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 episode, we wrote some code that plots some values of interest from our first supernova dataset, from 03D1a1.csv

We have a ~230 data sets right now and 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 printing each character in a word on a line of its own.

word = 'lead'

We can access a character in a string using its index. For example, we can get the first character of the word 'lead', by using word[0]. One way to print each character is to use four print statements:

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

l
e
a
d

This is a bad approach for three reasons:

1. Not scalable. Imagine you need to print characters of a string that is hundreds of letters long. It might be easier just to type them in manually.

2. Difficult to maintain. If we want to decorate each printed character with an asterix or any other character, we would have to change four lines of code. While this might not be a problem for short strings, it would definitely be a problem for longer ones.

3. Fragile. If we use it with a word that has more characters than what we initially envisioned, it will only display part of the word’s characters. A shorter string, on the other hand, will cause an error because it will be trying to display part of the string that don’t exist.

Here’s a better approach:

word = 'lead'
for char in word:
    print(char)

l
e
a
d

This is shorter — certainly shorter than something that prints every character in a hundred-letter string — and more robust as well:

word = 'oxygen'
for char in word:
    print(char)

o
x
y
g
e
n

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 using variable

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

where each character (char) in the variable word is looped through and printed one character after another. The 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 char as a mnemonic; it is short for ‘character’. 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:

word = 'oxygen'
for banana in word:
    print(banana)

o
x
y
g
e
n

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:

length = 0
for vowel in 'aeiou':
    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.

Note that 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

Note also that finding the length of a string 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.

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 using 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.