HOMEWORK 4.


1. Write a program for factorial computation using an accumulator.

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2. Write a program sum_and_squaresum that from a given list of
numbers finds the sum of its elements and the sum of their squares.
Use accumulators. Sample run:

?- sum_and_squaresum([1,-3,2,0],Sum,SQS).

Sum = 0
SQS = 14 ;

No


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3. Write a predicate twice_as_long(L1,L2) that succeeds if the list
L2 is twice as long as the list L1. Do NOT compute the lengths of
the lists. Sample run:

?- twice_as_long([],[]).

Yes.

?- twice_as_long([a],[1,2]).

Yes.

?- twice_as_long([a,b],X).

X = [_G328, _G331, _G334, _G337] ;

No


?- twice_as_long(X,[_,_]).

X = [_G328] ;

No

?- twice_as_long([_],X).

X = [_G313, _G316] ;

No


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4. Write predicate fib(N,F) that is true if F is the Nth Fibonacci number. 
Compute fib(5,F), fib(10,F), fib(50,F).

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5. Implement Extended Euclidean Algorithm to compute greatest common divisors in integers.

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