Numbers and Strings
Solution to grad year program
update21 to get a sample solution to the grad year program from last Friday.
Python math operators
Mathematical calculations are one of the most common uses of computer programming. Below is a quick summary of python3 math syntax and semantics. I encourage you to try examples in the python interpreter and ask questions about strange cases.
/represent addition, subtraction, multiplication, and division. When you add, subtract, or multiply two integers, you get an integer. When you add, subtract, or multiply two floats, you get a float. Any addition, subtraction, multiplication, or division that involves one float and one integer results in a float answer.
Division using '/' in python3 always results in a float, regardless of the input types. Perhaps this makes sense to you. Why wouldn’t 3/2 be 1.5? If this is the case,
python3agrees with you, but in many other programming languages, including C and C++ used in CS31 and C35, the rules for division are a bit different.
Sometimes, you might want to divide an integer by another and get an integer instead of a decimal number. The
//operator rounds the value down returning an integer, e.g. 3//2 returns 1.
Exponents. To raise a number to a power, use the exponential operator
mod. Python also supports division with remainder using the "mod" operator
%. We’ll explain this more when we need it.
You can also combine many operators in one statement e.g.
2*x+10, but note you must explicitly include the
* to multiply. The algebraic form
2x+3 is a syntax error.
Take a minute or two, open up a python interpreter window, and play around with math operators. Do they do anything unexpected? Try to combine them in larger expressions. What happens?
$ python3 Python 3.6.7 (default, Oct 22 2018, 11:32:17) [GCC 8.2.0] on linux Type "help", "copyright", "credits" or "license" for more information. >>> >>> 5+2 7 >>> 5-2 3 >>> 5*2 10 >>> 5/2 2.5 >>> 5//2 2 >>> 2**5 32 >>> 2**32 4294967296 >>> 19/5 3.8 >>> 19//5 3 >>> 19%5 4 >>> 3*5 + 4 19 >>> quit()
Some math operators can be used with strings:
+for string concatenation.
You can use
<str>*<int>to repeat a string multiple times
>>> hw = "hello" + "world!" >>> print(hw) helloworld! >>> "hello"*3 `hellohellohello`
Some other math operators can also be used with strings, but in somewhat more complicated ways. We will explore these operators a little later in the semester. Stay tuned!
Expressions, operator precedence
An expression is a combination of values, variables, operators, outputs of Python commands like
input, and even other expressions! The evaluation of an expression produces a value. e.g. the evaluation of
41. This is why expressions can appear on the right-hand side of assignment statements. Large mathematical expressions are common in Python.
Order of Operations
When more than one operator appears in an expression, which gets executed first depends on the rules of precedence. Python follows the following rules
Parentheses have the highest precedence and can be used to force the expression to evaluate in the order you want. Since expressions are evaluated first,
Exponents have the next highest precedence, so
Multiplication and Division have the same precedence, which is higher than Addition and Subtraction, which also have the same precedence. So
1(remember that in integer division,
Operators with the same precedence are evaluated from left to right. So in the expression
minute*100//60, the multiplication happens first. If
minute=59, this would yield
5900//60, which in turn yields
98. If the operations had been evaluated from right to left, the result would have been
59*1, which is
59, which is wrong.
A good rule of thumb when using expressions with lots of operators is to keep things simple. Use parentheses rather than relying on operator precedence rules. Better yet, if you have large math expressions, divide your Python statement into multiple lines of code.
Python supports many other useful mathematical functions, but these are stored in separate library. A library is a separate collection of functionality not part of the main Python language.
To load math functions, include
from math import pi, sin, cos, sqrtonce at the top of your program, even before the `def main(): ` block
Once you’ve loaded the library you can call a math function as follows:
With the remaining time, write a program to compute the area of a circle. First, ask the user for a radius. Then, print out the area using the formula \$A=\pi r^2\$ (
area = pi * r**2)
Extra challenge: write a program that computes the radius of a circle, given the area.
$ python3 circle.py Enter the radius of a circle: 3 The area of a circle of radius 3 equals: 28.274333882308138
Repetition using for loops
To this point, all of our programs have been sequential - with one line of code following the other. Often, we need to repeat a task several times. If we know the number of times, we use definite loops which are called for loops in Python. The syntax is:
for VAR in SEQUENCE: BODY
For example, we can print numbers 1 through 5:
for i in [1,2,3,4,5]: print(i)
i is our loop variable - it keeps track of where we are in the sequence. Defining the sequence explicitly does not scale to large numbers (e.g., 1000) so we instead use the
for i in range(5): print(i)
0 1 2 3 4
introduction to accumulator pattern
Loop syntax recap
See previous section
Exercise: What do these loops do?
What is the output of this loop?
for i in [0,1,2,3]: print(i*2)
Notice the special syntax that uses brackets around a sequence. This is
how we designate a value of type
list is a collection of values
itself, which can be of any type (e.g.,
int in the above example). Now
try this example where the list consists of a sequence of strings:
print("Pets:") for animal in ["Corgis", "Cavaliers", "Mini Ponies"]: print(animal) print() print("Done!")
You can see examples similar to these and a few extras in your
$ cd $ cd cs21/inclass/w02-numstr $ atom ./ $ python3 loopExamples.py
cd cd cs21/inclass/w02-nums-strs-loops atom ./
loop.py to get some practice writing loops by completing one or more of the following tasks:
Print the string
trickythree times, once per line, using a loop. Would your design change if you were asked to print
Print the squared value of the integers 1 through 5 (i.e., 1,4,9,16,25). Use the range function to define your sequence, and then manipulate
iby adding 1 and squaring the value.
Write a loop that repeats three times and asks the user for a number that you then square. Note that this loop shows that the loop variable isn’t always used to do the calculation.
Ask the user for an integer \$n\$ and then print the values from \$n\$ to 1 in reverse, with one number per line.
A very common use of loops is to aggregate, or combine, the result of a repetitive set of steps. For example, we may want to sum the numbers from 1 to \$n\$. To create an accumulator pattern, we should first answer these questions to help us code the solution:
What are we accumulating? (should create a variable to store this)
Where does the accumulator start? (initialize variable; not always 0)
How many iterations/times do we loop? (use to set the range)
What do we need to calculate inside the loop? How do we update the accumulator (updating the variable must be a part of the loop)
What do we do with result of accumulation?
Looping over strings
Use the example solution for total to complete the program in
avg.py and use an accumulator pattern to average a series of numbers entered by a user.
Work with a neighbor and sketch out your solution to calculating the factorial of a number. Do
not start to code until you have answered all of the questions above for
designing an accumulation pattern.
Your program should ask the user for a number (integer) and calculate the factorial. The factorial of a number is \$x! = x \cdot (x-1) \cdot (x-2) \cdot \ldots \cdot 2 \cdot 1\$ e.g., \$5! = 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 = 120\$. Begin by answering the accumulator questions above and then start to write your program in
More String Operations
You’ve seen several instances of strings already this semester, and you’ve likely used string concatenation to build up a string. There are many other useful string operations. Here are some highlights:
length. To get the length of a string, use the
len("cs21") = 4
indexing. Access a single character in a string using its position indexing from zero. For example, if
name = "u".
concatenation. Concatenate with the
"hello" + "world" == "helloworld"
str_practice.py to complete four tasks and a couple of
extensions if you desire. Be sure to incrementally develop---complete
one task, run your program to see if that tasks works, and then move
onto the next. Tasks 4 and bonus will require for loops and
$ python3 str_practice.py Task 1: Enter first name: Tina Enter last name: Fey Welcome Tina Fey Task 2: There are 7 characters in your name Task 3: Initials: T.F. BONUS: Last initials: a.y. Task 4: T i n a