###  Modular Program Components; If-Else and While Loops.

# Now that we've learned how to write boolean expressions, we can
# use them to form if statements, if-else statements, and while loops.

x = input("Enter a number: ")

if x<0: print "x is negative"
if x>0: print "x is positive"
if x==0: print "x is zero"

# The statement after the : will only be executed if the boolean expression
# evaluates to True.  Each if statement will be tested and executed in turn.

# A if statement can also optionally have an else part:

if x!=0: print 1/x
else: print "can't divide by zero"

# The else part will be executed if the boolean condition is false: thus in
# an if-else statement something will always be executed.

# What does the following print?

x, y = 4,2  # simultaneously assigns x to 4 and y to 2

if x>y: print "x is bigger"
if x<y: print "y is bigger"
else: print "x and y are the same"

# answer: it prints "x is bigger" AND THEN it also prints "x and y are the
# same".  Why?  because the two if statements are executed in turn, but
# something will ALWAYS be executed by the second if-else statement
# regardless of what happened with the first statement.  Think about this
# to make sure you understand.

### if statements that does more than one thing:

if x==0:
    print "A"
    print "B"

# if x is indeed 0, it will print both A and B, otherwise it prints nothing.
# The indentation determines the SCOPE of the if statment.  One should think
# of any set of code that's properly aligned (indented the same way) as
# forming a program module, a coherent piece of code.


### nested if statements.

# The body or scope of an if statement can contain any number of other
# statements as long as they're aligned.  This naturally means that
# if statements can contain other if statements.

if x>y: print "x is bigger"
else:
    if x<y: print "y is bigger"
    else: print "x and y are the same"

# Assuming that x,y are still 4,2, this time it will just print x is bigger,
# because the entire second if-else will be skipped, because it's inside
# the scode of the first if-else.

# the following code tries to test if a and b are equal and that both are
# positive.
a,b = input("Enter two numbers:")

if a==b:
    if a>0:
        if b>0: print "ok"

# This is equivalent to:

if (a==b and a>0 and b>0): print "ok"

# As general practice, do not nest more if statements than necessary.

# QUIZ: what does the following print?

a,b = 2,2
if a != b:   # same as if not(a==b):
    if a>b:
        print "a is bigger"
    else: print "a is not bigger"
print "a and b are the same"

# ???????


#### while loops.

# A while loop is like an if statement (with no else: part), except it
# retests the boolean condition after each execution of its body, until
# the boolean condition becomes false, which is possible because we can
# change the value of variables.

x = 1
while x<10:
    print x*x
    x = x+1
# end while x

# While loops will usually contain more than one statement, properly aligned.
# The comment at the end is REQUIRED, otherwise your code will become
# unreadable when it gets large.

# If the boolean condition is true, it will execute the body, then retest
# the condition, jumping out of the loop when it becomes false.  It
# always executes the entire body of the while loop before retesting the
# boolean condition: it does not terminate in the middle.  The following
# prints something slightly different.

x = 1
while x<10:
    x = x+1
    print x*x
# end while x

# count the number of lines printed: you should notice that this time
# it printed 10 numbers, not 9. Why? Understanding such details is
# crucially important.  The trickiest part of writing while loops is to
# understand HOW IT STARTS and WHEN IT ENDS.  The beginning and the end
# are usually where mistakes are made.

# The following prints 1, 4, 9, etc.. up to 100.
x = 0
while x<10:
    x = x+1
    print x*x
# end while x

# The Fibonacci sequence is 1 1 2 3 5 8 13 21 ...  The following prints the
# the first 30 Fibonacci numbers:

n = 30  # counts downward how many numbers are left to be printed.
a,b = 0,1
while n>0:
    print b, " ",  # The , at the end means there's no line break.
    a,b = b,a+b
    n -= 1    # this is shorthand for n = n-1
# while n
print ""      # prints line break AFTER the while loop.


## The body of while loops can be arbitrarily large and complex.  It can
# contain if statements, as well as nested while loops.

x = 1
while x<10:
    y = 1
    while y<10:
        print x*y, "\t",    # \t is the tab character
        y = y+1             
    # inner while
    print ""          # prints blank, then line break
    x = x+1
# outer while

# This prints a multiplication table.

### At this point, it is important for you to realize that a program is much
# more complex than just a sequence of commands.  The program must be
# STRUCTURED correctly.  It's not just one line followed by another: how
# these lines relate to eachother is crucially important.

# To better understand a nested while loop such as above, you can't just
# read the code line-by line.  It is important to be able to identify the
# five principal components that makes up a while loop:

#  1. preamble: sets up initial conditions before loop begins
#  2. boolean expression: determines whether loop continues or ends
#  3. update: condition must be updated for loop to stop eventually
#  4. main body of the while loop
#  5. postamble: final or clean-up action after the loop stops.
#     The postamble is sometimes empty, but conceptually we should still
#     think that it's present.

# Exercise: take any of the sample loops below, and identify the component
# that each line belongs to.

### More sample while loops:

# The following loop computes the greatest common divisor of a and b
# by implementing Euclid's algorithm, which can be described as follows.
# Given two numbers:
# 1. divide the larger number by the smaller number and find the remainder.
# 2. replace the larger number by the remainder found above.
# 3. repeat steps 1 and 2 until one of the two numbers is zero
# 4. the gcd is the remaining (non-zero) number.
# 5: clarification, if two numbers are equal, divide any one by the other.
#    and if one number is zero to begin with, the other is the answer.

a,b = input("enter two numbers: ")
while (a!=0 and b!=0):
  if a>b: a = a%b
  else: b = b%a
# while
gcd = a+b  # one of a or b will be zero and automatically canceled
print "the gcd is",gcd
  

# The following while loop checks if a number is a prime number.  A number
# is prime if it is evenly divisible (does not leave remainder) only by
# one and itself.

n = input("enter a number: ")  # number to test for primality
testcase = 2                   # first number to test against
answer = true
while testcase<n and answer:
    if (n % testcase == 0): answer = false
    testcase = testcase +1
# while
if (answer):
    print n,"is prime"
else:
    print n,"is not prime"

# Question, what will happen if n is 2?
# In that case the loop will never run, and it will print correctly that
# 2 is prime.

# note that the "and answer" clause in the boolean condition means that
# the loop will stop as soon as answer becomes false.
# saying "answer" here is the same as "answer==true" because what does
# answer==true evaluate to?

# Excercise: improve the prime testing algorithm by skipping even numbers.
# That is, once we confirm that n is not divisible by 2, then we know it's 
# not divisible by 4, 6, 8, ...  It is also possible to stop as soon as
# testcase becomes >= n/2, or even sqrt(n).