GATE-CS-2005

The steps to read complicated declarations : 1)Convert C declaration to postfix format and read from left to right. 2)To convert expression to postfix, start from innermost parenthesis, If innermost parenthesis is not present then start from declarations name and go right first. When first ending parenthesis encounters then go left. Once the whole parenthesis is parsed then come out from parenthesis. 3)Continue until complete declaration has been parsed. At First, we convert the following given declaration into postfix:

int ( * f) (int * )

Since there is no innermost bracket, so first we take declaration name f, so print “f” and then go to the right, since there is nothing to parse, so go to the left. There is * at the left side, so print “*”.Come out of parenthesis. Hence postfix notation of given declaration can be written as follows:

f * (int * ) int

Meaning: f is a pointer to function (which takes one argument of int pointer type) returning int . Refer http://www.geeksforgeeks.org/complicated-declarations-in-c/ This solution is contributed by Nirmal Bharadwaj.

See http://en.wikipedia.org/wiki/Abstract_data_type

Abstraction, Encapsulation, Polymorphism and Inheritance are the essential features of a OOP Language (See the Wiki page for OOP).

See question 1 of http://www.geeksforgeeks.org/data-structures-and-algorithms-set-22/

See Question 2 of http://www.geeksforgeeks.org/data-structures-and-algorithms-set-22/

See question 3 of http://www.geeksforgeeks.org/data-structures-and-algorithms-set-22/

We can solve it by making Venn diagram

It is a lattice but not a distributive lattice.

Table for Join Operation of above Hesse diagram

V |a b c d e
________________
a |a a a a a
b |a b a a b
c |a a c a c
d |a a a d d
e |a b c d e

Table for Meet Operation of above Hesse diagram

^ |a b c d e
_______________
a |a b c d e
b |b b e e e
c |c e c e e
d |d e e d e
e |e e e e e

Therefore for any two element p, q in the lattice (A,<=)

p <= p V q ; p^q <= p

This satisfies for all element (a,b,c,d,e).

which has 'a' as unique least upper bound and 'e' as unique 
greatest lower bound.

The given lattice doesn't obey distributive law, so it is 
not distributive lattice,

Note that for b,c,d we have distributive law

b^(cVd) = (b^c) V (b^d). From the diagram / tables given above 
we can verify as follows,

(i) L.H.S. = b ^ (c V d) = b ^ a = b

(ii) R.H.S. = (b^c) V (b^d) = e v e = e

b != e which contradict the distributive law. 
Hence it is not distributive lattice.

so, option (B) is correct. 

An undirected graph is called a planar graph if it can be drawn on a paper without having two edges cross and such a drawing is called Planar Embedding. We say that a graph can be embedded in the plane, if it planar. A planar graph divides the plane into regions (bounded by the edges), called faces. Graph K4 is palanar graph, because it has a planar embedding as shown in figure below. Euler's Formula : For any polyhedron that doesn't intersect itself (Connected Planar Graph),the • Number of Faces(F) • plus the Number of Vertices (corner points) (V) • minus the Number of Edges(E) , always equals 2. This can be written: F + V − E = 2. Solution : Here as given, F=?,V=13 and E=19 -> F+13-19=2 -> F=8 So Answer is (B). This solution is contributed by Nirmal Bharadwaj We can apply Euler's Formula of planar graphs. The formula is v − e + f = 2.