Q. How does path compression improve the efficiency of the 'Find' operation in Disjoint Set Union?
A.
By storing the size of each set
B.
By flattening the structure of the tree
C.
By using a stack to keep track of elements
D.
By sorting the elements
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Solution
Path compression improves the efficiency of the 'Find' operation by flattening the structure of the tree, making future queries faster.
Correct Answer:
B
— By flattening the structure of the tree
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Q. How does path compression improve the efficiency of the Disjoint Set Union?
A.
By reducing the number of elements in a set
B.
By flattening the structure of the tree representing the sets
C.
By increasing the depth of the trees
D.
By merging smaller sets into larger ones
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Solution
Path compression improves efficiency by flattening the structure of the tree representing the sets, making future find operations faster.
Correct Answer:
B
— By flattening the structure of the tree representing the sets
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Q. In a Disjoint Set Union, what does the 'find' operation return?
A.
The size of the set
B.
The representative of the set
C.
The number of elements in the set
D.
The depth of the tree
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Solution
The 'find' operation in a Disjoint Set Union returns the representative (or leader) of the set containing the specified element.
Correct Answer:
B
— The representative of the set
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Q. In which scenario is the Disjoint Set Union most commonly used?
A.
Finding the shortest path in a graph
B.
Detecting cycles in a graph
C.
Sorting an array
D.
Searching for an element in a list
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Solution
The Disjoint Set Union is commonly used for detecting cycles in a graph, particularly in algorithms like Kruskal's for finding the minimum spanning tree.
Correct Answer:
B
— Detecting cycles in a graph
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Q. What is the 'union by rank' optimization in Disjoint Set Union?
A.
Always attaching the smaller tree under the larger tree
B.
Always attaching the larger tree under the smaller tree
C.
Randomly attaching trees
D.
Merging trees based on their height
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Solution
'Union by rank' optimization involves always attaching the smaller tree under the larger tree to keep the overall tree height minimized.
Correct Answer:
A
— Always attaching the smaller tree under the larger tree
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Q. What is the time complexity of the 'find' operation in a Disjoint Set Union with path compression?
A.
O(1)
B.
O(log n)
C.
O(n)
D.
O(α(n))
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Solution
The time complexity of the 'find' operation in a Disjoint Set Union with path compression is O(α(n)), where α is the inverse Ackermann function.
Correct Answer:
D
— O(α(n))
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Q. What is the time complexity of the 'find' operation in a well-optimized Disjoint Set Union with path compression?
A.
O(1)
B.
O(log n)
C.
O(n)
D.
O(α(n))
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Solution
The time complexity of the 'find' operation in a well-optimized Disjoint Set Union with path compression is O(α(n)), where α is the inverse Ackermann function.
Correct Answer:
D
— O(α(n))
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Q. What is the time complexity of the 'Union' operation in an optimized Disjoint Set Union with path compression?
A.
O(1)
B.
O(log n)
C.
O(n)
D.
O(α(n))
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Solution
The time complexity of the 'Union' operation in an optimized Disjoint Set Union with path compression is O(α(n)), where α is the inverse Ackermann function.
Correct Answer:
D
— O(α(n))
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Q. What is the worst-case time complexity of the union operation in a basic Disjoint Set Union without optimizations?
A.
O(1)
B.
O(log n)
C.
O(n)
D.
O(n^2)
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Solution
The worst-case time complexity of the union operation in a basic Disjoint Set Union without optimizations is O(n).
Correct Answer:
C
— O(n)
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Q. What technique is often used alongside Disjoint Set Union to optimize the union operation?
A.
Binary search
B.
Path compression
C.
Heap data structure
D.
Graph traversal
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Solution
Path compression is a technique used to optimize the union operation in Disjoint Set Union, making future find operations faster.
Correct Answer:
B
— Path compression
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Q. Which data structure can be efficiently implemented using Disjoint Set Union?
A.
Binary tree
B.
Graph
C.
Priority queue
D.
Sparse matrix
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Solution
Disjoint Set Union can be efficiently used to manage connected components in a graph.
Correct Answer:
B
— Graph
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Q. Which of the following algorithms utilizes Disjoint Set Union for its implementation?
A.
Dijkstra's algorithm
B.
Kruskal's algorithm
C.
Merge sort
D.
Binary search
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Solution
Kruskal's algorithm utilizes Disjoint Set Union to efficiently manage and merge sets of vertices while finding the minimum spanning tree.
Correct Answer:
B
— Kruskal's algorithm
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Q. Which of the following applications can benefit from using Disjoint Set Union?
A.
Cycle detection in a graph
B.
Binary search on sorted arrays
C.
Heap operations
D.
Dynamic programming
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Solution
Cycle detection in a graph can benefit from using Disjoint Set Union, as it helps in efficiently managing and merging sets of vertices.
Correct Answer:
A
— Cycle detection in a graph
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Q. Which of the following is NOT a typical use case for Disjoint Set Union?
A.
Kruskal's algorithm for Minimum Spanning Tree
B.
Finding connected components in a graph
C.
Implementing a priority queue
D.
Dynamic connectivity queries
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Solution
Implementing a priority queue is not a typical use case for Disjoint Set Union; it is primarily used for managing disjoint sets.
Correct Answer:
C
— Implementing a priority queue
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Q. Which of the following is NOT an application of Disjoint Set Union?
A.
Network connectivity
B.
Image processing
C.
Dynamic connectivity
D.
Sorting algorithms
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Solution
Sorting algorithms are not an application of Disjoint Set Union; it is primarily used for network connectivity and dynamic connectivity problems.
Correct Answer:
D
— Sorting algorithms
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Q. Which operation in Disjoint Set Union is used to combine two sets?
A.
Find
B.
Union
C.
Merge
D.
Connect
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Solution
The operation used to combine two sets in Disjoint Set Union is called 'Union'.
Correct Answer:
B
— Union
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