    2if (lo > hi) return -1;3final mid = lo + (hi - lo) ~/ 2;4if (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;3final mid = lo + (hi - lo) ~/ 2;4if (arr[mid] == target) return mid;
    values this step5mid11arr[mid]5result4lo6hi

  4. stdout ← 5

    11  const target = 11;12  print(search(arr, target, 0, arr.length - 1));13}
    values this step5stdout5result

Complexity

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

Implementation notes

  • Keep the explicit control flow. Library shortcuts would hide the state changes this lesson is meant to replay.
  • The final output is intentionally small and deterministic for cross-language comparison.