In a Binary Search Tree, all elements below a given a node have values that are

Question

In a Binary Search Tree, all elements below a given a node have values that are < that node's value.

BlackTom AI · Accepted Answer

In a binary search tree (BST) the defining property is that for every node, all values in its left subtree are less than (or sometimes less than or equal to) the node’s value, and all values in its right subtree are greater than (or sometimes greater than or equal to) the node’s value.

Step-by-step reasoning:
1. Relevant concept: “below a given node” means all descendants (both left and right subtrees), not only the left subtree. The BST invariant applies separately to left and right subtrees: left < node < right.
2. Consider a node N with value 10. Its left child might be 5 and its right child might be 15. The right child 15 is a descendant that is greater than 10, not less than 10.
3. Because descendants in the right subtree are greater, the blanket statement “all elements below a given node have values that are < that node’s value” is false.
4. A concrete counterexample: Tree with root 10, left child 5, right child 15. The element 15 is below the node 10 but 15 > 10, contradicting the claim.

Why the correct answer is correct:
- The correct BST rule distinguishes left and right: left subtree values are less than the node, right subtree values are greater. The original statement ignores the right subtree, so it misstates the invariant.

Why the other option is incorrect:
- “True” would imply every descendant (both left and right) is less than the node, which contradicts the existence of right-subtree values greater than the node (as shown by the counterexample).

Conclusion: The statement is False, which matches the provided answer.

In a Binary Search Tree, all elements below a given a node have values that are < that node's value.True/False

Similar Questions

BST Properties Below is a binary search tree of integers. Choose the correct statement 1: The largest number 2: The predecessor of S 3: The successor of G 4: The 2nd smallest number 5: The predecessor of A

BST-Rightmost/Leftmost Starting with an empty tree, build a BST by inserting nodes in the order 12, 101, 23, 48, 3, 33, 105, 2, 4 11. Which number will the rightmost node of the tree have? [Fill in the blank] Which number will the leftmost node of the tree have? [Fill in the blank]

BST-Search If the new node to be inserted is 270, it will be inserted as the _A_ child of node _B_ _A_= [ Select ] right left _B_ = [ Select ] 25 260 75 250 150 350

Binary-Search-Tree-Property Assume all the numbers in the following tree are unique integers. Choose the correct statements about the binary search tree.

BST-Review We can check if a binary tree T is a binary search tree as follows. Collect nodes in T by a in-order tree traversal into an ArrayList A. Check if all the nodes in A are in a ascending order.

BST-Property Which of the following rules does a valid BST follow?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler