Objectives. Write simple Python programs that involve the following:

1. One-dimensional lists.

2. Two-dimensional (non-ragged and ragged) lists.

Problem 1. (Basic Stats) Write a program stats.py that writes the mean , variance V ar, and standard deviation of the oats x1,x2,...,xn supplied as command-line arguments, computed using the formulae:

=

x1 + x2 ++ xn n

,V ar =

(x1 )2 + (x2 )2 ++ (xn )2 n

, and = V ar.

$ python3 stats.py 77 41 3 76 19 48 92 10 26 63 45.5 856.65 29.268583840015218

Problem 2. (Longest Stretch) Write a program longest_stretch.py that writes the longest contiguous sequence of equal integer values, from the sequence of integers read from the command line. If there are multiple stretches of the same length, the program should write the rst one.

$ python3 longest_stretch.py 1 1 2 3 4 4 4 5 5 6 6 6 7 4 4 4 $ python3 longest_stretch.py 1 1 2 3 4 4 4 5 5 6 6 6 6 6 6 6 6 $ python3 longest_stretch.py 1 1 2 3 4 4 4 5 5 6 6 6 6 7 6 6 6 6 $ python3 longest_stretch.py 1 2 3 4 5 1

Problem 3. (Inverse Permutation) Write a program inverse_permutation.py that accepts a permutation of the integers 0 through n1 as n command-line arguments and writes its inverse. If the permutation is a list a, its inverse is the list b such that a[b[i]] = b[a[i]] = i. Be sure to check that the input is a valid permutation. If not, the program must exit with the message Not a permutation you can do this by calling the function sys.exit(msg), where msg is the message you want to write.

$ python3 inverse_permutation.py 1 2 3 4 5 Not a permutation $ python3 inverse_permutation.py 5 3 4 0 1 2 3 4 5 1 2 0 $ python3 inverse_permutation.py 0 1 2 3 4 5 0 1 2 3 4 5 $ python3 inverse_permutation.py 5 4 3 2 1 0 5 4 3 2 1 0

Problem 4. (Birthday Problem) Suppose that people enter an empty room until a pair of people share a birthday. On average, how many people will have to enter before there is a match? Write a program birthday.py that takes an integer trials from the command line and runs trials experiments to estimate this quantity, where each experiment involves sampling individuals until a pair of them share a birthday. Assume birthdays to be uniform random integers from the interval [0,365).

$ python3 birthday.py 1000 24

Problem 5. (Pascals Triangle) Pascals triangle Pn is a triangular array with n+1 rows, each listing the coecients of the binomial expansion (x + y)i, where 0 i n. For example, P4 is the triangular array: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 The term Pn(i,j) is calculated as Pn(i1,j1) +Pn(i1,j), where 0 i n and 1 j < i, with Pn(i,0) = Pn(i,i) = 1 for all i. Write a program pascal.py that takes an integer n as command-line argument and writes Pn. $ python3 pascal.py 10 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1