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.判断题

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