# some more functions and while loops

def f(a):
    a = a+1

a = 3
f(a)
print a


# function to add up all the elements of an array A
# sum([3,4,7,1]) should return 15
def sum(A):
    n = len(A)
    i = 0  # loop counter
    ax = 0 # running total
    while i<n:
        ax = ax + A[i]
        i = i+1
    # end while
    return ax
# end sum

# function to find the smallest element of an array A:
def smallest(A):
    n = len(A)
    sm = A[0]  # sm is the candidate for the smallest value
    i = 1
    while i<n:
        if A[i] < sm:
            sm = A[i]
        i = i+1
    #end while
    return sm
# end smallest



# nested loop to print multiplication table
i = 1  # outer loop counter
while i<10:
    j = 1  # inner loop counter
    while j<10-i+1:
        print (i*j), "\t",
        j =j+1
    # end while j
    print ""   # new line
    i = i+1
#end while i


# factorial function : 6! = 6*5*4*3*2*1. 1! = 1,  n! = n*(n-1)!

def factorial(n):
    ax = 1       # running product
    while n>1:
        ax = ax *n
        n = n-1
    return ax
# end factorial


# function to compute the greatest common divisor of two numbers:
def gcd(a,b):
   while a!=0 or b!=0:
       if a>b: a = a % b
       else: b = b % a
   # while
   return a+b  # the 0 value will automatically be canceled out
#gcd


####### from class:
# function to return day of week:
def dw(day,start):  #usage: dw(14,"Wednesday") returns "Tuesday"
   D = ["Monday","Tuesday","Wednesday","Thursday","Friday","Saturday","Sunday"]
   # find start date index:
   si = 0
   while (si<len(D) and D[si]!=start): si =si+1
   if si==len(D): raise "input error"
   ai = (day-1)+si  # day of week in numerical format (0-6)
   return D[ai]
#dw


# loop to print calendar for 31-day month given start day of week.
def printcal(start):
   D = ["Monday","Tuesday","Wednesday","Thursday","Friday","Saturday","Sunday"]
   # find start date index:
   si = 0
   while (si<len(D) and D[si]!=start): si =si+1
   if si==len(D): raise "input error"
   # print initial line:
   print "Mon\tTue\tWed\tThr\tFri\tSat\tSun"
   # print inital spaces
   i = 0 # loop counter
   while i<si:
        print "\t",  # note , at end
        i = i+1
   # end while i<si
   day = 1 # loop counter
   while day<=31:
        print day,"\t",
        day = day+1 # advance to next day
        si = si +1  # day of week index
        if (si>6):
                si = 0 # reset to Monday
                print ""  # new line
   # while day
#printcal