Monday, July 24, 2023
The divide-and-conquer approach
The divide-and-conquer approach
The divide-and-conquer paradigm involves three steps at each level of the recursion:
Divide the problem into a number of subproblems that are smaller instances of the
same problem.
Conquer the subproblems by solving them recursively. If the subproblem sizes are
small enough, however, just solve the subproblems in a straightforward manner.
Combine the solutions to the subproblems into the solution for the original problem.
EXAMPLE
The merge sort algorithm closely follows the divide-and-conquer paradigm. Intuitively, it operates as follows.
Divide: Divide the n-element sequence to be sorted into two subsequences of n=2
elements each.
Conquer: Sort the two subsequences recursively using merge sort.
Combine: Merge the two sorted subsequences to produce the sorted answer.
Sunday, July 23, 2023
ISCE- LIST OF PROGRAMS
| 1 | Magic number | CLICK |
| 2 | Happy number | CLICK |
| 3 | Fibonacci series | CLICK |
| 4 | Check twin prime from a series | CLICK |
| 5 | Armstrong number | CLICK |
| 6 | Automorphic number | CLICK |
| 7 | decimal to binary conversion | CLICK |
| 8 | a+a/2! +a/3! +a/4! +.... n th term | |
| 9 | neon number in java | CLICK |
| 10 | KaprekarNumbers | CLICK |
| 11 | Fascinating Number | CLICK |
| 12 | square Matrix | CLICK |
| 13 | string having repeating characters | CLICK |
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UNION MAKE SET FIND SET
void make_set(int v) {
parent[v] = v;
}
int find_set(int v) {
if (v == parent[v])
return v;
return find_set(parent[v]);
}
void union_sets(int a, int b) {
a = find_set(a);
b = find_set(b);
if (a != b)
parent[b] = a;
}
There are two ways to improve it:
1. Path Compression
2. Union by Rank
Saturday, July 22, 2023
GRAPHICS ADVANCED LEARNER
1.
The Cohen-Sutherland Algorithm
2.
The Sutherland-Hodgman Algorithm
3.
Midpoint Subdivision Algorithm
AI-ADVANCED LEARNER
1.
If P represents 'This book is good' and Q represents 'This
book is cheap', write the following sentences in symbolic form:
(a) This book is good and cheap.
(b) This book is not good but cheap.
(c) This book is costly but good.
(d) This book is neither good nor cheap.
(e) This book is either good or cheap.
2.
Translate the following sentences
into propositional forms:
(a) If it is not raining and I
have the time. then I will go to a movie.
(b) It is raining and I will not
go to a movie.
(c) It is not raining.
(d) I will not go to a movie.
(e) I will go to a movie only if
it is not raining.
Hints:
Let P be the proposition 'It is raining'.
Let Q be the proposition 'I have
the time'.
Let R be the proposition '1 will
go to a movie'.
3.
Write the following sentences in
symbolic form: (
a) This book is interesting but
the exercises are difficult.
(b) This book is interesting but
the subject is difficult.
(c) This book is not interesting.
the exercises are difficult but the subject is not difficult.
(d) If this book is interesting
and the exercises are not difficult then the subject is not difficult.
(e) This book is interesting means
that the subject is not difficult, and conversely.
(f) The subject is not difficult
but this book is interesting and the exercises are difficult.
(g) The subject is not difficult
but the exercises are difficult.
(h) Either the book is interesting
or the subject is difficult.
4.
Derive S from the following
premises using a valid argument:
(i)
P => Q
(ii)
Q => ¬R
(iii)
P v S
(iv)
R
5.
Check the validity of the
following argument:
If Ram has completed B.E.
(Computer Science) or MBA, then he is assured of a good job.
If Ram is assured of a good job, he is happy.
Ram is not happy.
So Ram has not completed MBA.
6.
Express the following sentences
involving predicates in symbolic form:
1. All students are clever.
2. Some students are not
successful.
3. Every clever student is
successful.
4. There are some successful
students who are not clever.
5. Some students are clever and
successful.
7.
Discuss the validity of the
following argument:
All educated persons are well
behaved.
Ram is educated.
No well-behaved person is
quarrelsome.
Therefore. Ram is not quarrelsome.
8.
Test the validity of the following
argument:
Babies are illogical.
Nobody is despised who can manage
a crocodile.
Illogical persons are despised.
Therefore babies cannot manage
crocodiles.
9.
Show that the following argument
is valid:
All men are mortal.
Socrates is a man.
So Socrates is mortal.
10.
Test the validity of the following
argument:
If Ram is clever then Prem is
well-behaved.
If Joe is good then Sam is bad and
Prem is not well-behaved.
If Lal is educated then Joe is
good or Ram is clever.
Hence if Lal is educated and Prem
is not well-behaved then Sam is bad.
Monday, July 17, 2023
15. Write a Prolog program to implement maxlist(List,Max) so that Max is the greatest number in the list of numbers List using cut predicate.
15. Write a Prolog program to implement maxlist(List,Max) so that Max is the greatest number in the list of numbers List using cut predicate.
maxlist([H],H).
maxlist([H|T],R):-
maxlist(T,M1),
H>=M1,
R is H,!.
maxlist([H|T],R):-
maxlist(T,M1),
H<M1,
R is M1.
OUTPUT:.
maxlist([1,20,2],X).
X = 20
16. Write a Prolog program to implement GCD of two numbers.
16. Write a Prolog program to implement GCD of two numbers.
gcd(X,0,X).
gcd(X,Y,Z):-
R is mod(X,Y),
gcd(Y,R,Z).
OUTPUT:
gcd(6,9,X).
X = 3
17. Write a prolog program that implements Semantic Networks/Frame Structures.
17. Write a prolog program that implements Semantic Networks/Frame Structures.
OUTPUT:
11. Write a Prolog program to implement maxlist(List,Max) so that Max is the greatest number in the list of numbers List.
11. Write a Prolog program to implement maxlist(List,Max) so that Max is the greatest number in the list of numbers List.
max([H|T],R):-
length(T,L),
L>0 -> ( max(T,R1), ( H > R1 -> R is H ; R is R1 ) ) ; R is H.
OUTPUT:
max([6,9,7],X).
X = 9
max([6,9,70],X).
X = 70
10. Write a Prolog program to implement max(X,Y,Max) so that Max is the greater of two numbers X and Y.
10. Write a Prolog program to implement max(X,Y,Max) so that Max is the greater of two numbers X and Y.
max(X,Y,R):-
X>=Y ->
R is X,
write(R)
;
R is Y,
write(R).
OUTPUT:
max(2,6,X).
6
X = 6
12. Write a Prolog program to implement sumlist(List,Sum) so that Sum is the sum of a given list of numbers List.
12. Write a Prolog program to implement sumlist(List,Sum) so that Sum is the sum of a given list of numbers List.
sumlist([],0).
sumlist([H|T],R):-
sumlist(T,R1),
R is H+R1.
OUTPUT:
sumlist([6,9,70],X).
X = 85
14. Write a Prolog program to implement reverse(List,ReversedList) that reverses lists.
14. Write a Prolog program to implement reverse(List,ReversedList) that reverses lists.
reverse([],[]).
reverse([X|T],REV):-reverse(T,R),append(R,[X],REV).
OUTPUT:
reverse([1,2,2],X).
X = [2, 2, 1]
13. Write a Prolog program to implement two predicates evenlength(List) and oddlength(List) so that they are true if their argument is a list of even or odd length respectively.
13. Write a Prolog program to implement two predicates evenlength(List) and oddlength(List) so that they are true if their argument is a list of even or odd length respectively.
evenlength:-
write('true --> even').
oddlength:-
write('true --> odd').
oddeven([_|T]):- length(T,L), L>=0 -> ( L1 is L+1, L2 is mod(L1,2), L2=:=0 ->evenlength ; oddlength ).
OUTPUT:
oddeven([5,8,9]).
true
--> odd
1true
oddeven([5,8,6,9]).
true
--> even
1true
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