Final answer:
In Binary Search Trees (BSTs), duplicates can be handled by consistently inserting them on the same side, typically the right, making the nodes in the right subtree have equal or greater values. An alternative method is to include a count within the nodes to track the number of duplicates, which saves space by not creating additional nodes.
Step-by-step explanation:
Handling of Duplicates in Binary Search Trees (BSTs)
The handling of duplicates in Binary Search Trees (BSTs) varies depending on the specific implementation. However, a common approach is to allow duplicates on either the left or the right subtree. Typically, in a BST, every node contains some data along with references to its left child node and right child node. The basic rule is that for any given node, all nodes in its left subtree have lesser values, while all nodes in the right subtree have greater values. When duplicates are encountered, they can be inserted into either the left or the right subtree depending on the BST's policy - but consistently on the same side. Some implementations might place duplicates on the right subtree, implying that the definition of the BST is changed slightly to allow nodes in the right subtree to have equal or greater values than the parent node.
Another option is to keep a count of duplicates. In this method, the node will have an additional field that keeps track of the number of duplicate values. Whenever a duplicate is inserted, instead of adding a new node, the count is incremented. This approach avoids additional nodes for the same value, making the BST more efficient in terms of space.
It is important to maintain consistency in how duplicates are handled within a BST to ensure the efficiency of search operations. The choice of strategy may depend on the specific use case or the desired operations' complexity. For instance, a count-based approach might be more suitable where frequent counts of duplicates are needed.