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 the same set in a Disjoint Set Union, what will the 'Find' operation return for both elements?
A.Different roots
B.The same root
C.An error
D.The size of the set
Solution
If two elements belong to the same set in a Disjoint Set Union, the 'Find' operation will return the same root for both elements.
Correct Answer: B — The same root
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' operation do?
A.Combines two sets into one
B.Finds the maximum element in a set
C.Removes an element from a set
D.Sorts the elements in a set
Solution
The 'Union' operation combines two sets into one in the Disjoint Set Union data structure.
Correct Answer: A — Combines two sets into one
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 union by rank in Disjoint Set Union?
A.It increases the size of the sets
B.It minimizes the height of the trees
C.It allows for faster sorting
D.It simplifies the code
Solution
The main advantage of using union by rank is that it minimizes the height of the trees, leading to more efficient 'Find' operations.
Correct Answer: B — It minimizes the height of the trees
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 result of performing a 'Union' operation on two sets A and B in Disjoint Set Union?
A.A and B remain separate
B.A and B are merged into one set
C.A is deleted
D.B is deleted
Solution
Performing a 'Union' operation on two sets A and B merges them into one set, effectively combining their elements.
Correct Answer: B — A and B are merged into one set
Q. What is the result of performing a 'Union' operation on two sets that are already connected in Disjoint Set Union?
A.The sets remain unchanged
B.A new set is created
C.An error occurs
D.The operation fails
Solution
If two sets are already connected, performing a 'Union' operation on them will leave the sets unchanged, as they are already part of the same set.
Correct Answer: A — The sets remain unchanged
Q. What is the result of performing a 'Union' operation on two sets that are already connected?
A.The sets remain unchanged
B.A new set is created
C.An error occurs
D.The sets are split
Solution
Performing a 'Union' operation on two sets that are already connected leaves the sets unchanged.
Correct Answer: A — The sets remain unchanged
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.
Correct Answer: D — O(α(n))
Q. What technique is commonly used to optimize the 'Find' operation in Disjoint Set Union?
A.Binary Search
B.Path Compression
C.Merge Sort
D.Heapify
Solution
Path Compression is a technique used to optimize the 'Find' operation by flattening the structure of the tree whenever 'Find' is called.
Correct Answer: B — Path Compression
Q. Which of the following is NOT a characteristic of Disjoint Set Union?
A.Supports dynamic connectivity
B.Allows for efficient merging of sets
C.Requires elements to be contiguous in memory
D.Can be implemented with trees
Solution
Disjoint Set Union does not require elements to be contiguous in memory; it can be implemented with trees or arrays.
Correct Answer: C — Requires elements to be contiguous in memory
Q. Which of the following is NOT a characteristic of the Disjoint Set Union data structure?
A.Supports union and find operations
B.Can handle dynamic connectivity
C.Maintains a sorted order of elements
D.Can be implemented using trees
Solution
Maintaining a sorted order of elements is NOT a characteristic of the Disjoint Set Union data structure; it focuses on managing disjoint sets.
Correct Answer: C — Maintains a sorted order of elements
Q. Which of the following is NOT a characteristic of the Disjoint Set Union?
A.Supports union and find operations
B.Can handle dynamic connectivity
C.Requires elements to be integers
D.Can be implemented with trees
Solution
Disjoint Set Union does not require elements to be integers; it can handle any type of elements as long as they can be uniquely identified.
Correct Answer: C — Requires elements to be integers
Q. Which of the following scenarios is best suited for using a Disjoint Set Union?
A.Finding the maximum element in an array
B.Detecting cycles in a graph
C.Sorting a list of numbers
D.Searching for an element in a sorted array
Solution
Disjoint Set Union is particularly useful for detecting cycles in a graph, as it can efficiently manage and merge sets of connected components.
Correct Answer: B — Detecting cycles in a graph
Q. Which of the following scenarios is best suited for using Disjoint Set Union?
A.Finding the maximum element in an array
B.Detecting cycles in a graph
C.Sorting a list of numbers
D.Searching for an element in a linked list
Solution
Disjoint Set Union is best suited for detecting cycles in a graph, as it efficiently manages connected components.
Correct Answer: B — Detecting cycles in a graph
Q. Which operation in the Disjoint Set Union is used to determine which set a particular element belongs to?
A.Union
B.Find
C.Insert
D.Delete
Solution
The 'Find' operation is used to determine which set a particular element belongs to in the Disjoint Set Union.
