15-110 Fall 2010 Quiz 6
15 Minutes

* No calculators, no notes, no books, no computers.
* Show your work.  Correct answers without supporting calculations will not receive full credit.

1.  Tracing (30 pts)
Indicate what the following code will print.

A) (15 pts)

a = [1, 2, 3, 4]
x = 9
while (x > a[0]):
    x -= a.pop(0)
    print x
    print a

B) (15 pts)

a1 = [ "a" , "bcd", "efg" , "ij" ]
a2 = [ "kl", "m"  , "nop" , "q" ]
a3 = [ ]
for i in range(len(a1)):
    if (len(a1[i]) > len(a2[i])):
        a3.append(a1[i])
    else:
        print a2[i]
print a3

2.  Mystery Method (20 pts)
State in just a few words of plain English what the following function does in general:

def mystery(a):
    # assume a is a list
    b = [ ]
    for i in range(len(a)):
        for j in range(i+1, len(a)):
            if ((a[i] == a[j]) and (a[i] not in b)):
                b.append(a[i])
    return b

3.  (50 pts) Write the function isIdentity(matrix).  This function takes a matrix (a rectangular 2d list), and returns True if the matrix is an “identity” matrix and False otherwise.  An Identity Matrix must be a square matrix (same number of rows as cols), and every value must be zero except on the top-left to bottom-right diagonal, where the values must be one.

4.  Bonus/Optional (5 pts)
State in just a few words of plain English what the following function does in general:

def mystery(a):
    # assume a is a list of non-negative integers
    b = range(len(a))
    b.remove(0)
    b.append(len(a))
    for x in a:
        if (x not in b):
            return False
        b.remove(x)
    return (b == [ ])