Binary Tree Traversal Quiz: Time Complexity Explained

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Questions and Answers

What is the defining characteristic of the Preorder traversal?

The root is visited last

Each node is visited before its children are visited (correct)

Every node is visited after its descendents are visited

The children of a node are visited before the node itself

Which traversal requires a postorder approach for calculating the space occupied by files and directories in a file system?

Preorder traversal

Inorder traversal

Postorder traversal (correct)

None of the above

What is the time complexity of preorder traversal?

T(n) = O(1)

T(n) = O(n^2)

T(n) = O(n log n)

T(n) = O(n) (correct)

What is the defining characteristic of Postorder traversal?

Every node is visited after its descendents are visited Signup and view all the answers

Which tree traversal visits the root node last?

Postorder traversal Signup and view all the answers

What is the time complexity of post order traversal of a tree?

O(n) Signup and view all the answers

Which type of tree traversal can be best described by an expression tree?

Inorder traversal Signup and view all the answers

What is the total number of nodes in a binary tree with depth d?

$2^{d+1} - 1$ Signup and view all the answers

If a binary tree contains n nodes, how many edges does it contain?

$n - 1$ Signup and view all the answers

What is the height of a binary tree containing 100 nodes?

$\lceil\log_{2}(100 + 1)\rceil$ Signup and view all the answers

What is the defining characteristic of Inorder traversal?

The children of a node are visited before the node itself Signup and view all the answers

What is the time complexity of postorder traversal?

T(n) = O(n) Signup and view all the answers

Which traversal requires a postorder approach for calculating the space occupied by files and directories in a file system?

Postorder traversal Signup and view all the answers

What type of tree traversal can be best described by an expression tree?

Inorder traversal Signup and view all the answers

What is the defining characteristic of Preorder traversal?

The root is visited first Signup and view all the answers

In a binary tree with 100 nodes, what is the minimum and maximum possible height of the tree?

Minimum height is 7 and maximum height is 99 Signup and view all the answers

What is the total number of nodes in a binary tree of height 5?

32 Signup and view all the answers

Which tree traversal visits the root node first?

Preorder traversal Signup and view all the answers

If a full binary tree has 63 vertices, how many leaves does it have?

127 Signup and view all the answers

What is the maximum number of nodes in a level l of a binary tree?

$2^{(l+1)}$ Signup and view all the answers

Study Notes

Tree Traversals

Preorder traversal visits the root node first, followed by left and then right subtrees.
Postorder traversal is optimal for calculating space in file systems as it processes children before the parent node.
Time complexity for preorder traversal is O(n), where n is the number of nodes.
In postorder traversal, the root node is visited last after traversing left and right subtrees.
Time complexity for postorder traversal is also O(n).

Types of Tree Traversals

Expression trees are best represented using preorder traversal, as they reflect the order of operations.
Inorder traversal visits nodes in a sequence where the left subtree is processed first, then the root, and finally the right subtree.

Binary Tree Properties

A binary tree with depth d will contain a total of 2^(d+1) - 1 nodes.
If a binary tree has n nodes, it contains exactly n - 1 edges.
The height of a binary tree can vary; with 100 nodes, the minimum height is 7 (perfectly balanced) and the maximum is 100 (degenerate tree).
In a full binary tree with 63 vertices, there are 32 leaves.
The maximum number of nodes at level l of a binary tree is 2^l.

Additional Notes

The relationship between height and nodes in binary trees indicates that as the number of nodes increases, the structure can vary from balanced (minimum height) to skewed (maximum height).

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Description

Test your knowledge about the three types of tree traversals: Preorder, Postorder, and Inorder. Learn about the algorithms and examples for pre order traversal, and enhance your understanding of how nodes are visited in different sequences.