19. For Loops
By Bernd Klein. Last modified: 29 Jun 2022.
Introduction
Like the while loop the for loop is a programming language statement, i.e. an iteration statement, which allows a code block to be repeated a certain number of times.
There are hardly any programming languages without for loops, but the for loop exists in many different flavours, i.e. both the syntax and the semantics differs from one programming language to another.
Different kinds of for loops:
-
Count-controlled for loop (Three-expression for loop)
This is by far the most common type. This statement is the one used by C. The header of this kind of for loop consists of a three-parameter loop control expression. Generally it has the form: for (A; Z; I) A is the initialisation part, Z determines a termination expression and I is the counting expression, where the loop variable is incremented or dcremented. An example of this kind of loop is the for-loop of the programming language C: for (i=0; i <= n; i++) This kind of for loop is not implemented in Python!
-
Numeric Ranges
This kind of for loop is a simplification of the previous kind. It's a counting or enumerating loop. Starting with a start value and counting up to an end value, like for i = 1 to 100 Python doesn't use this either.
-
Vectorized for loops
They behave as if all iterations are executed in parallel. That is, for example, all expressions on the right side of assignment statements get evaluated before the assignments.
-
Iterator-based for loop
Finally, we come to the one used by Python. This kind of for loop iterates over an enumeration of a set of items. It is usually characterized by the use of an implicit or explicit iterator. In each iteration step a loop variable is set to a value in a sequence or other data collection. This kind of for loop is known in most Unix and Linux shells and it is the one which is implemented in Python.
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Syntax of the For Loop
As we mentioned earlier, the Python for loop is an iterator based for loop. It steps through the items of lists, tuples, strings, the keys of dictionaries and other iterables. The Python for loop starts with the keyword "for" followed by an arbitrary variable name, which will hold the values of the following sequence object, which is stepped through. The general syntax looks like this:
for <variable> in <sequence>:
<statements>
else:
<statements>
The items of the sequence object are assigned one after the other to the loop variable; to be precise the variable points to the items. For each item the loop body is executed.
Example of a simple for loop in Python:
languages = ["C", "C++", "Perl", "Python"]
for language in languages:
print(language)
OUTPUT:
C C++ Perl Python
The else block is special; while Perl programmer are familiar with it, it's an unknown concept to C and C++ programmers. Semantically, it works exactly as the optional else of a while loop. It will be executed only if the loop hasn't been "broken" by a break statement. So it will only be executed, after all the items of the sequence in the header have been used.
If a break statement has to be executed in the program flow of the for loop, the loop will be exited and the program flow will continue with the first statement following the for loop, if there is any at all. Usually break statements are wrapped into conditional statements, e.g.
edibles = ["bacon", "spam", "eggs", "nuts"]
for food in edibles:
if food == "spam":
print("No more spam please!")
break
print("Great, delicious " + food)
else:
print("I am so glad: No spam!")
print("Finally, I finished stuffing myself")
OUTPUT:
Great, delicious bacon No more spam please! Finally, I finished stuffing myself
Removing "spam" from our list of edibles, we will gain the following output:
$ python for.py Great, delicious bacon Great, delicious eggs Great, delicious nuts I am so glad: No spam! Finally, I finished stuffing myself $
Maybe, our disgust with spam is not so high that we want to stop consuming the other food. Now, this calls the continue statement into play . In the following little script, we use the continue statement to go on with our list of edibles, when we have encountered a spam item. So continue prevents us from eating spam!
edibles = ["bacon", "spam", "eggs","nuts"]
for food in edibles:
if food == "spam":
print("No more spam please!")
continue
print("Great, delicious " + food)
print("Finally, I finished stuffing myself")
OUTPUT:
Great, delicious bacon No more spam please! Great, delicious eggs Great, delicious nuts Finally, I finished stuffing myself
The range() Function
The built-in function range() is the right function to iterate over a sequence of numbers. It generates an iterator of arithmetic progressions: Example:
range(5)
OUTPUT:
range(0, 5)
This result is not self-explanatory. It is an object which is capable of producing the numbers from 0 to 4. We can use it in a for loop and you will see what is meant by this:
for i in range(5):
print(i)
OUTPUT:
0 1 2 3 4
range(n) generates an iterator to progress the integer numbers starting with 0 and ending with (n -1). To produce the list with these numbers, we have to cast range() with the list(), as we do in the following example.
list(range(10))
OUTPUT:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
range() can also be called with two arguments:
range(begin, end)
The above call produces the list iterator of numbers starting with begin (inclusive) and ending with one less than the number end.
Example:
range(4, 10)
OUTPUT:
range(4, 10)
list(range(4, 10))
OUTPUT:
[4, 5, 6, 7, 8, 9]
So far the increment of range() has been 1. We can specify a different increment with a third argument. The increment is called the step. It can be both negative and positive, but not zero:
range(begin,end, step)
Example with step:
list(range(4, 50, 5))
OUTPUT:
[4, 9, 14, 19, 24, 29, 34, 39, 44, 49]
It can be done backwards as well:
list(range(42, -12, -7))
OUTPUT:
[42, 35, 28, 21, 14, 7, 0, -7]
The range() function is especially useful in combination with the for loop, as we can see in the following example. The range() function supplies the numbers from 1 to 100 for the for loop to calculate the sum of these numbers:
n = 100
sum = 0
for counter in range(1, n+1):
sum = sum + counter
print("Sum of 1 until %d: %d" % (n, sum))
OUTPUT:
Sum of 1 until 100: 5050
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Calculation of the Pythagorean Numbers
Generally, it is assumed that the Pythagorean theorem was discovered by Pythagoras that is why it has his name. However, there is a debate whether the Pythagorean theorem might have been discovered earlier or by others independently. For the Pythagoreans, - a mystical movement, based on mathematics, religion and philosophy, - the integer numbers satisfying the theorem were special numbers, which had been sacred to them.
These days Pythagorean numbers are not mystical anymore. Though to some pupils at school or other people, who are not on good terms with mathematics, they may still appear so.
So the definition is very simple: Three integers satisfying a2+b2=c2 are called Pythagorean numbers.
The following program calculates all pythagorean numbers less than a maximal number. Remark: We have to import the math module to be able to calculate the square root of a number.
from math import sqrt
n = int(input("Maximal Number? "))
for a in range(1, n+1):
for b in range(a, n):
c_square = a**2 + b**2
c = int(sqrt(c_square))
if ((c_square - c**2) == 0):
print(a, b, c)
OUTPUT:
3 4 5 5 12 13 6 8 10 7 24 25 8 15 17 9 12 15 9 40 41 10 24 26 11 60 61 12 16 20 12 35 37 13 84 85 14 48 50 15 20 25 15 36 39 16 30 34 16 63 65 18 24 30 18 80 82 20 21 29 20 48 52 20 99 101 21 28 35 21 72 75 24 32 40 24 45 51 24 70 74 25 60 65 27 36 45 28 45 53 28 96 100 30 40 50 30 72 78 32 60 68 33 44 55 33 56 65 35 84 91 36 48 60 36 77 85 39 52 65 39 80 89 40 42 58 40 75 85 40 96 104 42 56 70 45 60 75 48 55 73 48 64 80 48 90 102 51 68 85 54 72 90 56 90 106 57 76 95 60 63 87 60 80 100 60 91 109 63 84 105 65 72 97 66 88 110 69 92 115 72 96 120 80 84 116
Iterating over Lists with range()
If you have to access the indices of a list, it doesn't seem to be a good idea to use the for loop to iterate over the lists. We can access all the elements, but the index of an element is not available. However, there is a way to access both the index of an element and the element itself. The solution lies in using range() in combination with the length function len():
fibonacci = [0, 1, 1, 2, 3, 5, 8, 13, 21]
for i in range(len(fibonacci)):
print(i,fibonacci[i])
print()
OUTPUT:
0 0 1 1 2 1 3 2 4 3 5 5 6 8 7 13 8 21
Remark: If you apply len() to a list or a tuple, you get the number of elements of this sequence.
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List iteration with Side Effects
If you loop over a list, it's best to avoid changing the list in the loop body. Take a look at the following example:
colours = ["red"]
for i in colours:
if i == "red":
colours += ["black"]
if i == "black":
colours += ["white"]
print(colours)
OUTPUT:
['red', 'black', 'white']
To avoid these side effects, it's best to work on a copy by using the slicing operator, as can be seen in the next example:
colours = ["red"]
for i in colours[:]:
if i == "red":
colours += ["black"]
if i == "black":
colours += ["white"]
print(colours)
OUTPUT:
['red', 'black']
We still might have done something, we shouldn't have done. We changed the list "colours", but our change didn't have any effect on the loop. The elements to be looped remained the same during the iterations.
Exercises with for Loops
Exercise 1
This exercise is about the Ramanujan-Hardy number. There is a little anecdote of the Mathematician G.H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital. It goes like this:
I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."
For this reason 1732 is known as the Ramanujan-Hardy number.
Can you verify this with a Python program?
Exercise 2
1729 is the lowest number which can be represented by a Loeschian quadratic form $a^2 + ab + b^2$ in four different ways, with positive integers a and b .
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Solutions
Solution to Exercise 1
import math
number = 1729
n = int(number ** (1/3))
cubes = {}
for i in range(n+1):
for j in range(i):
result = i ** 3 + j ** 3
if result in cubes:
cubes[result].append((i, j))
else:
cubes[result] = [(i,j)]
if result > number:
break
for x in cubes:
if len(cubes[x]) > 1:
print(x, cubes[x])
OUTPUT:
1729 [(10, 9), (12, 1)]
Solution to Exercise 2
import math
number = 1729
n = int(number ** (1/2))
results = {}
for a in range(n+1):
for b in range(a):
result = a**2 + a*b + b**2
if result in results:
results[result].append((a, b))
else:
results[result] = [(a,b)]
if result > number:
break
for x in results:
if len(results[x]) > 3:
print(x, results[x])
OUTPUT:
1729 [(25, 23), (32, 15), (37, 8), (40, 3)]
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