Modeling Motion Midterm

Computing In-clas test question

lower = 3
upper = 8
n=lower
sum = 0
count = 0
while n <= upper:
    sum = sum + n     #keep a running sum
    count = count + 1
    n=n+1
print sum/count

• (a) Why doesn't the print statement print anything?

  Answer

  The variable n which is used in the while loop's expression, "while n <= upper:", starts out set to 3 and is never updated to anything else, so the while loop never terminates. The program is stuck in an infinite loop.
• (b) What additional line of code will allow the program to print? Mark wherre the new line should be inserted.

  Answer

  See the blue n=n+1 line added to the code above.
• (c) Does the program print the expected answer after your change? If not why not and how would you fix it?

  Answer

  No! The final print sum/count statement contain an expression which divides two integers. Integer division will truncate the result to 5 instead of 5.5. We need to make either the numerator or the denominator of this expression a float to force a floating point division to occur. This would work: print float(sum)/count

Computing Take-home

1. Write a function called mean()which takes an arbitrarily long list of numbers as an argument and returns the arithmetic mean of all of the numbers in that list. Following program should print "3.025":

   print mean( [1,2,3,4,5.125] )
   

   Solution

   def mean(numbers):
       total=0
       for n in numbers:
           total += n
       return float(total)/len(numbers)
   
   #test out the function
   print mean( [1,2,3,4,5.125] )
   

2. Write a function called backwards which takes a list as an argument and returns a new list with the same items in reverse order. It should make the following program print "you are how ?":

   import string
   sentence = ['how', 'are', 'you']
   print string.join(backwards(sentence)),'?'
   

   Solution

   import string
   
   def backwards(wordlist):
       wordlist.reverse()
       return wordlist
   
   #an alternate but harder to write solution
   def backwards2(wordlist):
       backlist = []
       for word in wordlist:
           backlist.insert(0,word)
       return backlist
   
   #a third possible solution
   def backwards3(wordlist):
       backlist = []
       for i in range(len(wordlist)-1, -1, -1):
           backlist.append(wordlist[i])
       return backlist
   
   sentence = ['how', 'are', 'you']
   print string.join(backwards(sentence)),'?'
   
   #test the second solution
   sentence = ['how', 'are', 'you']
   print string.join(backwards2(sentence)),'?'
   
   #test the third solution
   print string.join(backwards2(sentence)),'?'
   

3. Write a program which draws a sine wave by printing out successive lines to the terminal which contain a capital 'O' character with a varying number of spaces in front of it. The the number of spaces should be determined by formula 30*(1+sin(theta)). Make it print one full period of sine in 30 lines Hint: the print can print copies of a string by using the '*' operator to "multiply" strings as follows:

   >>> print "Hello"*3
   HelloHelloHello 
   

   Solution

   from math import pi,sin
   
   theta=0
   while theta<2*pi:
       spaces=int(30*(1+sin(theta)))
       print ' '*spaces,'O'
       theta+=pi/30
   
   

4. A useful operation on vectors is the dot product. The dot product of two vectors (Ai+Bj) and (Ci+Dj) is AC+BD, a scalar quantity. Using our convention of representing 2D vectors as two element Python lists, write a function called dot() which takes two vectors as parameters and returns the dot product. For example:

   >>> vector1=[1,2]
   >>> vector2=[3,4]
   >>> print dot(vector1,vector2)
   11
   

   Solution

   def dot(a,b):
       return a[0]*b[0] + a[1]*b[1]
   
   vector1=[1,2]
   vector2=[3,4]
   
   print dot(vector1,vector2)
   
   #It works on words too!
   wordvector = ['ha','ho']
   repeatvector  = [3,2]
   print dot(wordvector,repeatvector)
   
   

5. Write a function, vecadd() which takes as an argument an arbitrarily long list of 2D vectors, adds them all together and returns the resultant vector.

   >>> vec1 = [6,1]
   >>> vec2 = [1,6]
   >>> vec3 = [-7,-7]
   >>> veclist = [vec1,vec2,vec3]
   >>> print vecadd(veclist)
   [0, 0]
   

   Solution

   def vecadd(vectors):
       resultant = [0,0]
       for v in vectors:
           resultant = [resultant[0]+v[0], resultant[1]+v[1]]
       return resultant
   
   #Another way of writing it
   def vecadd2(vectors):
       resultant = [0,0]
       for v in vectors:
           resultant[0] = resultant[0]+v[0]
           resultant[1] = resultant[1]+v[1]
       return resultant
   
   vec1 = [6,1]
   vec2 = [1,6]
   vec3 = [-7,-7]
   veclist = [vec1,vec2,vec3]
   print vecadd(veclist) # vectors should sum to [0,0]
   print vecadd2(veclist)# vectors should sum to [0,0]