What is a binary search tree and what is its key property?

What is a binary search tree and what is its key property?

• A. A BST is a balanced tree where every node has the same number of children.
• B. A BST stores keys in random order for fast insertion.
• C. A BST stores keys in sorted order where left subtree keys are less than the node and right subtree keys are greater, enabling efficient search, insert, and delete.
• D. A BST is a graph with cycles.

Answer: (C)

A binary search tree stores keys in a hierarchical order where every node has all keys in its left subtree smaller than the node’s key and all keys in its right subtree greater than the node’s key. This ordering is what makes searching, inserting, and deleting efficient: by comparing the target key to a node, you can decide to go left or right, cutting the remaining search space in roughly half each step. If the tree stays balanced, the height grows logarithmically with the number of nodes, giving fast operations; if it becomes skewed, performance can degrade toward linear time. This structure specifically describes storing keys in sorted order with the left side smaller and the right side larger, which is what enables those efficient operations. The other descriptions don’t fit a binary search tree: it isn’t defined as a graph with cycles, it isn’t about random ordering, and it doesn’t require every node to have the same number of children.

A binary search tree stores keys in a hierarchical order where every node has all keys in its left subtree smaller than the node’s key and all keys in its right subtree greater than the node’s key. This ordering is what makes searching, inserting, and deleting efficient: by comparing the target key to a node, you can decide to go left or right, cutting the remaining search space in roughly half each step. If the tree stays balanced, the height grows logarithmically with the number of nodes, giving fast operations; if it becomes skewed, performance can degrade toward linear time. This structure specifically describes storing keys in sorted order with the left side smaller and the right side larger, which is what enables those efficient operations. The other descriptions don’t fit a binary search tree: it isn’t defined as a graph with cycles, it isn’t about random ordering, and it doesn’t require every node to have the same number of children.