Podcast
Questions and Answers
What distinguishes a binary tree from a normal tree?
What distinguishes a binary tree from a normal tree?
- Binary trees can have an unlimited number of children, while normal trees can only have two.
- Every node in a binary tree can have a maximum of 2 children, while nodes in a normal tree can have any number of children. (correct)
- Normal trees do not have a root node.
- Binary trees can only store numerical data; normal trees can store any data type.
In a binary tree, a node can have more than two children.
In a binary tree, a node can have more than two children.
False (B)
Name the two children a node can have in a binary tree.
Name the two children a node can have in a binary tree.
left child, right child
The maximum number of children a node can have in a binary tree is ______.
The maximum number of children a node can have in a binary tree is ______.
Which of the following is a reason to use trees for data storage?
Which of the following is a reason to use trees for data storage?
Trees are slower than linked lists for moderate access and search operations.
Trees are slower than linked lists for moderate access and search operations.
Compared to arrays and unordered linked lists, how do trees perform regarding insertion and deletion?
Compared to arrays and unordered linked lists, how do trees perform regarding insertion and deletion?
Unlike arrays, trees don't have an upper limit on the number of nodes because nodes are linked using ______.
Unlike arrays, trees don't have an upper limit on the number of nodes because nodes are linked using ______.
When representing a binary tree of depth 'n' using an array, what is the maximum size of the array required?
When representing a binary tree of depth 'n' using an array, what is the maximum size of the array required?
In an array representation of a binary tree, the left child of a node at index i is located at index 2*i + 1.
In an array representation of a binary tree, the left child of a node at index i is located at index 2*i + 1.
In the array representation of a binary tree, how is the index of a node's right child calculated, given the index 'i' of the node?
In the array representation of a binary tree, how is the index of a node's right child calculated, given the index 'i' of the node?
To represent a binary tree of depth 'n' using an array, one needs a ______ array with a maximum size of $2^n - 1$.
To represent a binary tree of depth 'n' using an array, one needs a ______ array with a maximum size of $2^n - 1$.
Which traversal visits the root node before the left and right subtrees?
Which traversal visits the root node before the left and right subtrees?
In an in-order traversal, the root node is visited after the left subtree but before the right subtree.
In an in-order traversal, the root node is visited after the left subtree but before the right subtree.
Which binary tree traversal method visits the root node last?
Which binary tree traversal method visits the root node last?
In a post-order traversal, after the left and right subtrees are visited, the ______ is visited.
In a post-order traversal, after the left and right subtrees are visited, the ______ is visited.
Match each tree traversal method with its correct order of visiting nodes:
Match each tree traversal method with its correct order of visiting nodes:
Given the binary tree traversal A - B - D - I - J - F - C - G - K - H, which traversal is represented?
Given the binary tree traversal A - B - D - I - J - F - C - G - K - H, which traversal is represented?
The in-order traversal of the provided tree is A - B - D - I - J - F - C - G - K - H.
The in-order traversal of the provided tree is A - B - D - I - J - F - C - G - K - H.
What is the post-order traversal sequence for the binary tree provided?
What is the post-order traversal sequence for the binary tree provided?
Flashcards
What is a Binary Tree?
What is a Binary Tree?
A tree data structure where each node has at most two children, referred to as the left child and the right child.
What is a Normal Tree?
What is a Normal Tree?
Every node in a normal tree can have any number of children.
What are some advantages of using Trees?
What are some advantages of using Trees?
Storing data in a hierarchical format, moderate access/search, insertion/deletion, and no upper limit on the number of nodes.
How to represent a binary tree using an array?
How to represent a binary tree using an array?
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How to represent a binary tree using Linked List?
How to represent a binary tree using Linked List?
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What is Tree Traversal?
What is Tree Traversal?
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What is Pre-Order Traversal?
What is Pre-Order Traversal?
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What is In-Order Traversal?
What is In-Order Traversal?
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What is Post-Order Traversal?
What is Post-Order Traversal?
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Study Notes
- Binary Tree 1, Algorithms 2
Binary Tree
- A binary tree is a data structure where each node has a maximum of two children, referred to as the left child and the right child.
- In a normal tree, nodes can have any number of children.
- In a binary tree, nodes can have 0, 1, or 2 children, but not more than 2.
- Trees are used to store information that naturally forms a hierarchy.
- Trees with ordering(i.e BST) allow moderate access and search capabilities, quicker than linked lists but slower than arrays.
- Trees provide moderate insertion and deletion speeds, quicker than arrays but slower than unordered linked lists.
- Like linked lists, trees don't have an upper limit on the number of nodes. Nodes are linked using pointers.
BT (Binary Tree) Representations
- Binary trees can be represented using arrays or linked lists.
- For array representation of a binary tree of depth 'n', a one-dimensional array with a maximum size of 2^n - 1 is needed.
- In an array, starting from the root:
- The left child of a node at index i will be at index 2*i.
- The right child of a node at index i will be at index 2*i + 1.
- Representation via linked list contains the Data, a Left Child Address, and a Right Child Address
BT Traversals
- Tree traversal involves visiting each node in the tree in a specific order.
- There are three common types of traversals: Pre-Order, In-Order, and Post-Order.
Pre-Order Traversal
- Steps:
- Visit the current node, if the node exists.
- Recursively traverse the left subtree.
- Recursively traverse the right subtree.
- Example: A - B - D - I - J - F - C - G - K - H
In-Order Traversal
- Steps:
- Recursively traverse the left subtree.
- Visit the current node, if the node exists.
- Recursively traverse the right subtree.
- Example: I - D -J - B - F - A - G -K-C-H
Post-Order Traversal
- Steps:
- Recursively traverse the left subtree.
- Recursively traverse the right subtree.
- Visit the current node, if the node exists.
- Example: I-J-D-F- B - K - G - H - C - A
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