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Questions and Answers
In the context of binary trees, if the preorder traversal is given, what does it help identify?
In the context of binary trees, if the preorder traversal is given, what does it help identify?
- The last node
- The first node (correct)
- The middle node
- All leaf nodes
What information can be obtained from the postorder traversal in the context of binary trees?
What information can be obtained from the postorder traversal in the context of binary trees?
- The left child nodes
- All leaf nodes
- The root node (correct)
- The right child nodes
If the preorder traversal of a binary tree is 'A B D E H C F I J G', what node is the root node?
If the preorder traversal of a binary tree is 'A B D E H C F I J G', what node is the root node?
- C
- B
- A (correct)
- H
When constructing a binary tree, what nodes belong to the left sub-tree based on the inorder traversal?
When constructing a binary tree, what nodes belong to the left sub-tree based on the inorder traversal?
What does the postorder traversal of a binary tree help identify?
What does the postorder traversal of a binary tree help identify?
In constructing binary trees, what can be inferred from knowing both inorder and preorder traversals?
In constructing binary trees, what can be inferred from knowing both inorder and preorder traversals?
Which traversal method is used to identify all nodes that belong to the right sub-tree in binary tree construction?
Which traversal method is used to identify all nodes that belong to the right sub-tree in binary tree construction?
If the postorder traversal is 'n1 n3 n5 n4 n2 n8 n7 n9 n6', which node is identified as the root node?
If the postorder traversal is 'n1 n3 n5 n4 n2 n8 n7 n9 n6', which node is identified as the root node?
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Study Notes
Binary Tree Traversal
- Postorder traversal visits the left sub-tree, then the right sub-tree, and finally the root node.
- It can be defined as:
- Traverse the left sub-tree of the root in postorder.
- Traverse the right sub-tree of the root in postorder.
- Visit the root node.
Procedure RPOSTORDER (T)
- This procedure traverses a binary tree in a recursive manner.
- It checks for an empty tree, and if so, writes "Empty Tree" and returns.
- It processes the left subtree, then the right subtree, and finally the root node.
Expression Tree
- An expression tree is a binary tree that stores an arithmetic expression.
- Leaves of the expression tree are operands (constants or variable names).
- All internal nodes are operators (e.g., +, -, /, *, etc.).
- Expression trees are always binary trees because arithmetic expressions contain binary operators.
Inorder Traversal
- Inorder traversal visits the left sub-tree, then the root node, and finally the right sub-tree.
- It can be defined as:
- Traverse the left sub-tree of the root in inorder.
- Visit the root node.
- Traverse the right sub-tree of the root in inorder.
Procedure RINORDER (T)
- This procedure traverses a binary tree in a recursive manner.
- It checks for an empty tree, and if so, writes "Empty Tree" and returns.
- It processes the left subtree, then the root node, and finally the right subtree.
Preorder Traversal
- Preorder traversal visits the root node, then the left sub-tree, and finally the right sub-tree.
- It can be defined as:
- Visit the root node.
- Traverse the left sub-tree of the root in preorder.
- Traverse the right sub-tree of the root in preorder.
Procedure RPREORDER (T)
- This procedure traverses a binary tree in a recursive manner.
- It checks for an empty tree, and if so, writes "Empty Tree" and returns.
- It processes the root node, then the left subtree, and finally the right subtree.
Example Binary Tree Traversal
- Preorder traversal: + - A B * C / D E
- Inorder traversal: A – B + C * D / E
- Postorder traversal: A B – C D E / * +
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