Binary Tree Traversal Methods Quiz
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Questions and Answers

What is the primary strategy used in depth-first search (DFS)?

  • Starts from the root and explores all depth nodes before backtracking. (correct)
  • Only examines leaf nodes in the binary tree first.
  • Visits nodes in a breadth-first manner.
  • Explores all nodes at a present depth level first.

Which method would you use to explore nodes at the current level before moving deeper into the tree?

  • Breadth-First Search (BFS) (correct)
  • Heuristic Search
  • Random Search
  • Depth-First Search (DFS)

What does the DFS function return if the value being searched for is not found?

  • The node containing the value
  • An error message
  • True
  • False (correct)

In the context of BFS, what signifies the end of the search process?

<p>Finding the node with the desired value. (C)</p> Signup and view all the answers

What is indicated when the DFS search function's root parameter is null?

<p>The tree is empty. (D)</p> Signup and view all the answers

What are the three main components of a node in a binary tree?

<p>Data, Pointer to left child, Pointer to right child (C)</p> Signup and view all the answers

What traversal method does Breadth-First Search (BFS) use in a binary tree?

<p>Queues (D)</p> Signup and view all the answers

Which of the following is NOT a method used in Depth-First Search (DFS) traversal for binary trees?

<p>Level order (D)</p> Signup and view all the answers

What does the preorder traversal function do first?

<p>Processes the root node (B)</p> Signup and view all the answers

What is the role of the 'root' pointer in the BinaryTree class?

<p>It points to the topmost node in the tree (B)</p> Signup and view all the answers

In the context of BFS, what is another name for Level Order Traversal?

<p>Depth Level Traversal (B)</p> Signup and view all the answers

What happens in the preorder traversal if the current node is null?

<p>The function stops and returns (D)</p> Signup and view all the answers

Which technique is primarily used to implement Depth-First Search (DFS) in binary trees?

<p>Recursion (C)</p> Signup and view all the answers

What characterizes a full binary tree?

<p>Every node has either 0 or 2 child nodes. (B)</p> Signup and view all the answers

Which type of tree allows for more than two child nodes per parent?

<p>General Tree (A)</p> Signup and view all the answers

In a complete binary tree, which of the following statements is true?

<p>All levels must be completely filled except possibly the last. (D)</p> Signup and view all the answers

What is the height of a binary tree with 4 levels?

<p>5 (C)</p> Signup and view all the answers

Which of the following trees has all leaf nodes at the same level?

<p>Perfect Binary Tree (A)</p> Signup and view all the answers

What distinguishes a binary search tree (BST) from other types of binary trees?

<p>All left descendants are less than the node and all right descendants are greater. (B)</p> Signup and view all the answers

Which tree type can have more than two children but has no specific rules for hierarchy?

<p>General Tree (D)</p> Signup and view all the answers

What is the depth of a binary tree with a height of 5?

<p>4 (C)</p> Signup and view all the answers

What is the definition of a leaf node in a binary tree?

<p>A node that has no children or both children are null. (A)</p> Signup and view all the answers

Which statement about the height of a binary tree is correct?

<p>Height is the total number of nodes from the root to the deepest leaf node. (B), Height can be at least log2(N+1) for N nodes. (C)</p> Signup and view all the answers

How is the depth of a node defined in a binary tree?

<p>The total number of edges from a specific node to the root node. (A)</p> Signup and view all the answers

What is the maximum number of nodes in a binary tree of height H?

<p>2H - 1 (D)</p> Signup and view all the answers

What does the degree of a node represent in a binary tree?

<p>The total number of child nodes that a node has. (B)</p> Signup and view all the answers

What is true about the root node of a binary tree?

<p>It has no parent and is the starting point for all nodes. (C)</p> Signup and view all the answers

In terms of nodes in a binary tree, which of the following statements is accurate?

<p>The minimum number of nodes is equal to the height of the tree. (D)</p> Signup and view all the answers

Which of the following defines the in-degree of a node?

<p>It is the number of edges arriving at that node. (A)</p> Signup and view all the answers

Flashcards

What is a Tree?

A tree is a hierarchical data structure where nodes are connected by edges. It resembles an upside-down tree, with a root at the top and branches extending downwards.

General Tree

A general tree has no restrictions on the number of children a node can have. It can have zero, one, or multiple subtrees.

Binary Tree

A binary tree is a tree where each node has at most two children, known as the left child and the right child. The topmost node is the root, and the bottommost nodes are called leaves.

Full Binary Tree

In a full binary tree, every node has either zero or two child nodes. It's like a tree completely filled with leaves, with no gaps.

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Complete Binary Tree

A complete binary tree is a binary tree with two properties: every level is completely filled, except possibly the last, and all nodes are positioned as far left as possible. It's like a tree packed tightly.

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Perfect Binary Tree

A perfect binary tree is a binary tree where all leaf nodes are at the same level, and every node except leaf nodes has two children. It's like a perfectly balanced tree.

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Prefix Tree (Trie)

A prefix tree (Trie) is a specialized tree used for efficient storage and retrieval of strings based on prefixes.

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B-Tree

A B-tree is a self-balancing tree structure designed for efficient storage and retrieval of data on disk. It's optimized for accessing data in large volumes.

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Root Node

The topmost node in a tree, with no parent. It's the starting point for all nodes.

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Parent Node

A node that has one or more child nodes. In a binary tree, each node can have at most two children.

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Child Node

A node that is a descendant of another node (its parent).

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Leaf Node

A node with no children. It's like the end of a branch.

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Edge

A connection between two nodes, representing the relationship between a parent and a child.

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Path

A sequence of consecutive edges, forming a path from one node to another.

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Depth of a Node

The number of edges from a specific node to the root node. The root node has a depth of zero.

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Height of a Binary Tree

The maximum number of nodes on the path from the root node to the deepest leaf node.

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What is a Binary Tree?

A binary tree is a hierarchical data structure where each node has at most two children, known as the left child and the right child. The topmost node is the root, and the bottommost nodes are called leaves.

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What are the parts of a Binary Tree Node?

A node in a binary tree consists of three parts: data, a pointer to the left child, and a pointer to the right child.

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What is Binary Tree Traversal?

Traversal in a binary tree involves visiting all nodes in a specific order. There are two main categories of traversal algorithms: Breadth-First Search (BFS) and Depth-First Search (DFS).

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What is Breadth-First Search (BFS) in a Binary Tree?

Breadth-First Search (BFS) explores all nodes at the current level before moving to the next level. It is typically implemented using a queue.

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What is Depth-First Search (DFS) in a Binary Tree?

Depth-First Search (DFS) explores as far down a branch as possible before backtracking. It is implemented using recursion. The main traversal methods in DFS for binary trees are: Preorder, Inorder, and Postorder.

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What is Preorder Traversal in a Binary Tree?

Preorder traversal visits the root node first, then recursively traverses the left subtree, and finally the right subtree. The order is: Root - Left - Right.

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What is a Balanced Binary Tree?

A binary tree is considered balanced if the height of the left subtree and the height of the right subtree of every node differ by at most one. This ensures efficient search and insertion operations.

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How do you insert a new node into a Binary Tree?

Inserting a new node in a binary tree involves finding its appropriate position based on the value of the node and the tree's structure. The insertion process ensures that the tree remains valid and maintains its properties.

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What is Depth-First Search (DFS) in a tree?

Depth-First Search (DFS) explores the depth of the tree first, traversing as far as possible along one branch before backtracking and trying another path.

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What is Breadth-First Search (BFS) in a tree?

Breadth-First Search (BFS) explores all nodes at the current level before moving on to the next level. This is like exploring a maze level by level.

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How does Depth-First Search (DFS) find a value in a tree?

A recursive function is used to traverse through branches of the tree to check if a value exists. When the searched value is found, it returns true; otherwise, it continues exploring.

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When is a value considered found in DFS?

A value is considered to be found if it matches the data of a visited node during traversal.

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What happens in a DFS search if a value is not found?

If a value is not found after traversing all nodes, the search concludes that the value does not exist in the tree. This indicates that the value is not present within the data structure.

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Study Notes

Tree Data Structure

  • A tree is a non-linear, hierarchical data structure consisting of nodes connected by edges.
  • This structure has a root node, parent nodes, child nodes, leaf nodes, and subtrees.
  • Nodes are connected by edges.
  • Trees are non-linear, unlike linear data structures such as linked lists, stacks, or queues.

Types of Trees

  • General Tree: A general tree has no constraints on the number of children a node can have. A node may have a minimum of 0 or a maximum of 'n' children.

  • Binary Tree: A binary tree is a special type of tree where each node can have a maximum of two children (left and right).

  • Binary Search Tree (BST): A binary tree where values in the left subtree are less than the root node's value and values in the right subtree are greater than the root node's value

  • Full Binary Tree: All nodes have either zero or two children. No nodes have only one child.

  • Complete Binary Tree: All levels except possibly the last are filled. The last level is filled from left to right.

  • Perfect Binary Tree: A complete binary tree where all leaf nodes are on the same level. Each internal node has two children.

Properties of Trees/Binary Trees

  • Root: The topmost node in a tree.
  • Node: A single element within a tree
  • Edge: A connection between two nodes in a tree.
  • Parent Node: A node that has one or more child nodes.
  • Child Node: A node that is directly connected to a parent node.
  • Leaf Node: A node with no children.
  • Level: The level of a node is determined by its distance from the root. The root node is at level 0.
  • Depth: The depth of a node is the number of edges from the root to that node.
  • Height: The height of a tree is the number of edges from the root to the farthest leaf node.
  • Subtree: A subtree consists of a node and all its descendants.
  • Sibling: Nodes that share the same parent.
  • Path: A sequence of edges connecting two nodes.
  • Degree of a Node: The number of child nodes a node has.

Binary Tree Operations

  • Traversal: Visiting all nodes in a specific order. (Level order, Pre-order, In order, Post-order) -Level Order: Visiting all nodes at a given level before moving to the next level.
  • Preorder: Visiting the root node, then the left subtree, then the right subtree
  • Inorder: Visiting the left subtree, then the root node, then the right subtree.
  • Postorder: Visiting the left subtree, then the right subtree, then the root node.
  • Searching: Finding a node with a specific value.
  • Insertion: Adding a new node to the tree.
  • Deletion: Removing a node from the tree.

Binary Tree Representations

  • Typically, each node in a binary tree stores:
  • Data (the value)
  • A pointer to the left child
  • A pointer to the right child

Binary Search Tree (BST):

  • A binary tree where every node's value is greater than all values in its left subtree and less than all values in its right subtree.
  • Efficient for searching.

Complexity Analysis

  • Time complexity for an operation in a BST or binary tree depends on balanced/unbalanced nature
  • Operations such a searching, insertion and deletion can take either O(n) or O(log n).

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Related Documents

Lecture 7 - Tree & BST PDF

Description

Test your knowledge on binary tree traversal techniques including Depth-First Search (DFS) and Breadth-First Search (BFS). This quiz covers key methods, components of nodes, and traversal properties essential for understanding binary trees. Perfect for computer science students eager to master these concepts!

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