Disjoint Set Union (Union Find) MCQ & Objective Questions
Disjoint Set Union (Union Find) is a crucial topic in computer science that students must master for their exams. Understanding this concept not only enhances problem-solving skills but also boosts performance in objective questions and MCQs. Practicing Disjoint Set Union (Union Find) MCQs helps students identify important questions and solidify their knowledge, making exam preparation more effective.
What You Will Practise Here
Fundamentals of Disjoint Set Union (Union Find) and its applications.
Key operations: Union and Find, and their implementations.
Path compression technique for optimizing the Find operation.
Union by rank to improve efficiency in merging sets.
Real-world applications of Disjoint Set Union in algorithms.
Common problems and challenges associated with Union Find.
Diagrams illustrating the structure of disjoint sets.
Exam Relevance
The Disjoint Set Union (Union Find) topic is frequently included in various examinations such as CBSE, State Boards, NEET, and JEE. Students can expect questions that test their understanding of the basic operations and efficiency of the algorithm. Common patterns include scenario-based questions where students must apply Union Find to solve problems related to connectivity and grouping.
Common Mistakes Students Make
Confusing the Union and Find operations, leading to incorrect implementations.
Neglecting the importance of path compression, resulting in inefficient solutions.
Overlooking the significance of union by rank, which can affect performance.
Failing to visualize the disjoint sets, making it hard to understand merging.
FAQs
Question: What is the main purpose of the Disjoint Set Union (Union Find) algorithm? Answer: The main purpose is to efficiently manage and merge disjoint sets while allowing quick queries to determine which set an element belongs to.
Question: How does path compression improve the efficiency of the Union Find algorithm? Answer: Path compression flattens the structure of the tree whenever Find is called, making future queries faster by reducing the height of the tree.
Now is the time to enhance your understanding of Disjoint Set Union (Union Find). Dive into our practice MCQs and test your knowledge to excel in your exams!
Q. How does path compression affect the structure of the Disjoint Set Union?
A.
It increases the depth of the trees
B.
It flattens the trees to make future queries faster
C.
It creates new sets
D.
It has no effect on the structure
Solution
Path compression flattens the trees in the Disjoint Set Union, making future queries faster by reducing the depth of the trees.
Correct Answer:
B
— It flattens the trees to make future queries faster
Q. If two elements belong to different sets, what will the 'Find' operation return after a 'Union' operation is performed on them?
A.
The first element's set identifier
B.
The second element's set identifier
C.
A new unique identifier
D.
An error message
Solution
After a 'Union' operation is performed on two elements from different sets, the 'Find' operation will return a new unique identifier representing the combined set.
Q. In the context of Disjoint Set Union, what does the 'Union by Rank' optimization do?
A.
It merges two sets based on their size
B.
It keeps track of the height of trees to minimize depth
C.
It sorts the elements in each set
D.
It finds the maximum element in a set
Solution
The 'Union by Rank' optimization keeps track of the height of trees to minimize depth, ensuring that the smaller tree is always added under the root of the larger tree.
Correct Answer:
B
— It keeps track of the height of trees to minimize depth
Q. In the context of Disjoint Set Union, what does the 'Union by Rank' technique do?
A.
It merges two sets based on their size
B.
It merges two sets based on their depth
C.
It keeps track of the number of elements in each set
D.
It optimizes the 'Find' operation
Solution
The 'Union by Rank' technique merges two sets based on their depth, ensuring that the smaller tree is always added under the root of the larger tree to keep the overall tree shallow.
Correct Answer:
B
— It merges two sets based on their depth
Q. In the context of Disjoint Set Union, what does the term 'union by rank' refer to?
A.
Combining two sets based on their size
B.
Combining two sets based on their depth
C.
Finding the maximum element in a set
D.
Sorting elements in a set
Solution
Union by rank refers to the strategy of combining two sets by attaching the smaller tree under the root of the larger tree, thus keeping the overall tree shallow.
Correct Answer:
B
— Combining two sets based on their depth
Q. What is the main advantage of using path compression in Disjoint Set Union?
A.
It reduces the number of elements in a set
B.
It speeds up the union operation
C.
It flattens the structure of the tree for faster future queries
D.
It allows for duplicate elements
Solution
The main advantage of using path compression is that it flattens the structure of the tree, leading to faster future queries by reducing the depth of the trees.
Correct Answer:
C
— It flattens the structure of the tree for faster future queries
Q. What is the primary purpose of the Disjoint Set Union (Union Find) data structure?
A.
To sort elements efficiently
B.
To find the shortest path in a graph
C.
To manage a collection of disjoint sets
D.
To implement a stack
Solution
The primary purpose of the Disjoint Set Union (Union Find) data structure is to manage a collection of disjoint sets, allowing for efficient union and find operations.
Correct Answer:
C
— To manage a collection of disjoint sets
Q. What is the time complexity of the 'Union' operation in an optimized Disjoint Set Union with path compression and union by rank?
A.
O(1)
B.
O(log n)
C.
O(n)
D.
O(α(n))
Solution
The time complexity of the 'Union' operation in an optimized Disjoint Set Union with path compression and union by rank is O(α(n)), where α is the inverse Ackermann function.
Q. What technique is commonly used in Disjoint Set Union to optimize the 'Find' operation?
A.
Binary Search
B.
Path Compression
C.
Merge Sort
D.
Heapify
Solution
Path Compression is a technique used in Disjoint Set Union to optimize the 'Find' operation by flattening the structure of the tree whenever 'Find' is called.
Q. Which of the following is NOT a typical application of Disjoint Set Union?
A.
Network connectivity
B.
Kruskal's algorithm for minimum spanning tree
C.
Finding the shortest path in a graph
D.
Image processing for region labeling
Solution
Finding the shortest path in a graph is not a typical application of Disjoint Set Union; it is more related to algorithms like Dijkstra's or Bellman-Ford.
Correct Answer:
C
— Finding the shortest path in a graph
