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Questions and Answers
A binary tree has two subtrees called the left and right subtrees.
A binary tree has two subtrees called the left and right subtrees.
True (A)
What are the three classical traversal methods for a binary tree?
What are the three classical traversal methods for a binary tree?
Preorder traversal, Inorder traversal, and Postorder traversal.
Which of these methods traverses the tree in a 'Top Down' approach?
Which of these methods traverses the tree in a 'Top Down' approach?
- Postorder Traversal
- Inorder Traversal
- Preorder Traversal (correct)
Which of these methods traverses the tree in a 'Left to Right' approach?
Which of these methods traverses the tree in a 'Left to Right' approach?
Which of these methods traverses the tree in a 'Bottom Up' approach?
Which of these methods traverses the tree in a 'Bottom Up' approach?
It is possible to rebuild a unique binary tree using only a single traversal.
It is possible to rebuild a unique binary tree using only a single traversal.
Which pair of traversals can be used to uniquely reconstruct a binary tree?
Which pair of traversals can be used to uniquely reconstruct a binary tree?
In the context of binary tree traversals, what does a 'red dot' represent?
In the context of binary tree traversals, what does a 'red dot' represent?
In the context of binary tree traversals, what does a 'yellow' dot represent?
In the context of binary tree traversals, what does a 'yellow' dot represent?
What traversal method is particularly useful for finding the minimum or maximum item within a binary tree?
What traversal method is particularly useful for finding the minimum or maximum item within a binary tree?
Flashcards
Binary Tree
Binary Tree
A data structure that is either empty (null) or comprised of a root node with disjoint left and right binary subtrees.
Binary Tree Traversal
Binary Tree Traversal
A way to visit each node in a binary tree in a specific order.
Preorder Traversal
Preorder Traversal
Starts at the root, then visits the left subtree, then the right subtree. (Root, Left, Right)
Inorder Traversal
Inorder Traversal
Visits the left subtree, then the root, then the right subtree. (Left, Root, Right)
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Postorder Traversal
Postorder Traversal
Visits the left subtree, then the right subtree, then the root (Left, Right, Root).
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Node Class
Node Class
A Python class that represents a node in a binary tree. It contains an item, a left child, and a right child.
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BinaryTree Class
BinaryTree Class
A Python class that represents a binary tree. It contains a root node and methods for traversing and manipulating the tree.
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Reconstructing a Binary Tree
Reconstructing a Binary Tree
The process of creating a binary tree from its preorder and inorder traversal data.
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Print Binary Tree Method
Print Binary Tree Method
A recursive method that prints a binary tree in a visually appealing way, with indentation to represent the tree structure.
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Unique Binary Tree
Unique Binary Tree
A single traversal (preorder, inorder, or postorder) does not provide enough information to uniquely reconstruct a binary tree.
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Unique Binary Tree Reconstruction
Unique Binary Tree Reconstruction
A binary tree can be uniquely reconstructed using the inorder traversal and either the preorder or postorder traversal.
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Time Complexity of Inorder Traversal
Time Complexity of Inorder Traversal
The time complexity of an inorder traversal of a binary tree on n nodes is O(n), meaning that the time taken increases linearly with the number of nodes.
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Finding Minimum Item in a Binary Tree
Finding Minimum Item in a Binary Tree
A recursive method that finds the minimum item in a binary tree. This method usually utilizes the postorder traversal.
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Binary Tree Traversals
- A binary tree is a data structure that can be empty or consists of a root node with disjoint left and right subtrees.
- Different ways exist to visit or traverse the nodes in a binary tree. These are called traversals.
- Common traversals include preorder, inorder, and postorder.
Preorder Traversal
- Visit the root node first.
- Traverse the left subtree recursively.
- Traverse the right subtree recursively.
- The process is done in a top-down fashion.
- This traversal method lists nodes in the order of root, left-subtree, and right-subtree.
Inorder Traversal
- Traverse the left subtree recursively.
- Visit the root node.
- Traverse the right subtree recursively.
- This traversal method lists the nodes in the left-subtree, root, then the right-subtree.
Postorder Traversal
- Traverse the left subtree recursively.
- Traverse the right subtree recursively.
- Visit the root node.
- This traversal method lists the nodes in the left-subtree, right-subtree, and then root.
Recursive Implementation of Traversals
- Preorder, inorder, and postorder traversals can be implemented recursively.
- The recursive method typically operates on the root node and makes recursive calls to the left and right subtrees.
Binary Tree Class
- A binary tree class typically defines nodes and methods to handle root nodes and trees.
- A tree can be empty represented by a null root(e.g.:root = null) or has child nodes.
- Example:
class BinaryTree<T> { Node<T> root; }
Reconstructing a Binary Tree
- It is not possible to reconstruct a binary tree from only one traversal.
- To reconstruct a binary tree, you need at least the inorder and preorder (or postorder) traversals.
- Inorder tells us how nodes are arranged in left-root-right order.
- Preorder (or postorder) reveals the root.
Exercises
- Binary trees can be built based on given traversals.
- You can find the minimum element(value) in a binary tree by using recursive postorder traversal method.
- Inorder traversal takes linear time complexity, O(n) in a binary tree with n nodes.
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