Challenge lab in Binary Search Trees

Mission

Sum keys in an inclusive range while pruning impossible subtrees.

Learning outcome: Prune a range-sum traversal

Correctness contract

Invariant: Each left-subtree key is smaller and each right-subtree key is larger than its root.

Required technique: Prune the left or right subtree whenever BST ordering proves it cannot contain an in-range key.

Complexity target: time O(visited nodes); space O(height).

Input and output

Input: n, then n distinct BST keys, then inclusive low and high bounds. Whitespace may be spaces or line breaks.

Output: Print the single exact numeric result with no label. Return it as a String; Main.java prints it without adding other text.

Assumptions:

• Inserted BST keys are distinct.
• All values fit in signed 32-bit integers.

Before you code

1. Restate the input and output contract, then predict the visible example without running code.
2. Implement the core state transition: Prune the left or right subtree whenever BST ordering proves it cannot contain an in-range key.
3. Trace the smallest boundary case, verify exact formatting, and justify the authored time and auxiliary-space bounds.

Implement Practice.solve(Scanner sc). Keep every provided filename and public class name unchanged.

Sample input

5 8 4 12 2 6 4 10

Sample output

18

Why the sample works: Visible walkthrough for the ordinary non-trivial path. Keys outside the inclusive range prune the impossible subtree; in-range keys contribute and explore both sides. Input `5 8 4 12 2 6 4 10` therefore produces `18`.

Progressive hints

Try the trace and first milestone before opening a hint. Open them in order.

Hint 1 — Contract: identify what each parsed variable represents and write the invariant beside the loop or recursive method.

Hint 2 — Next step: Trace the smallest non-trivial input and write the structure state after the operation before coding the loop.

Hint 3 — Verification: compare the structure state before and after one operation, then test the smallest valid input and a duplicate or unreachable case when allowed.