PYTHON
ITERATION
CHAPTER 5 READ!!!
THE FOR LOOP
The for loop as shown below will perform the block of code 5 time and
for each iteration the variable i will take on the values 0,1,2,3, and 4
Here are two examples
for i in range(5):
w = ‘hello’
for s in range(5)
print i
print w[s]
>>>
>>>
0
h
1
e
2
l
3
l
4
o
>>>
>>>
THE FOR LOOP
Note that the variable need not be used at all
for i in range(5):
print(“Hello”)
>>>
for _ in range(3):
print() #blank lines
>>>
Hello
Hello
Hello
Hello
>>>
Hello
#note the _ ?!!?
RANGE FUNCTION
The range function has three ways it can be used
Using one parameter
range(n) ->>
[0,1,2,3,…,n-1]
Using two parameters
range(a,n) ->>
[a,a+1,a+2,…,n-1]
Using three parameters
range(a,n,s) ->> [a, a+s, a+2s, a+3s,… ,n-1?]
range(start, end, step) is a good way to think about it.
PRINTING VALUES 1 TO 10
#forward
for i in range(1,11):
#backwards
for i in range(10,0,-1)
print(i, end=‘ ’)
print()
print(i,end=‘ ’ )
print()
>>>
>>>
1 2 3 4 5 6 7 8 9 10
10 9 8 7 6 5 4 3 2 1
SIDE NOTE ON PRINTING
print(...)
print(value, ..., sep=' ', end='\n', file=sys.stdout,ie screen)
Prints the values to screen by default.
sep: string inserted between values, default a space.
end: string appended after the last value, default a newline.
file: You can place a filename here if you like
example
print (‘Hello’,’Tom’,sep=‘:’,end=‘;\n’)
Hello:Tom;
>>>
WHAT IS PRINTED
BELOW
for i in range(5):
print(i,i*i, i*i*i)
print(‘Done’)
sum=0
for i in range(10):
sum=sum+i
print(‘Sum=‘,sum,sep=‘’)
--------------------------------------------------------------------------------------sum=0
sum=0
for i in range(1,10,2):
for i in range(1,10):
sum=sum+i
print(sum)
sum=sum+math.sqrt(i)
print(sum)
A MATH APPLICATION
CALCULATING PI
There is a series that turns out to generate PI in the LONG run
Pi = 4(1/1-1/3+1/5-1/7+1/9… )and so on. See the pattern?
sum=0
sign=1
for denom in range(1,1000000,2): #in steps of 2
term=1/denom
sum=sum+term*sign
# what is the first term that added
sign=sign*-1
# flip flop the sign
print('PI is approximately=',4*sum)
>>>
PI is approximately= 3.141590653589692
WHAT DOES THIS MEAN
X=X+1
x = 10
print (x)
x=x+1
print (x)
x=x+1
print (x)
#output is
10
11
12
14
Increments x by 1
x=x+2
print (x)
Increments x by 2
THE WHILE LOOP
(NO AUTO INCREMENTING)
x=1
while x < 10:
# this is the condition
print (x,end=‘’)
x=x+1
#The body of the loop (repeated until the
# while condition is false)
#OUTPUT is
123456789
What if we forget this instruction!
WHAT? IS 1+2+3+…+N
Mathematically we have
+
2
+
3
+ … + (n-1) + n
S=
1
S=
n + (n-1) + (n-2) + … +
2
+1
2S = (n+1)+(n+1)+ (n+1) + … (n+1)+(n+1)
2S = n(n+1)
S = n(n+1)/2
 Sum of the numbers from 1 to n
S = 100(101)/2 = 5050  Sum of the numbers from 1 to 100
LETS DO THIS IN PYTHON
( IN TWO WAYS)
#using a for
s=0
for i in range(100) #note in this case we start with a 0
s=s+i+1
 why do I have a 1 here
Because range(100) is [0,1,2,3,4,…,99]
print (‘The sum from 1 to 100 is’,s)
#using a while loop
i=1
s=0
while i<=100:
s=s+i
i=i+1
print (‘The sum from 1 to 100 is’,s)
ADD EVEN NUMBERS
FROM 2 TO 100
i=2
# first number is 2
s=0
while i<=100:
# stop looping at 100
s=s+i
i=i+2
# increment by 2
print (‘The sum of evens from 2 to 100 is’,s)
What about the odds.?
What about the sum of squares from 1 to 100?
WHAT DOES THIS WEIRD
FUNCTION DO????
def sequence(n):
while n!=1:
print (n, end=‘’)
if n%2 == 0:
n = n/2
Will this always
terminate?
else:
n=n*3+1
sequence(101)
>>>
101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5
16 8 4 2
>>>
HOMEWORK: CALCULATE THE
PERCENTAGE OF EVENS IN THE
SEQUENCE
This is the sequence for 101
>>>
101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10
5 16 8 4 2
>>>
Its percentage is 18/25.0 =72.0
I calculated the percentage of evens for all the values from 2
to 100 and graphed this in Excel?
I will show you how to do this later on.
100
97
94
91
88
85
82
79
76
73
70
67
64
61
58
55
52
49
46
43
40
37
34
31
28
25
22
19
16
13
10
7
4
1
HERE IS MY OUTPUT
????
120
100
80
60
40
20
0
CALCULATING
SQUARE ROOT
A very old method for calculating the square root of a number is to use Newton’s method.
Suppose we would like to find the square root of a. We begin using a guess x and use the
following formula to get a closer estimate y of the square root .
𝒂
𝒙+
𝒙
𝒚=
𝟐
def sqroot(a):
x = a/2.0 # our initial estimate
while abs(a-x**2)> .0000001:
x = (x + a/x)/2.0
return x
print sqroot(4)
print sqroot(16)
print sqroot(25)
>>>
2.0
4.0
5.00000000002
>>>
READ A SET OF NUMBERS FROM THE
KEYBOARD AND DO SOMETHING TO
THEM (USES INFINITE LOOP AND BREAK)
s=0
ct=0
while True:
x = input('Enter a number ') # Remember x is a str!
if x == 'done':
break
# The break instruction exits the loop
# Do something to the values of x
ct = ct+1 #count the numbers
s = s+ float(x)
#accumulate them and convert x to a float
# Display the results
print( 'The average is ',float(s)/ct)
DETERMINE IF A NUMBER IS
PRIME
# This is a very inefficient algorithm. Can you do it better?
def prime(n):
if n < 2 :
return False
ans = True
for i in range(2,n):
if n%i == 0 :
ans=False
return ans
print prime(5)
print prime(64)
print prime(101)
print prime (1001)
>>>
True
False
True
False
>>>
PRIMENESS OF
1000001?
Suppose I would like to determine if 11, 101,1001,10001,
100001, 1000001, and so on are prime. How can I do this?
First lets just print these.
for i in range(1, 20):
v = 10**i + 1
print (v,prime(v))
READ IN A STRING AND COUNT
SPECIFIC CHARACTERS
#Count the number of a’s in the string
x = input('Enter a dna sequence ( i.e. actggect) ')
ct_a=0 #variable we count with
for i in range(len(x)):
if x[i]=='a':
ct_a=ct_a + 1
print (ct_a)
EXAMPLE PROBLEMS
1.
Read in integers until 0 is entered, then print the sum,
average, largest and smallest of the entered numbers
2.
Read in real numbers from the keyboard and calculate and
print the square root of the numbers using Newton’s,
method. See chapter 7. Stop when ‘done’ is typed.
3.
Calculate PI using ( Ramanujan’s pi formula)
https://crypto.stanford.edu/pbc/notes/pi/ramanujan.html
4.
Write a function called prime(p) that returns true if p is prime
and false otherwise. Test it carefully
5.
(a little tougher) Print out the prime factorization of a
number.
6.
Write a function that receives and input a dna string and a
char ( a,c,t,g) and then returns the number of copies of that
character that exist in the string.