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?
Consider the following expression: $x[i] = (p + r) * -s[i] + \frac{u}{w}$. The following sequence shows the list of triples representing the given expression, with entries missing for triples (1), (3), and (6).
| (0) | + | p | r |
| (1) | |||
| (2) | uminus | (1) | |
| (3) | |||
| (4) | / | u | w |
| (5) | + | (3) | (4) |
| (6) | |||
| (7) | = | (6) | (5) |
Which one of the following options fills in the missing entries CORRECTLY?
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 ____________.