PopS1 (w) PopS2 (y) PushS1 (y) PushS2 (w) PopS2 (y) PopS2 (w)

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Two stacks S1 and S2 are to be stored in a single array A[1:n], with
PushS1 (x) and PushS2 (x) handling their respective push operations with
regard to element x and PopS1 (x) and PopS2 (x) handling their respective pop
operations, with the output variable x indicating the element popped out from the
stack. Let TopS1 and TopS2 be their respective top-of-stack variables. The stacks
share their storage space in such a way that their respective bottom of stacks are
positioned in the middle of the array, as shown in Figure P4.1, and the stacks grow
in the opposite directions.
Array A:
[1]
[2]
[3]...
Stack S₁
... [[n/2]][[n/21+1] [n-2] [n-1] [n]
Bottom of
Stack S₁
...
PopS1 (w)
PopS2 (y)
PushS1 (y)
PushS2 (w)
PopS2 (y)
PopS2 (w)
Stack S₂
Bottom of
Stack S₂
Figure P4.1. Two stacks are stored in a single array A with
the bottom of stacks positioned in the middle of the array
i) For n = 5, if S1 = {a, b} and S2 = {m, n}, how would array A look after all of
the elements of stacks S1 and S2 were pushed into it invoking PushS1(x) and
PushS2(x)?
ii) How would array A look if the following operations were carried out in a
sequence? What values do the variables w and y represent at the end of the
operations?
Transcribed Image Text:Two stacks S1 and S2 are to be stored in a single array A[1:n], with PushS1 (x) and PushS2 (x) handling their respective push operations with regard to element x and PopS1 (x) and PopS2 (x) handling their respective pop operations, with the output variable x indicating the element popped out from the stack. Let TopS1 and TopS2 be their respective top-of-stack variables. The stacks share their storage space in such a way that their respective bottom of stacks are positioned in the middle of the array, as shown in Figure P4.1, and the stacks grow in the opposite directions. Array A: [1] [2] [3]... Stack S₁ ... [[n/2]][[n/21+1] [n-2] [n-1] [n] Bottom of Stack S₁ ... PopS1 (w) PopS2 (y) PushS1 (y) PushS2 (w) PopS2 (y) PopS2 (w) Stack S₂ Bottom of Stack S₂ Figure P4.1. Two stacks are stored in a single array A with the bottom of stacks positioned in the middle of the array i) For n = 5, if S1 = {a, b} and S2 = {m, n}, how would array A look after all of the elements of stacks S1 and S2 were pushed into it invoking PushS1(x) and PushS2(x)? ii) How would array A look if the following operations were carried out in a sequence? What values do the variables w and y represent at the end of the operations?
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