CS 2073, Computer Programming with Engineering Applications
Spring 1992
Exam 2
(30)	1.	Write a complete Pascal program that will print a bar graph of the function  y = sin(x),  for 
0 £ x £ p.  The output should look like what is printed below.  You do not need any  x  or  
y-axes.  Notice that the graph has been rotated by 90 degrees as we did in class.
		(a)  First write a procedure stars, with one integer parameter n, which will print out n 
stars on a line and then skip to the next line.
		(b)  Now finish the complete program.  Keep it as simple as possible.  Use 51 x values, 
starting with x = 0.0, and increasing x by 1/16 at each iteration.  Get the corresponding 
value  y = sin(x), and scale it by multiplying by 20.0.  Then truncate to an integer and write 
that many stars.  Besides stars, you do not need to write any other procedures or 
functions.
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(35)	2.	Recall the random number generator random that we used in class.  In order to use it, you 
need the following declarations and initializations:
			var seed: double;
			function random(var seed:double): double;
			(* the rest of random here *)
			begin (* main program *)
			   seed := 474747.0; (* or any value from 1.0 to 2^31-1 *)
			   (* now make use of random *)
			end.
		(a)  Write a segment of code which will use this random number generator to print 10 
random real numbers between 0.0 and 1.0.
		(b)  Write a code segment that will use random to simulate flipping a coin.  Your segment 
should print out ªHEADSº half the time and ªTAILSº half the time.
		(c)  Write a segment of code that will use the random number generator to produce pairs of 
numbers (x,y), where both x and y are in the range from -0.5 to 0.5.  As they are generated, 
count the number of pairs satisfying x2 + y2 £ 0.25.  Suppose this count is stored in a 
variable COUNT.  Your segment should continue for N pairs, where N is 1000, say.  After N 
pairs altogether, the segment should finally print the ratio COUNT/N.  (This ratio is a 
monte-carlo approximation to p/4.)

(35)	3.	Suppose we have an array type declared as follows:
			const N = 4; 
			type Atype = array[1..N] of integer; 
	(a)	Show how to declare 3 global arrays A, B, and C, each of N integers.
	(b)	Write a procedure READ_ARR with one parameter of type Atype that will read N 
numbers from the terminal and insert them into its parameter.  (Don't worry about 
end-of-file.)
	(c)	Write a function SUM with one parameter of type Atype that will add up the N 
integers in its parameter and return the sum as the function value.  Thus if A holds 
values 2, 3, 1, and 4, then the reference SUM(A) would return 10 as its value.
	(d)	Consider the procedure PROD below 
			PROCEDURE PROD (X, Y: Atype; VAR Z: Atype);
			VAR I: integer;
			BEGIN
				FOR I := 1 TO N DO
					Z[I] := X[I]*Y[I]
			END; 
		If A has values 2, 3, 1, and 4, and B has values 1, 4, 0, and 2, then after the call 
PROD(A, B, C), what will the values in C be?  (Show how you get the answer.)
	(e)	Write a function INNER_PROD with two input parameters of type Atype.  
INNER_PROD should return as its value the sum of the products of corresponding 
array positions.  Thus with A and B with values as in (d) above, INNER_PROD 
should calculate and return the value
			2*1 + 3*4 + 1*0 + 4*2 = 22.
		For full credit, INNER_PROD should use both PROD and SUM above.