In class notes week 2

The goal for this week is to become comfortable with four basic data types in python: integers, floats, strings, and lists. By now you should be familiar with some basic linux (cd, ls); the vim editor; editing, saving, and running python files in your cs21 directory; recognizing the linux shell ($) and the python shell (>>>), and running basic python commands in the python shell. On the python side of things we talked about print(), raw_input(), saving data in variables, and the basic structure of a program (descriptive comment, definition of function, calling the function). If you have any questions about these topics, please let me know. We will be building on them this week.

Numbers

Two types: integers or whole number and floating point or decimal numbers.

Built in operations: + (addition), - (subtraction), * (multiplication), / (division), ** (exponentiation), % (remainder or mod), abs() (absolute value).

One tricky thing about python is that if a mathematical expression involves only integers, the result must be an integer. If an expression has at least one floating point number, the result is a float. Floating point numbers are approximations to real numbers. Usually this approximation is good enough (unless you are flying a spacecraft to Mars or trying to forecast the path of a Hurricane), but the answers may surprise you.

You may want to convert an int to a float. This can be done via casting using e.g., float(3). Alternatively, if we remember that an operation involving a float and an int returns a float, we can convert a possible integer variable val to a float using val=1.0*val, or val=1.*val.

What is the output of the following expressions? Are any expressions invalid? Are any results surprising?

int("3")
int("3.2")
float("3")
float("3.2")
str(3)
str(3.2)
3/2
float(3/2)
float(3)/2
3.0/2
3*1./2
5%4
6%4
8%4
7.2%4

You can import additional math functions from the math library.

>>> from math import *
>>> pi
3.1415926535897931
>>> sqrt(2)
1.4142135623730951
>>> sin(pi/4)
0.70710678118654746
>>> sin(pi/2)
1.0
>>> import math
>>> help(math) #displays all functions available to you.

If you need to import additional feature use the from <library> import * at the top of your program. You only need to import a library once. If you want to get help on a library, start a python shell, run import <library> followed by help(<library>).

Lists

We now introduce a new data type, the list, which can store multiple elements. Run the following range commands in the python shell. Remember to start python by typing python from the linux prompt.

cumin[~]$ python
Python 2.5.2 (r252:60911, Jul 31 2008, 17:28:52) 
[GCC 4.2.3 (Ubuntu 4.2.3-2ubuntu7)] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> range(5)
[0, 1, 2, 3, 4]
>>>

#List types. A list of what? 
range(5)
range(1,5)
range(1,5,2)

Think about the following questions and discuss them with a neighbor:

What is the syntax for a python list? What symbols mark the beginning and end of list and what symbol separates items in a list
The range function can be called at least three different ways (one, two, or three arguments). What are the semantics for these three versions of range? Are there more ways to call range? What type of data can you supply as arguments to range?
Try to create calls to range that generate the following lists. It may not be possible to generate all lists shown below.

[2, 4, 6, 8]
[-1, 0, 1, 2, 3]
[0, 3, 6, 9, 12]
[1, 1.5, 2, 2.5]
[4, 3, 2, 1, 0]
[1, 2, 4, 8, 16]

Loops

Just generating lists can be pretty boring, but we can loop over a list to have python execute code multiple times. This construct is called a for loop and it has the following syntax:

for <var> in <sequence>:
  <body>

Whitespace is significant. Loop body starts when indentation starts. Loop body ends when indentation ends.

for i in range(1,5,2):
  print(i)

for i in range(3):
  print("Hello there")
  print("i=%d" % (i))

Tracing. Loop semantics.

Strings

The string data type represents text. A string can be thought of as a list of characters, though there is a slight difference between a string and a list of characters. More on this later.

Python supports a few standard operations on strings including + (concatenation), * (duplication), and % (string formatting, more later).

List indexing and slicing

We can loop over any list and since strings are almost like a list of characters, we can can loop over strings:

>>> s="Swarthmore"
>>> for ch in s:
...   print(ch)
... 
S
w
a
r
t
h
m
o
r
e

For any list, we can also use the function len() to determine the number of items in the list.

>>> len(s)
10
>>> values=range(3)
>>> len(values)
3

We can also select parts of a list using the indexing operator. Try the following statements in the python shell. What are the semantics of ls[0], ls[-1], ls[2:4], ls[:-1], and ls[2:]? Try some more examples to experiment.

ls=range(1,11)
s="Swarthmore"
ls[0]
ls[-1]
ls[2:4]
ls[:-1]
ls[2:]
s[0]
s[-1]
s[-4:]
s[:3]+s[4]

The primary difference between lists and strings is that lists are mutable while strings are not. Thus, we can change elements in a list, but not in a string.

print(ls)
ls[0]=2009
s[3]='a'

The accumulator pattern

A design pattern is a generic method for solving a class of problems. The standard algorithm might be described as follows:

get input
process input and do computation
display output

Almost any computational problem can be set up in this very general way, but step two is a very vague. Let's look at another common pattern, the accumulator.

initialize accumulator variable(s)
loop until done:
  update accumulator variable(s)
display output

Many useful computational problems fit this pattern. Examples include computing a sum, average, or standard deviation of a list of numbers, reversing a string, or counting the number of times a particular value occurs in a list. Let's try to compute the average of a list of numbers entered by the user. Prompt the user to first enter the number of values he/she wishes to average and then prompt for each number. Finally display the average. Start with pseudocode, a written idea that organizes your thought process. Then write your solution in python and test.

String Formatting

We can get more control over how data values are displayed using string formatting.

myInt = 86
myFloat = 1./3
print("The value %d is an integer but %0.2f is not" % (myInt, myFloat))

Using this new style requires a few steps. First, set up a string that contains one or more formatting tags. All tags have the form %<width><.><precision><type-char>. The type-char is s for strings, d for integers (don't ask why), and f for floats. Do not put any variable names in the format string, just tags which serve as placeholders for data that will come later. After the format string put a single % symbol after the close quote. Finally, place the data elements that you wish to substitute for the tags separated by commas and enclosed in parentheses. Let's step through a few examples in the python shell.

>>> month="Sep"
>>> day=8
>>> year=2015
>>> print("Today is %d %s %d" % (day, month, year))
Today is 8 Sep 2015
>>> print("Tomorrow is %d/%d/%d" %(9,day+1, year))
Tomorrow is 9/8/2015
>>> for val in range(1,200,20):
...   print("%7.2f" % (val*6.582118))
... 
   6.58
 138.22
 269.87
 401.51
 533.15
 664.79
 796.44
 928.08
1059.72
1191.36

Loops, Numbers, and Strings