Stack:

Stack is a container in which elements inserted and removed in LIFO (Last In First Out) manner.

• “top” is address of top element of stack. 
• Basic stack operations are given below:
  • push(): Insert an object into stack top.
  • pop(): Delete object in stack top.
  • top(): Get object in stack top.

1. a.

Given stack is "S" and the additional stacks are "S1" and "S2".

The elements in stack "S" can be reverse as shown below:

• First pop each element from "S" and push it into "S1" till "S" becomes empty.
• Pop each element from "S1" and push it into "S2" till "S1" becomes empty.
• Pop each element from "S2" and push it into "S" till "S2" becomes empty.
• Now "S" contains elements in reverse order.

Example,

Initially "S" contains 1, 2, 3 and 4.

First pop each element from "S" and push it into "S1".

EBK DATA STRUCTURES AND ALGORITHMS IN C, Chapter 4, Problem 1E , additional homework tip 1

Then pop each element from "S1" and push it into "S2".

EBK DATA STRUCTURES AND ALGORITHMS IN C, Chapter 4, Problem 1E , additional homework tip 2

Last pop each element from "S2" and push it into "S".

EBK DATA STRUCTURES AND ALGORITHMS IN C, Chapter 4, Problem 1E , additional homework tip 3

Finally "S" contains in reverse order.

Queue:

• Queue is another data structure in which insertion and removal of elements are in FIFO(First In First Out) manner.
• Basic operations are given below:
  • Enqueue: Insert element into back of queue.
  • Dequeue: Remove item from queue’s front.

1. b.

Given stack is "S" and additional queue is "Q".

The elements in stack "S" can be reverse as shown below:

• Pop each element from "S" and insert it into "Q" till "S" becomes empty.
• Delete each element from "Q" and push it into "S" till "Q" becomes empty.
• Now stack "S" contains elements in reverse order.

Example,

Initially "S" contains 1, 2, 3 and 4.

First pop each element from "S" and insert it into "Q".

EBK DATA STRUCTURES AND ALGORITHMS IN C, Chapter 4, Problem 1E , additional homework tip 4

Then delete each element from "Q" and push it into "S".

EBK DATA STRUCTURES AND ALGORITHMS IN C, Chapter 4, Problem 1E , additional homework tip 5

Finally, "S" contains in reverse order.

1. c.

Given stack is "S", additional stack is "S1" and additional variables are "Num", Num2 and "top_element". The elements in stack "S" can be reverse as shown below.

• "Num" is number of elements initially in stack "S".
• Decrement "Num" by one.
• Till "Num" becomes zero.
  • Equate "Num" into "Num2".
  • Pop stack top of "S" and store in "top_element".
  • Pop "Num2" elements from "S" and push into "S1".
  • Then push element in "top_element" into "S".
  • Then pop each element from "S1" and push into "S" till "S1" becomes empty.
  • Decrement value of "Num" by one.
• Finally "S" contains elements in reverse order.

Example,

Initially "S" contains 1, 2, 3 and 4. Stack contains four elements. So, "Num" is 4. Decrement it by one.

First iteration:

"Num" is 3, pop stack top and store in "top_element". Then pop other three elements from "S" and push into "S1".

• Then push element in "top_element" into "S" and pop each element from "S1" and push into "S".

EBK DATA STRUCTURES AND ALGORITHMS IN C, Chapter 4, Problem 1E , additional homework tip 6

Second iteration:

"Num" is 2, pop stack top and store in "top_element". Then pop other two elements from "S" and push into "S1".

• Push element in "top_element" into "S" and pop each element from "S1" and push into "S".

EBK DATA STRUCTURES AND ALGORITHMS IN C, Chapter 4, Problem 1E , additional homework tip 7

Third iteration:

"Num" is 1, pop stack top and store in "top_element". Then pop one element from "S" and push into "S1".

• Push element in "top_element" into "S" and pop each element from "S1" and push into "S"

EBK DATA STRUCTURES AND ALGORITHMS IN C, Chapter 4, Problem 1E , additional homework tip 8

Fourth iteration:

"Num" is 0, exit loop.

Finally, the stack "S" contains elements in reverse order.