Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Imperative programming (resit) / 1 / c / Solution 2026-10-31
View more
Give the visiting procedure a procedure type:
TYPE Visit = PROCEDURE(x: INTEGER);

PROCEDURE Inorder(t: Tree; p: Visit);
BEGIN
  IF t # NIL THEN
    Inorder(t.left, p);
    p(t.label);
    Inorder(t.right, p)
  END
END Inorder;
Structural induction establishes algorithm correctness: an empty binary tree makes no calls; otherwise the first recursive call visits precisely the left subtree, then the root is visited once, then the second recursive call visits precisely the right subtree. Assume p does not modify the binary tree. With constant-cost p, there is constant work per node and empty child occurrence:
(1)
where is the height of a binary tree and storage is the call stack.
Read the full article