1. SuperStack (based on a problem by Prof. Michael Dillencourt) Consider a "superstack" data structure which supports four operations: Create, Push, Pop, and MultiPop. The new MultiPop operation is given a non- negative integer k and array A, pops the top k elements, and stores them in A. MultiPop throws an exception if k is greater than the number of elements on the stack, or the size of A. All four operations are implemented using an underlying standard stack as shown below. SS_Create(): S = Stack.Create() SS_Push(x): S. Push(x) SS_Pop(): return S.pop) SS_MultiPop(k, A): if (k > S.Size()) or (k > A.Size()): throw exception for (i = 0; i < k; i++) A[i] = S.pop() Argue that each of these operations takes O (1) amortized time. Your argument should
1. SuperStack (based on a problem by Prof. Michael Dillencourt) Consider a "superstack" data structure which supports four operations: Create, Push, Pop, and MultiPop. The new MultiPop operation is given a non- negative integer k and array A, pops the top k elements, and stores them in A. MultiPop throws an exception if k is greater than the number of elements on the stack, or the size of A. All four operations are implemented using an underlying standard stack as shown below. SS_Create(): S = Stack.Create() SS_Push(x): S. Push(x) SS_Pop(): return S.pop) SS_MultiPop(k, A): if (k > S.Size()) or (k > A.Size()): throw exception for (i = 0; i < k; i++) A[i] = S.pop() Argue that each of these operations takes O (1) amortized time. Your argument should
Computer Networking: A Top-Down Approach (7th Edition)
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![1. SuperStack
(based on a problem by Prof. Michael Dillencourt)
Consider a "superstack" data structure which supports four operations: Create, Push, Pop, and MultiPop. The new MultiPop operation is given a non-
negative integer k and array A, pops the top k elements, and stores them in A. MultiPop throws an exception if k is greater than the number of elements
on the stack, or the size of A. All four operations are implemented using an underlying standard stack as shown below.
SS_Create():
S =
Stack.Create()
SS_Push(x):
S. Push(x)
SS_Pop():
return S.pop()
SS_MultiPop(k, A):
if (k > S.Size()) or (k > A.Size()):
throw exception
for (i = 0; i < k; i++)
A[i]
%3D
S. pop()
Argue that each of these operations takes O (1) amortized time. Your argument should
• define a potential function Ø, and
• state, for each operation, the operation's actual time, change in potential, and amortized time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84a310e0-6f97-4def-b827-628265d91c57%2F08c81eff-97de-4981-8c4f-bd6b712cc7bf%2F77uqkxu_processed.png&w=3840&q=75)
Transcribed Image Text:1. SuperStack
(based on a problem by Prof. Michael Dillencourt)
Consider a "superstack" data structure which supports four operations: Create, Push, Pop, and MultiPop. The new MultiPop operation is given a non-
negative integer k and array A, pops the top k elements, and stores them in A. MultiPop throws an exception if k is greater than the number of elements
on the stack, or the size of A. All four operations are implemented using an underlying standard stack as shown below.
SS_Create():
S =
Stack.Create()
SS_Push(x):
S. Push(x)
SS_Pop():
return S.pop()
SS_MultiPop(k, A):
if (k > S.Size()) or (k > A.Size()):
throw exception
for (i = 0; i < k; i++)
A[i]
%3D
S. pop()
Argue that each of these operations takes O (1) amortized time. Your argument should
• define a potential function Ø, and
• state, for each operation, the operation's actual time, change in potential, and amortized time.
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