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A priority queue Q is used to implement a stack S that stores characters. PUSH(C) is implemented as 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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Most Upvoted Answer
A priority queue Q is used to implement a stack S that stores characte...
We are implementing a STACK using Priority Queue. Note that Stack implementation is always last in first out (LIFO) order.
As given “POP is implemented as DELETEMIN(Q)” that means Stack returns minimum element always.
So, we need to implement PUSH(C) using INSERT(Q, C, K) where K is key chosen from strictly-decreasing order(only this order will ensure stack will return minimum element when we POP an element). That will satify Last In First Out (LIFO) property of stack.
That is answer, option (D) is true.
Option (A) non-increasing order can not be true because two same (identical) numbers can not have same priority as priority should be distinguishable for each number.
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A priority queue Q is used to implement a stack S that stores characte...
Explanation:
The priority queue Q is used to implement a stack S, where PUSH operation is implemented as INSERT(Q, C, K) and POP operation is implemented as DELETEMIN(Q). The key K is an integer chosen by the implementation.
To understand why the correct answer is option 'D' (strictly decreasing order), let's look at the PUSH and POP operations in more detail.
PUSH Operation:
- The PUSH operation is implemented as INSERT(Q, C, K) where C is the character to be pushed onto the stack and K is the key chosen by the implementation.
- When a character is pushed onto the stack, it is added to the priority queue Q with an appropriate key.
- In order to implement the stack behavior, the key K should be chosen in such a way that the characters are sorted in decreasing order based on their keys.
- This ensures that the character with the highest priority (i.e., the character on top of the stack) has the lowest key value.
POP Operation:
- The POP operation is implemented as DELETEMIN(Q) where the character with the lowest key value is removed from the priority queue Q.
- Since the characters are stored in the priority queue Q with decreasing key values, the character with the lowest key value will be the character on top of the stack.
- Therefore, the POP operation effectively removes the character on top of the stack.
Why strictly decreasing order is the correct choice?
- If the keys chosen were in non-increasing order, it would mean that characters with the same key value can be popped in any order, which would violate the stack property of last-in, first-out (LIFO).
- If the keys chosen were in non-decreasing order, it would mean that characters with the same key value can be popped in any order, which would again violate the stack property of LIFO.
- If the keys chosen were in strictly increasing order, it would mean that the character with the lowest key value would not be on top of the stack, which would make the POP operation incorrect.
Conclusion:
- Choosing the keys in strictly decreasing order ensures that the priority queue Q behaves as a stack, where the character with the highest priority (i.e., the character on top of the stack) has the lowest key value.
- This allows the PUSH and POP operations to correctly implement the stack behavior.
The priority queue Q is used to implement a stack S, where PUSH operation is implemented as INSERT(Q, C, K) and POP operation is implemented as DELETEMIN(Q). The key K is an integer chosen by the implementation.
To understand why the correct answer is option 'D' (strictly decreasing order), let's look at the PUSH and POP operations in more detail.
PUSH Operation:
- The PUSH operation is implemented as INSERT(Q, C, K) where C is the character to be pushed onto the stack and K is the key chosen by the implementation.
- When a character is pushed onto the stack, it is added to the priority queue Q with an appropriate key.
- In order to implement the stack behavior, the key K should be chosen in such a way that the characters are sorted in decreasing order based on their keys.
- This ensures that the character with the highest priority (i.e., the character on top of the stack) has the lowest key value.
POP Operation:
- The POP operation is implemented as DELETEMIN(Q) where the character with the lowest key value is removed from the priority queue Q.
- Since the characters are stored in the priority queue Q with decreasing key values, the character with the lowest key value will be the character on top of the stack.
- Therefore, the POP operation effectively removes the character on top of the stack.
Why strictly decreasing order is the correct choice?
- If the keys chosen were in non-increasing order, it would mean that characters with the same key value can be popped in any order, which would violate the stack property of last-in, first-out (LIFO).
- If the keys chosen were in non-decreasing order, it would mean that characters with the same key value can be popped in any order, which would again violate the stack property of LIFO.
- If the keys chosen were in strictly increasing order, it would mean that the character with the lowest key value would not be on top of the stack, which would make the POP operation incorrect.
Conclusion:
- Choosing the keys in strictly decreasing order ensures that the priority queue Q behaves as a stack, where the character with the highest priority (i.e., the character on top of the stack) has the lowest key value.
- This allows the PUSH and POP operations to correctly implement the stack behavior.
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A priority queue Q is used to implement a stack S that stores characters. PUSH(C) is implemented as 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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