Stacks and Queues · Data Structures · GATE CSE
Marks 1
Consider the operator precedence and associativity rules for the integer arithmetic operators given in the table below.
| Operator | Precedence | Associativity |
|---|---|---|
| + | Highest | Left |
| − | High | Right |
| * | Medium | Right |
| / | Low | Right |
The value of the expression $3 + 1 + 5 * 2 / 7 + 2 − 4 − 7 − 6 / 2$ as per the above rules is _______
Consider the following sequence of operations on an empty stack.
push(54); push(52); pop(); push(55); push(62); s = pop();
Consider the following sequence of operations on an empty queue.
enqueue(21); enqueue(24); dequeue(); enqueue(28); enqueue(32); q = dequeue();
The value of s + q is ______
(i) First-in-first out types of computations are efficiently supported by STACKS.
(ii) Implementing LISTS on linked lists is more efficient than implementing LISTS on an array for almost all the basic LIST operations.
(iii) Implementing QUEUES on a circular array is more efficient than implementing QUEUES on a linear array with two indices.
(iv) Last-in-first-out type of computations are efficiently supported by QUEUES.
Marks 2
Consider a stack $S$ and a queue $Q$. Both of them are initially empty and have the capacity to store ten elements each. The elements $1,2,3,4$, and 5 arrive one by one, in that order. When an element arrives, it is assigned either to $S$ (pushed on $S$ ) or to $Q$ (enqueued to $Q)$. Once all the five elements are stored, the output is generated in two steps. First, stack $S$ is emptied by popping all elements. Then queue $Q$ is emptied by dequeueing all elements. The output obtained by following this process is 43125 .
Given the output, the objective is to predict whether an element was assigned to $S$ or $Q$. Which of the following options is/are possible valid assignment(s) of the elements?
Note: In the options, the notation $x S$ denotes that element $x$ was assigned to $S$ and $y Q$ denotes that element $y$ was assigned to $Q$.
Consider a stack data structure into which we can PUSH and POP records. Assume that each record pushed in the stack has a positive integer key and that all keys are distinct. We wish to augment the stack data structure with an $\mathrm{O}(1)$ time MIN operation that returns a pointer to the record with smallest key present in the stack
1. without deleting the corresponding record, and
2. without increasing the complexities of the standard stack operations.
Which one or more of the following approach(es) can achieve it?
Let S1 and S2 be two stacks. S1 has capacity of 4 elements. S2 has capacity of 2 elements. S1 already has 4 elements: 100, 200, 300, and 400, whereas S2 is empty, as shown below.
| Stack S1 |
|---|
| 400 (Top) |
| 300 |
| 200 |
| 100 |
| Stack S2 |
|---|
Only the following three operations are available:
PushToS2: Pop the top element from S1 and push it on S2.
PushToS1: Pop the top element from S2 and push it on S1.
GenerateOutput: Pop the top element from S1 and output it to the user.
Note that the pop operation is not allowed on an empty stack and the push operation is not allowed on a full stack.
Which of the following output sequences can be generated by using the above operations?
Consider a sequence a of elements $$a_0=1,a_1=5,a_2=7,a_3=8,a_4=9$$, and $$a_5=2$$. The following operations are performed on a stack S and a queue Q, both of which are initially empty.
I: push the elements of a from a$$_0$$ to a$$_5$$ in that order into S.
II: enqueue the elements of a from a$$_0$$ to a$$_5$$ in that order into Q.
III: pop an element from S.
IV: dequeue an element from Q.
V: pop an element from S.
VI: dequeue an element from Q.
VII: dequeue an element from Q and push the same
VIII: Repeat operation VII three times.
IX: pop an element from S.
X: pop an element from S.
The top element of S after executing the above operations is ____________.
Consider the queues Q1 containing four elements and Q2 containing none (shown as the Initial State in the figure). The only operations allowed on these two queues are Enqueue (Q, element) and Dequeue (Q). The minimum number of Enqueue operations on Q1 required to place the elements of Q1 in Q2 in reverse order (shown as the Final State in the figure) without using any additional storage is ______________.
#include
#define EOF -1
void push (int); /* push the argument on the stack */
int pop (void); /* pop the top of the stack */
void flagError ();
int main () {
int c, m, n, r;
while ((c = getchar ()) != EOF) {
if (isdigit (c) )
push (c);
else if ((c == '+') || (c == '*')) {
m = pop ();
n = pop ();
r = (c == '+') ? n + m : n*m;
push (r);
} else if (c != ' ')
flagError ();
}
printf("% c", pop ());
}
i. isEmpty (Q) — returns true if the queue is empty, false otherwise.
ii. delete (Q) — deletes the element at the front of the queue and returns its value.
iii. insert (Q, i) — inserts the integer i at the rear of the queue.
Consider the following function:
void f (queue Q) {
int i ;
if (!isEmpty(Q)) {
i = delete(Q);
f(Q);
insert(Q, i);
}
} void insert(Q, X){
push(S1, X);
}
void delete(Q){
if(stack - empty(S2)) then {
if(stack - empty(S1)) then {
print("Q is empty");
return;
}else while (!(stack - empty(S1))){
X = pop(S1);
push(S2, X);
}
X = pop(S2);
}int func(int m, int n)
{
if (E) return 1;
else return(func(m -1, n) + func(m - 1, n - 1));
} function fun (x:integer):integer;
Begin
If x > 100 then fun : x – 10
Else fun : fun(fun (x + 11))
End;