### Gate Questions on Regular Expressions

Q1. Which two of the following four regular expressions are equivalent? (ε is the empty string).
(i) (00)*(ε + 0)
(ii) (00)*
(iii) 0*
(iv) 0(00)*

(a) (i) & (ii)      (b) (ii) & (iii)      (c) (i) & (iii)      (d) (iii) & (iv)

(GATE-96)

Sol:
Option (b) is correct.

Explanation:
i. (00)*( ε + 0) = (00)*ε + (00)*0 = (00)* + (00)*0 = 0*
Note that (00)* Generates strings of even length and (00)*0 generated the strings of odd length. Since + operator Union of both sets results in 0*.

Q2. The string 1101 does not belong the set represented by
(a) 110*(0+1)
(b) 1(0+1)*101
(c) (10)*(01)*(00+11)*
(d) (00+(11)*0)*
(GATE-98)

Sol:
Both option (c) and (d) will not generate the string 1101

Q3. if the regular set A is represented by A = (01+1)* an the regular set B is represented by B = ((01)*1*)*, which of the following is true?
(a) A Ì B
(b) B Ì A
(c) A and B are incomparable
(d) A = B
(GATE-98)

Sol:
Option d is true.

Explanation:
A = (01+1)*
A = ( (01)* 1* )*       -- from rule (r1 + r2)* =( r1*r2*)*
A = B

Note:
If r1 and r2 are two regular expressions then,
(r1 + r2)* = (r1* + r2*)*
= (r1* + r2)*
= (r1 + r2*)*
= (r1* . r2*)*

Q4. Let S and T be languages over ∑ = {a,b} represented by the regular expression (a + b*)* and (a + b)*, respectively. Which of the following is true?

(a) S Ì T
(b) T Ì S
(c) S = T
(d) S È T = f
(GATE-00)

Sol:
Option c is true. From rule (r1 + r2)* =( r1 + r2*)*.
Note: Both S and T will generate the same language.

### C Questions

C Questions
C Questions

Note : All the programs are tested under Turbo C/C++ compilers.
It is assumed that,
Programs run under DOS environment, The underlying machine is an x86 system, Program is compiled using Turbo C/C++ compiler.
The program output may depend on the information based on this assumptions (for example sizeof(int) == 2 may be assumed).
Predict the output or error(s) for the following:

void main()
{
int const * p=5; printf("%d",++(*p));
}
Compiler error: Cannot modify a constant value.
Explanation:
p is a pointer to a "constant integer". But we tried to change the value of the "constant integer".
main()
{
char s[ ]="man"; int i;
for(i=0;s[ i ];i++)
printf("\n%c%c%c%c",s[ i ],*(s+i),*(i+s),i[s]);
}
aaaa nnnn
Explanation

### Zoho Interview | Set 1 (Advanced Programming Round)

Third Round: (Advanced Programming Round) Here they asked us to create a “Railway reservation system” and gave us 4 modules. The modules were:
1. Booking
2. Availability checking
3. Cancellation
4. Prepare chart
We were asked to create the modules for representing each data first and to continue with the implementation phase.

My Solution :