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Python Iteration chapter 7 READ!!!

Python Iteration chapter 7 READ!!!. From Think Python How to Think Like a Computer Scientist. The for loop. We already looked at an instruction that does iteration. It was the for command w = ‘hello’

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Python Iteration chapter 7 READ!!!

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  1. PythonIterationchapter 7 READ!!! From Think Python How to Think Like a Computer Scientist

  2. The for loop • We already looked at an instruction that does iteration. • It was the for command w = ‘hello’ • for i in range(5): for s in range(5) • print i print w[s] • >>> >>> • 0 h • 1 e • 2 l • 3 l • 4 o • >>> >>>

  3. What does this mean x = x + 1 • x = 10 • print x • x = x + 1 • print x • x = x + 1 • print x • x = x + 2 • print x #output is 10 11 12 14 Increments x by 1 Increments x by 2

  4. The While Loop • x = 1 • while x < 10: # this is the condition • print x, • x = x + 1 • #OUTPUT is • 1 2 3 4 5 6 7 8 9 #The body of the loop (repeated until the # while condition is false) What if we forget this instruction!

  5. What? is 1+2+3+…+n • Mathematically we have • S = 1 + 2 + 3 + … + (n-1) + n • 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

  6. Lets do this in Python ( in two ways) • #using a for • s=0 • for i in range(100) • s = s + i + 1  Again, 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

  7. 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?

  8. What does this function do???? • def sequence(n): • while n!=1: • print n, • if n%2 == 0: • n = n/2 • else: • n = n * 3 + 1 • sequence(101) • >>> • 101 304152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 • >>> Will this always terminate?

  9. Homework: Calculate the percentage of evens in the sequence • This is the sequence for 101 • >>> • 101 304152 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 • What about all the values from 2 to 101? • Calculate and graph the values in excel.

  10. Here is my output ????

  11. 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 . • defsqroot(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 >>>

  12. Read a set of numbers from the keyboard and do something to them • s=0 • ct=0 • whileTrue: • x = raw_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

  13. Determine if a number is prime • # This is a very inefficient algorithm. Can you do it better? • defprime(n): • if n < 2 : • return False • ans = True • for i in range(2,n): • if n%i == 0 : • ans=False • returnans • print prime(5) • print prime(64) • print prime(101) • print prime (1001) >>> True False True False >>>

  14. 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,

  15. Read in a string and count specific characters • #Count the number of a’s in the string • x = raw_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

  16. Example problems • Read in integers until 0 is entered, then print the sum, average, largest and smallest of the entered numbers • 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. • Do exercise 7.5 ( Ramanujan’s pi formula) • Write a function called prime(p) that returns true if p is prime and false otherwise. Test it carefully • (a little tougher) Print out the prime factorization of a number. • 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.

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