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Tree Representation Quiz

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40 comprehensive questions exploring different ways to represent trees in memory and code — with 16 code examples covering pointer-based structures, arrays, adjacency lists, and tree properties like degree, height, and depth in this cpp quiz.

40 Questions
~80 minutes
1

Question 1

What is pointer-based tree representation?

cpp
struct Node {
    int data;
    Node* left;
    Node* right;
};
A
Each node contains data and pointers to children, using dynamic memory allocation to create flexible tree structures that can grow and shrink as needed during runtime
B
Nodes are stored in contiguous memory locations
C
Tree is represented using arrays only
D
Pointers are not used in tree representation
2

Question 2

In array-based tree representation, where would the left child of node at index i be located?

text
Array: [A, B, C, D, E, F, G]
Index:  0  1  2  3  4  5  6
A
At index (2*i + 1), following the heap property where left children are stored at odd indices relative to their parent in the sequential array representation
B
At index (2*i)
C
At index (i-1)
D
At index (i+1)
3

Question 3

What is the degree of a node in tree representation?

A
The number of children the node has, which determines how many pointers or array positions are needed to represent the node's connections in the tree structure
B
The depth of the node
C
The height of the subtree
D
The total number of nodes in the tree
4

Question 4

In adjacency list representation for trees, how is each node represented?

cpp
vector<vector<int>> adj = {
    {1, 2},    // node 0
    {0, 3, 4}, // node 1
    {0, 5},    // node 2
    {1},       // node 3
    {1},       // node 4
    {2}        // node 5
};
A
Each node has a list of its children, creating a graph-like structure where each index represents a node and contains references to its direct descendants in the hierarchy
B
Each node points to its parent only
C
Nodes are stored in a single array
D
Adjacency lists cannot represent trees
5

Question 5

What is the height of a tree in terms of representation?

A
The length of the longest path from root to leaf, which affects the maximum number of pointer dereferences needed and influences algorithmic time complexity for tree operations
B
The number of nodes at the deepest level
C
The total number of nodes
D
The branching factor of the root
6

Question 6

In binary tree array representation, what is the maximum number of nodes that can be stored in an array of size n?

text
Array size: n
Root at index 0
Left child: 2*i + 1
Right child: 2*i + 2
A
All n positions can be used, but the tree will be complete with nodes filled from left to right, ensuring no gaps in the array representation for optimal space usage
B
Only n/2 nodes can be stored
C
Only the first node can be stored
D
Array representation cannot store complete trees
7

Question 7

What is the depth of a node in tree representation?

text
      A (depth 0)
     / \
    B   C (depth 1)
   / \
  D   E (depth 2)
A
The number of edges from root to the node, which determines the node's level in the hierarchy and affects how many recursive calls or iterations are needed to reach it
B
The number of children the node has
C
The height of the subtree rooted at the node
D
The total number of nodes in the tree
8

Question 8

When would you choose adjacency list representation over pointer-based representation for trees?

A
When dealing with general trees where nodes can have varying numbers of children, as adjacency lists handle variable degrees more efficiently than fixed pointer structures
B
When memory is not a concern
C
When all nodes have exactly two children
D
When trees are very small
9

Question 9

In array representation of a complete binary tree, what is the parent index of a node at index i?

text
Child indices: 2*i + 1 (left), 2*i + 2 (right)
Parent index: ?
A
Floor((i-1)/2), using integer division to calculate the parent index from any child position in the array-based complete binary tree representation
B
i/2
C
i-1
D
i+1
10

Question 10

What is the memory overhead of pointer-based tree representation compared to array representation?

A
Pointer-based representation requires additional memory for storing pointer references, while array representation uses contiguous memory with calculated indices instead of explicit pointers
B
Array representation has more overhead
C
Both have the same memory overhead
D
Pointer-based representation uses less memory
11

Question 11

How does array representation handle missing nodes in an incomplete binary tree?

text
Array: [A, B, null, D, E]
Tree:   A
       / \
      B   null
     / \
    D   E
A
Missing nodes are represented by null values or unused array positions, wasting space but maintaining the complete binary tree indexing properties for existing nodes
B
Array representation cannot handle incomplete trees
C
Missing nodes are removed from the array
D
Array size is reduced dynamically
12

Question 12

What is the advantage of adjacency list representation for trees with high degree nodes?

A
Adjacency lists can efficiently store nodes with many children without wasting memory on fixed-size pointer arrays, making them ideal for trees with varying node degrees
B
They use less memory for small trees
C
They are faster for binary trees
D
They don't support tree operations
13

Question 13

In pointer-based representation, how is a binary tree node typically implemented?

cpp
struct TreeNode {
    int val;
    TreeNode* left;
    TreeNode* right;
    TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
};
A
Node structure contains data and two pointers for left and right children, enabling dynamic tree construction with null pointers indicating missing subtrees
B
Node contains only data, no pointers
C
Node contains data and parent pointer only
D
Node contains array of children
14

Question 14

What is the space complexity of array representation for a complete binary tree with n nodes?

A
O(n), using exactly n array positions for n nodes with no wasted space, providing optimal memory usage for complete tree structures
B
O(n log n)
C
O(n²)
D
O(1)
15

Question 15

How does adjacency list representation differ from adjacency matrix for tree representation?

cpp
Adjacency List: vector<vector<int>> adj(n);
Adjacency Matrix: vector<vector<int>> matrix(n, vector<int>(n, 0));
A
Adjacency lists store only existing edges with variable-length lists per node, while matrices use fixed n×n space with many zeros, making lists more memory-efficient for sparse tree structures
B
Lists are less efficient than matrices
C
Matrices are always better for trees
D
Both use the same amount of memory
16

Question 16

In array representation, how do you calculate the level of a node at index i?

text
Level = floor(log2(i + 1))
Index 0: level 0
Index 1-2: level 1
Index 3-6: level 2
A
Using floor(log2(i + 1)), which gives the level based on the binary representation and cumulative node counts at each level in the complete binary tree
B
Level equals i
C
Level equals i/2
D
Level cannot be calculated from index
17

Question 17

What is the main disadvantage of array representation for trees?

A
Fixed size and potential wasted space for incomplete trees, making dynamic insertions and deletions expensive due to the need to maintain complete tree properties
B
Too much memory overhead
C
Cannot represent tree relationships
D
Too slow for access operations
18

Question 18

In pointer-based representation, how do you represent an empty tree?

cpp
TreeNode* root = nullptr;
A
Root pointer set to nullptr, indicating no nodes exist in the tree and all operations should handle the null case appropriately
B
Root points to a node with null data
C
Empty tree cannot be represented
D
Root points to an empty array
19

Question 19

What is the time complexity to find a node's parent in array representation?

A
O(1), using the formula floor((i-1)/2) to directly calculate parent index from child index without traversal or searching through the array
B
O(n)
C
O(log n)
D
O(n log n)
20

Question 20

When implementing a tree where parent pointers are needed, which representation is most appropriate?

A
Pointer-based representation with parent pointers added to node structure, enabling bidirectional navigation and efficient ancestor queries in the tree hierarchy
B
Array representation only
C
Adjacency list without parent information
D
Parent pointers cannot be added to trees
21

Question 21

In adjacency list representation, how do you determine if a node is a leaf?

cpp
vector<vector<int>> adj;
// leaf if adj[node].empty()
A
Check if the node's adjacency list is empty, indicating no children and confirming leaf status in the tree structure
B
Check if node has maximum children
C
Check the node's index value
D
Leaves cannot be identified in adjacency lists
22

Question 22

What is the space complexity of pointer-based representation for a binary tree with n nodes?

A
O(n), requiring space for n nodes plus 2n pointers, though some pointers may be null, resulting in linear space usage proportional to the number of nodes
B
O(1)
C
O(n log n)
D
O(n²)
23

Question 23

In array representation, how do you handle trees that grow beyond the array size?

A
Array must be resized or reallocated, which can be expensive and may require copying all elements to maintain the complete binary tree indexing properties
B
Array size is automatically adjusted
C
Tree cannot grow beyond array size
D
New nodes are added without resizing
24

Question 24

What representation is best for implementing heap data structure?

A
Array representation, providing O(1) parent-child access and efficient heapify operations due to contiguous memory layout and index-based calculations
B
Pointer-based representation
C
Adjacency list representation
D
Heap cannot be implemented with arrays
25

Question 25

In adjacency list representation, how do you calculate the degree of a node?

cpp
vector<vector<int>> adj;
// degree = adj[node].size()
A
By taking the size of the node's adjacency list, which directly gives the number of children and thus the degree of the node in the tree structure
B
By counting all nodes in the tree
C
By checking the node's index
D
Degree cannot be calculated in adjacency lists
26

Question 26

What is the advantage of pointer-based representation for tree traversals?

A
Natural support for recursive algorithms with direct pointer access to children, enabling elegant implementation of depth-first traversals like inorder, preorder, and postorder
B
Faster than array representation
C
Uses less memory
D
Pointer-based representation doesn't support traversals
27

Question 27

In array representation, what is the maximum height of a tree with n nodes?

A
O(log n), as the array can represent a complete binary tree where height grows logarithmically with the number of nodes in the structure
B
O(n)
C
O(1)
D
O(n²)
28

Question 28

When would you choose array representation over pointer-based representation?

A
When implementing complete binary trees with frequent parent-child navigation, as array indexing provides faster access than pointer dereferencing in performance-critical applications
B
When trees have high degree variation
C
When memory is scarce
D
When trees need to be very dynamic
29

Question 29

In pointer-based representation, how do you implement a tree with parent pointers?

cpp
struct TreeNode {
    int val;
    TreeNode* left;
    TreeNode* right;
    TreeNode* parent;
};
A
Add parent pointer to node structure and update it during insertion, enabling upward navigation and ancestor queries while maintaining the tree's hierarchical relationships
B
Remove child pointers
C
Use only parent pointers
D
Parent pointers cannot be added
30

Question 30

What is the disadvantage of adjacency list representation for binary trees?

A
No inherent ordering of left and right children, requiring additional information to distinguish between children when the distinction matters for tree operations
B
Too much memory usage
C
Cannot represent binary trees
D
Too slow for all operations
31

Question 31

In array representation, how do you determine if a position i represents a valid node?

text
Array size: n
Valid if: i < n && array[i] != null
A
Check if i is within array bounds and the position contains a non-null value, ensuring the node exists in the tree structure and is not a placeholder for completeness
B
Check if i is greater than n
C
Check if i equals 0
D
All positions are always valid
32

Question 32

What representation is most suitable for implementing threaded binary trees?

A
Pointer-based representation with additional threading pointers, enabling efficient inorder traversal without stack space by using null pointers for thread connections
B
Array representation
C
Adjacency list representation
D
Threaded trees cannot be implemented
33

Question 33

In adjacency list representation, how do you perform a level-order traversal?

cpp
queue<int> q;
q.push(root);
while (!q.empty()) {
    int node = q.front(); q.pop();
    for (int child : adj[node]) {
        q.push(child);
    }
}
A
Use a queue to process nodes level by level, enqueueing all children of current node before moving to next level, leveraging the adjacency list structure for breadth-first traversal
B
Use recursion only
C
Level-order cannot be performed with adjacency lists
D
Use a stack instead of queue
34

Question 34

What is the memory efficiency comparison between pointer-based and array representation for sparse trees?

A
Pointer-based representation is more memory efficient for sparse trees, as null pointers use minimal space compared to unused array positions that waste memory in incomplete tree structures
B
Array representation is more efficient
C
Both have same efficiency
D
Memory efficiency doesn't matter for trees
35

Question 35

In array representation, how do you find all nodes at a specific level?

text
Level k: indices 2^k - 1 to min(n-1, 2^{k+1} - 2)
A
Calculate the index range for level k using geometric progression, where level k starts at index 2^k - 1 and provides direct access to all nodes at that level
B
Search through the entire array
C
Use recursion to find level nodes
D
Level nodes cannot be found efficiently
36

Question 36

What representation is best for implementing a tree where nodes can have arbitrary numbers of children?

A
Adjacency list representation, providing flexibility to store any number of children per node without predefined limits or wasted space for unused child pointers
B
Fixed-size array in each node
C
Binary tree representation only
D
Arbitrary children cannot be represented
37

Question 37

In pointer-based representation, what is the time complexity to access a node's children?

A
O(1) per child pointer access, but O(degree) to iterate through all children, making it efficient for direct access but proportional to node degree for complete enumeration
B
O(n) always
C
O(log n) always
D
O(1) for all children access
38

Question 38

What is the cache performance advantage of array representation?

A
Contiguous memory layout enables better cache locality and prefetching, improving performance for sequential access patterns in complete binary tree operations
B
No cache performance advantage
C
Better than pointer-based for all cases
D
Cache performance doesn't apply to trees
39

Question 39

In adjacency list representation, how do you implement tree reconstruction from the representation?

cpp
vector<int> indegree(n, 0);
for (auto& children : adj) {
    for (int child : children) {
        indegree[child]++;
    }
}
// Root has indegree 0
A
Find node with indegree 0 as root, then reconstruct tree structure by following child relationships, enabling conversion from adjacency list back to explicit tree representation
B
Cannot reconstruct tree from adjacency list
C
Use random node as root
D
Reconstruction requires additional information
40

Question 40

Considering all tree representation methods, which factor most influences the choice between pointer-based, array-based, and adjacency list representations for implementing tree data structures in performance-critical applications?

A
Tree density and access patterns, where complete trees favor arrays for locality, sparse trees need pointers for memory efficiency, and variable-degree trees require adjacency lists for flexibility in balancing space and time complexity trade-offs
B
Only memory usage
C
Only programming language used
D
Only code simplicity

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