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A priority queue Q is used to implement a stack that stores characters. PUSH (C) is implemented INSERT (Q, C, K) where K is an appropriate integer key chosen by the implementation. POP is implemented as DELETEMIN(Q). For a sequence of operations, the keys chosen are in
- a)Non-increasing order
- b)Non-decreasing order
- c)Strictly increasing order
- d)Strictly decreasing order
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A priority queue Q is used to implement a stack that stores characters...
In stack last element will be deleted first but according to question, it should be wprk like queue. So last element deleted at last, for that we give lower priority to last element. So all elements should be in strictly decreasing order.
Most Upvoted Answer
A priority queue Q is used to implement a stack that stores characters...
Understanding the Priority Queue Implementation for Stack
In this implementation, a priority queue Q is used to simulate a stack's LIFO (Last In, First Out) behavior. The operations PUSH and POP are mapped to priority queue operations.
Operation Breakdown
- PUSH (C): This operation is implemented using `INSERT(Q, C, K)`, where K is a key that affects the ordering in the priority queue.
- POP: This is implemented using `DELETEMIN(Q)`, which removes the element with the highest priority (or the lowest key).
Choosing Keys for Stack Behavior
To ensure that the stack behaves correctly (LIFO), the keys assigned during the PUSH operation must be chosen appropriately:
- Strictly Decreasing Order: If we assign keys in strictly decreasing order (K1 > K2 > K3...), the most recently pushed element will always have the lowest key. This means that when we call `DELETEMIN(Q)`, the element with the highest priority (the one with the lowest key) is removed first, mimicking the stack behavior.
Why Other Options Fail
- Non-Increasing Order: This could lead to ambiguity since multiple elements could have the same key, resulting in a violation of the strict LIFO order.
- Non-Decreasing Order: This would prioritize earlier elements over later ones, essentially reversing the stack behavior.
- Strictly Increasing Order: This would also fail to maintain LIFO since the earliest pushed element would be removed first.
Conclusion
Thus, using strictly decreasing keys ensures that the stack's LIFO property is maintained, making option 'D' the correct choice for implementing a stack using a priority queue.
In this implementation, a priority queue Q is used to simulate a stack's LIFO (Last In, First Out) behavior. The operations PUSH and POP are mapped to priority queue operations.
Operation Breakdown
- PUSH (C): This operation is implemented using `INSERT(Q, C, K)`, where K is a key that affects the ordering in the priority queue.
- POP: This is implemented using `DELETEMIN(Q)`, which removes the element with the highest priority (or the lowest key).
Choosing Keys for Stack Behavior
To ensure that the stack behaves correctly (LIFO), the keys assigned during the PUSH operation must be chosen appropriately:
- Strictly Decreasing Order: If we assign keys in strictly decreasing order (K1 > K2 > K3...), the most recently pushed element will always have the lowest key. This means that when we call `DELETEMIN(Q)`, the element with the highest priority (the one with the lowest key) is removed first, mimicking the stack behavior.
Why Other Options Fail
- Non-Increasing Order: This could lead to ambiguity since multiple elements could have the same key, resulting in a violation of the strict LIFO order.
- Non-Decreasing Order: This would prioritize earlier elements over later ones, essentially reversing the stack behavior.
- Strictly Increasing Order: This would also fail to maintain LIFO since the earliest pushed element would be removed first.
Conclusion
Thus, using strictly decreasing keys ensures that the stack's LIFO property is maintained, making option 'D' the correct choice for implementing a stack using a priority queue.
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A priority queue Q is used to implement a stack that stores characters. PUSH (C) is implemented INSERT (Q, C, K) where K is an appropriate integer key chosen by the implementation. POP is implemented as DELETEMIN(Q). For a sequence of operations, the keys chosen are ina)Non-increasing orderb)Non-decreasing orderc)Strictly increasing orderd)Strictly decreasing orderCorrect answer is option 'D'. Can you explain this answer?
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