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In a Binary Search Tree, the left subtree of a node contains only nodes with keys _______ the node’s key.

Question

In a Binary Search Tree, the left subtree of a node contains only nodes with keys _______ the node’s key.

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Solution

In a Binary Search Tree (BST), the left subtree of a node contains only nodes with keys less than the node’s key. Conversely, the right subtree will contain only nodes with keys greater than the node’s key. This property is fundamental to the structure of a BST, allowing for efficient searching, insertion, and deletion of nodes.

When a value is to be searched within the tree, the search algorithm takes advantage of this property: starting at the root, it compares the target value with the key of the current node. If the target is less, the search continues in the left subtree; if greater, it moves to the right subtree. This divided approach significantly reduces the number of comparisons needed, typically resulting in O(log n) time complexity for balanced trees.

In summary, the left subtree contains nodes with keys less than the node's key, while the right subtree contains nodes with keys greater, ensuring the ordered structure which is essential in a binary search tree.

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