Almost Complete Binary Tree MCQ Quiz - Objective Question with Answer for Almost Complete Binary Tree - Download Free PDF

The correct answer is Option 4.

Key Points

• Prim's Algorithm:
  • Prim's Algorithm is used to find the Minimum Spanning Tree (MST) for a weighted undirected graph.
  • It starts from an arbitrary node and explores all the adjacent nodes using BFS to find the edge with the smallest weight that connects the tree to a new vertex.
  • It continues this process until all vertices are included in the MST.
• Dijkstra's Algorithm:
  • Dijkstra's Algorithm is used for finding the shortest paths between nodes in a graph.
  • It starts from the source node and uses BFS to explore all possible paths to other nodes, selecting the path with the smallest cumulative weight.
  • It is particularly useful for graphs with non-negative weights.

Additional Information

• Both Prim's and Dijkstra's algorithms rely on the BFS approach to explore nodes level by level, ensuring that the shortest path or smallest weight edge is chosen at each step.
• Prim's Algorithm is specifically used for creating MSTs, whereas Dijkstra's is for shortest path problems.
• While BFS is a fundamental concept, both algorithms incorporate additional logic, such as priority queues, to optimize their respective goals.

The Correct answer is : A, B, C & D are correct.Key Points

• A. Red Black Tree: ✅ True
  A Red-Black Tree is a self-balancing BST that guarantees O(log n) time for search, insert, and delete operations in the worst case.
• B. Trie: ✅ True
  Tries (prefix trees) are used for efficient prefix-based searching and are common in applications like autocomplete and dictionary lookups.
• C. AVL Tree: ✅ True
  AVL Trees are also self-balancing BSTs with a stricter balancing condition than Red-Black Trees (balance factor must be -1, 0, or 1). So this statement is also true.
• D. B-Tree: ✅ True
  B-Trees are optimized for disk-based storage systems and support efficient search, insert, and delete operations with fewer disk reads.

Conclusion: All options A, B, C, and D are correct.

Data:

Internal node with degree 1 = i = 12

Internal node with degree 2 = n = 29

Formula:

number of leaf nodes = n + 1

Calculation:

number of leaf nodes = 29 + 1 = 30

Examples:

It has 4 internal nodes with degree 2

∴ number of leaf nodes is 4 + 1 = 5.

In splay tree, the node that is inserted in the last will become the root of the tree. Splay tree are the self-adjusting form of binary search tree. In an n node splay tree, all the search tree operations takes O(log n) time.

• Every single operation in splay tree cannot be guaranteed to be efficient since element on which operation(search) is performed may not be root.
• for sufficiently long access sequences, splay trees are very efficient as they use a simple restructuring method.
• They avoid the worst-case time of all operations of binary search tree.

Max heap:

Deletion of 30

Deletion of 25

Sequence of Array element: 23, 22, 18, 12, 15, 10, 14

Important Points:

Since only two search keys (30 and 25) are missing in the option those two keys have been deleted.

Types of nodes in a Binary Tree:

Interval (i):

(i) Root node (single node), degree = 2

(ii) Node with 1 child, degree = 2

(iii) Non root node with 2 children, degree = 3

Load (l):

Degree = 1

Total nodes = n = i + l

Also $\sum _{i=l}^n{d}_i=2\left(n-1\right)$

$2+i_1\times 2+i_2\times 3+l\times 1=2\left(n-1\right)$

Also, $n=1+i_1+i_2+l$

$\begin{array}{l}{i}_1=n-l-i_2-1\\ \therefore 2+\left(n-l-i_2-1\right)\times 2+i_2\times 3+l\times 1\end{array}$

= 2n – 2

$\begin{array}{l}{i}_2-l=-2\\ i_2=l-2\end{array}$

Also, Total number of interval nodes with

2 children = i₂ + 1(root)

$=l-2+1=l-1$

= 200 - 1 = 199

The correct answer is Option 4.

Key Points

• Prim's Algorithm:
  • Prim's Algorithm is used to find the Minimum Spanning Tree (MST) for a weighted undirected graph.
  • It starts from an arbitrary node and explores all the adjacent nodes using BFS to find the edge with the smallest weight that connects the tree to a new vertex.
  • It continues this process until all vertices are included in the MST.
• Dijkstra's Algorithm:
  • Dijkstra's Algorithm is used for finding the shortest paths between nodes in a graph.
  • It starts from the source node and uses BFS to explore all possible paths to other nodes, selecting the path with the smallest cumulative weight.
  • It is particularly useful for graphs with non-negative weights.

Additional Information

• Both Prim's and Dijkstra's algorithms rely on the BFS approach to explore nodes level by level, ensuring that the shortest path or smallest weight edge is chosen at each step.
• Prim's Algorithm is specifically used for creating MSTs, whereas Dijkstra's is for shortest path problems.
• While BFS is a fundamental concept, both algorithms incorporate additional logic, such as priority queues, to optimize their respective goals.

The Correct answer is : A, B, C & D are correct.Key Points

• A. Red Black Tree: ✅ True
  A Red-Black Tree is a self-balancing BST that guarantees O(log n) time for search, insert, and delete operations in the worst case.
• B. Trie: ✅ True
  Tries (prefix trees) are used for efficient prefix-based searching and are common in applications like autocomplete and dictionary lookups.
• C. AVL Tree: ✅ True
  AVL Trees are also self-balancing BSTs with a stricter balancing condition than Red-Black Trees (balance factor must be -1, 0, or 1). So this statement is also true.
• D. B-Tree: ✅ True
  B-Trees are optimized for disk-based storage systems and support efficient search, insert, and delete operations with fewer disk reads.

Conclusion: All options A, B, C, and D are correct.

Data:

Internal node with degree 1 = i = 12

Internal node with degree 2 = n = 29

Formula:

number of leaf nodes = n + 1

Calculation:

number of leaf nodes = 29 + 1 = 30

Examples:

It has 4 internal nodes with degree 2

∴ number of leaf nodes is 4 + 1 = 5.

Max heap:

Deletion of 30

Deletion of 25

Sequence of Array element: 23, 22, 18, 12, 15, 10, 14

Important Points:

Since only two search keys (30 and 25) are missing in the option those two keys have been deleted.

Types of nodes in a Binary Tree:

Interval (i):

(i) Root node (single node), degree = 2

(ii) Node with 1 child, degree = 2

(iii) Non root node with 2 children, degree = 3

Load (l):

Degree = 1

Total nodes = n = i + l

Also $\sum _{i=l}^n{d}_i=2\left(n-1\right)$

$2+i_1\times 2+i_2\times 3+l\times 1=2\left(n-1\right)$

Also, $n=1+i_1+i_2+l$

$\begin{array}{l}{i}_1=n-l-i_2-1\\ \therefore 2+\left(n-l-i_2-1\right)\times 2+i_2\times 3+l\times 1\end{array}$

= 2n – 2

$\begin{array}{l}{i}_2-l=-2\\ i_2=l-2\end{array}$

Also, Total number of interval nodes with

2 children = i₂ + 1(root)

$=l-2+1=l-1$

= 200 - 1 = 199

In splay tree, the node that is inserted in the last will become the root of the tree. Splay tree are the self-adjusting form of binary search tree. In an n node splay tree, all the search tree operations takes O(log n) time.

• Every single operation in splay tree cannot be guaranteed to be efficient since element on which operation(search) is performed may not be root.
• for sufficiently long access sequences, splay trees are very efficient as they use a simple restructuring method.
• They avoid the worst-case time of all operations of binary search tree.

The correct answer is Option 4.

Key Points

• Prim's Algorithm:
  • Prim's Algorithm is used to find the Minimum Spanning Tree (MST) for a weighted undirected graph.
  • It starts from an arbitrary node and explores all the adjacent nodes using BFS to find the edge with the smallest weight that connects the tree to a new vertex.
  • It continues this process until all vertices are included in the MST.
• Dijkstra's Algorithm:
  • Dijkstra's Algorithm is used for finding the shortest paths between nodes in a graph.
  • It starts from the source node and uses BFS to explore all possible paths to other nodes, selecting the path with the smallest cumulative weight.
  • It is particularly useful for graphs with non-negative weights.

Additional Information

• Both Prim's and Dijkstra's algorithms rely on the BFS approach to explore nodes level by level, ensuring that the shortest path or smallest weight edge is chosen at each step.
• Prim's Algorithm is specifically used for creating MSTs, whereas Dijkstra's is for shortest path problems.
• While BFS is a fundamental concept, both algorithms incorporate additional logic, such as priority queues, to optimize their respective goals.

The Correct answer is : A, B, C & D are correct.Key Points

• A. Red Black Tree: ✅ True
  A Red-Black Tree is a self-balancing BST that guarantees O(log n) time for search, insert, and delete operations in the worst case.
• B. Trie: ✅ True
  Tries (prefix trees) are used for efficient prefix-based searching and are common in applications like autocomplete and dictionary lookups.
• C. AVL Tree: ✅ True
  AVL Trees are also self-balancing BSTs with a stricter balancing condition than Red-Black Trees (balance factor must be -1, 0, or 1). So this statement is also true.
• D. B-Tree: ✅ True
  B-Trees are optimized for disk-based storage systems and support efficient search, insert, and delete operations with fewer disk reads.

Conclusion: All options A, B, C, and D are correct.

Max heap:

Level Order Traversal 

Therefore 25 will be at index 2.