Suppose a node A has a successor node S. Then S must have a key that is larger than _____ but smaller than or equal to _______.
a. A, A's successor
b. A, A's left-child descendant
c. A's left-child descendant, A's right-child descendant
d. A, A's right-child descendant

Answers

Answer 1

If node A has a successor node S, then S must have a key that is larger than A but smaller than or equal to A's left-child descendant. So, the correct option is b.

In a binary search tree (BST), the successor of a node is defined as the node with the smallest key that is greater than the key of the given node. In this case, if A has a successor node S, it means that S comes immediately after A in terms of key value. Therefore, S must have a key that is larger than A, satisfying the first part of the statement.

Now, considering the second part of the statement, the left-child descendant of A represents the node with the smallest key value in the subtree rooted at A's left child. Therefore, S's key must be smaller than or equal to A's left-child descendant since S comes immediately after A and precedes A's left-child descendant.

By combining both conditions, we can conclude that S must have a key that is larger than A but smaller than or equal to A's left-child descendant in a binary search tree.

Learn more about binary search tree (BST)

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