Practical Exercise 3
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Question 1
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1.1 How many times are the loops, defined by the following statements,
executed:

a) DO I = 2, N/2, 3
with N having the value 2.

b) DO I = 1, N, 4
with N having the value 2.

c) DO I = 3, N**2, 5
with N having the value 2.

d) DO I = 2, N/2, 3
with N having the value 15.

e) DO I = 1, N, 4
with N having the value 15.

f) DO I = 3, N**2, 5
with N having the value 15.


Question 2
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2.1 Write a program to read in a vector defined by a length and an angle
in degrees, which prints out the corresponding Cartesian (x, y)
co-ordinates. Recall that arguments to trigonometric functions are in
radians.

Demonstrate correctness by giving the Cartesian co-ordinates for the
following vectors:

length angle
12 77
1000 0
1000 90
20 100
12 437


Question 3
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3.1 Write a Fortran program to count how many of a set of ten integers
typed in at the keyboard are multiples of five. Ignore any negative
numbers. If you read in an array of length 10 (using just the array
name in the READ statement), you can put all the numbers on one line.
Test it using the following sets of numbers:

5 73 53 12 65 92 39 -11 60 13
0 6 8 8 -2 5 -3 -3 8 3
33 -2 69 -6 -15 93 52 76 56 11


Question 4
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4.1 Write a program to accept three integer lengths and report back on
whether these lengths could define an equilateral, isoceles or scalene
triangle (3, 2 or 0 equal length sides), or whether they cannot form a
triangle.

Demonstrate that the program works by classifying the following:

Sides of length
1 1 1
2 2 1
1 1 0
3 4 5
3 2 1
1 2 4

Hint: if three lengths form a triangle then 2 times the longest side
must be less than the sum of all three sides. In Fortran 90 terms, the
following must be true:

2*MAX(sidel,side2,side3) < sidel+side2+side3


Question 5
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5.1 If you take a positive integer, halve it if it is even or triple it
and add one if it is odd, and repeat, then the number will eventually
become one. Warning: it may take a long time!

Set up a loop containing a statement to read in a number (input
terminated by zero) and to print out the sequence obtained from each
input. The number 13 is considered to be very unlucky and if it is
obtained as part of the sequence then execution should immediately
terminate with an appropriate message.

Demonstrate that your program works by outputting the sequences
generated by the following numbers:

7
106
46
3
0


Question 6
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6.1 Write a program that will read a sequence of colors input as names,
'red', 'green', 'blue', 'yellow', 'black', 'white' or something else.
Stop the program if a color 'blank' is read. Count the number of
occurrences of each color, including the unspecified colors and print
out the totals for each color before terminating the program. Use
the file Programs/spectrum.data to test it. You can do that by running
a command like: