Repeating Actions with Loops

Overview

Teaching: 30 min
Exercises: 0 min

Questions

• How can I do the same operations on many different values?

Objectives

• Explain what a for loop does.

• Correctly write for loops to repeat simple calculations.

• Trace changes to a loop variable as the loop runs.

• Trace changes to other variables as they are updated by a for loop.

In the last lesson, we wrote some code that plots some values of interest from our first inflammation dataset, and reveals some suspicious features in it, such as from inflammation-01.csv

We have a dozen data sets right now, though, and more on the way. We want to create plots for all of our data sets with a single statement. To do that, we’ll have to teach the computer how to repeat things.

An example task that we might want to repeat is accessing numbers in a list, which will will do by printing each number on a line of its own.

odds = [1, 3, 5, 7]

We can access a number in the list using its index. For example, we can get the first number in the list 'odds', by using odds[0]. One way to print each number is to use four print statements:

print(odds[0])
print(odds[1])
print(odds[2])
print(odds[3])

1
3
5
7

This is a bad approach for two reasons:

1. It doesn’t scale: if we want to print the numbers in a list that contains hundreds of numbers, we’d be better off just typing them in.

2. It’s fragile: if we give it a longer list, it only prints part of the data, and if we give it a shorter one, it produces an error because we’re asking for numbers that don’t exist.

odds = [1, 3, 5]
print(odds[0])
print(odds[1])
print(odds[2])
print(odds[3])

1
3
5

---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-3-7974b6cdaf14> in <module>()
      3 print(odds[1])
      4 print(odds[2])
----> 5 print(odds[3])

IndexError: list index out of range

Here’s a better approach:

odds = [1, 3, 5, 7]
for num in odds:
    print(num)

1
3
5
7

This is shorter—certainly shorter than something that prints every number in a hundred-element list—and more robust as well:

odds = [1, 3, 5, 7, 9, 11]
for num in odds:
    print(num)

1
3
5
7
9
11

The improved version uses a for loop to repeat an operation—in this case, printing—once for each thing in a sequence. The general form of a loop is:

for variable in collection:
    do things with variable

Using the example above, the loop might look like this:

where each number (num) in the variable odds is looped through and printed one number after another. The other numbers in the diagram denote which loop cycle the character was printed in (1 being the first loop, and 6 being the final loop).

We can call the loop variable anything we like, but there must be a colon at the end of the line starting the loop, and we must indent anything we want to run inside the loop. Unlike many other languages, there is no command to signify the end of the loop body (e.g. end for); what is indented after the for statement belongs to the loop.

What’s in a name?

In the example above, the loop variable was given the name num as a mnemonic; it is short for ‘number’. We can choose any name we want for variables. We might just as easily have chosen the name banana for the loop variable, as long as we use the same name when we invoke the variable inside the loop:

odds = [1, 3, 5, 7, 9, 11]
for banana in odds:
    print(banana)

1
3
5
7
9
11

It is a good idea to choose variable names that are meaningful, otherwise it would be more difficult to understand what the loop is doing.

Here’s another loop that repeatedly updates a variable and prints characters in a string.

length = 0
for vowel in 'aeiou':
    print(vowel)
    length = length + 1
print('There are', length, 'vowels')

There are 5 vowels

It’s worth tracing the execution of this little program step by step. Since there are five characters in 'aeiou', the statement on line 3 will be executed five times. The first time around, length is zero (the value assigned to it on line 1) and vowel is 'a'. The statement adds 1 to the old value of length, producing 1, and updates length to refer to that new value. The next time around, vowel is 'e' and length is 1, so length is updated to be 2. After three more updates, length is 5; since there is nothing left in 'aeiou' for Python to process, the loop finishes and the print statement on line 4 tells us our final answer.

Finding the length of a string or list is such a common operation that Python actually has a built-in function to do it called len:

print(len('aeiou'))

5

len is much faster than any function we could write ourselves, and much easier to read than a two-line loop; it will also give us the length of many other things that we haven’t met yet, so we should always use it when we can.

A loop variable is just a variable that’s being used to record progress in a loop. It still exists after the loop is over, and we can re-use variables previously defined as loop variables as well:

letter = 'z'
for letter in 'abc':
    print(letter)
print('after the loop, letter is', letter)

a
b
c
after the loop, letter is c

From 1 to N

Python has a built-in function called range that creates a sequence of numbers. range can accept 1, 2, or 3 parameters.

• If one parameter is given, range creates an array of that length, starting at zero and incrementing by 1. For example, range(3) produces the numbers 0, 1, 2.
• If two parameters are given, range starts at the first and ends just before the second, incrementing by one. For example, range(2, 5) produces 2, 3, 4.
• If range is given 3 parameters, it starts at the first one, ends just before the second one, and increments by the third one. For exmaple range(3, 10, 2) produces 3, 5, 7, 9.

Using range, write a loop that uses range to print the first 3 natural numbers:

1
2
3

Solution

for i in range(1, 4):
   print(i)

Computing Powers With Loops

Exponentiation is built into Python:

print(5 ** 3)

125

Write a loop that calculates the same result as 5 ** 3 using multiplication (and without exponentiation).

Solution

result = 1
for i in range(0, 3):
   result = result * 5
print(result)

Reverse a String

Knowing that two strings can be concatenated using the + operator, write a loop that takes a string and produces a new string with the characters in reverse order, so 'Newton' becomes 'notweN'.

Solution

newstring = ''
oldstring = 'Newton'
for char in oldstring:
   newstring = char + newstring
print(newstring)

Computing the Value of a Polynomial

The built-in function enumerate takes a sequence (e.g. a list) and generates a new sequence of the same length. Each element of the new sequence is a pair composed of the index (0, 1, 2,…) and the value from the original sequence:

for i, x in enumerate(xs):
    # Do something with i and x

The code above loops through xs, assigning the index to i and the value to x.

Suppose you have encoded a polynomial as a list of coefficients in the following way: the first element is the constant term, the second element is the coefficient of the linear term, the third is the coefficient of the quadratic term, etc.

x = 5
cc = [2, 4, 3]

y = cc[0] * x**0 + cc[1] * x**1 + cc[2] * x**2
y = 97

Write a loop using enumerate(cc) which computes the value y of any polynomial, given x and cc.

Solution

y = 0
for i, c in enumerate(cc):
    y = y + x**i * c

Key Points

• Use for variable in sequence to process the elements of a sequence one at a time.

• The body of a for loop must be indented.

• Use len(thing) to determine the length of something that contains other values.