Hello friends and welcome to the tutorial on Sets
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In this tutorial, we shall learn
* sets
* operations on sets
Sets are data structures which contain unique elements. In other words,
duplicates are not allowed in sets.
Lets look at how to input sets.
type
::
a_list = [1, 2, 1, 4, 5, 6, 7]
a = set(a_list)
a
We can see that duplicates are removed and the set contains only unique
elements.
::
f10 = set([1, 2, 3, 5, 8])
p10 = set([2, 3, 5, 7])
f10 is the set of fibonacci numbers from 1 to 10.
p10 is the set of prime numbers from 1 to 10.
Various operations that we do on sets are possible here also.
The | character stands for union
::
f10 | p10
gives us the union of f10 and p10
The & character stands for intersection.
::
f10 & p10
gives the intersection
similarly,
::
f10 - p10
gives all the elements that are in f10 but not in p10
::
f10 ^ p10
is all the elements in f10 union p10 but not in f10 intersection p10. In
mathematical terms, it gives the symmectric difference.
Sets also support checking of subsets.
::
b = set([1, 2])
b < f10
gives a True since b is a proper subset of f10.
Similarly,
::
f10 < f10
gives a False since f10 is not a proper subset.
hence the right way to do would be
::
f10 <= f10
and we get a True since every set is a subset of itself.
Sets can be iterated upon just like lists and tuples.
::
for i in f10:
print i,
prints the elements of f10.
The length and containership check on sets is similar as in lists and tuples.
::
len(f10)
shows 5. And
::
1 in f10
2 in f10
prints True and False respectively
The order in which elements are organised in a set is not to be relied upon
since sets do not support indexing. Hence, slicing and striding are not valid
on sets.
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%% 1 %% Given a list of marks, marks = [20, 23, 22, 23, 20, 21, 23]
list all the duplicates
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Duplicates marks are the marks left out when we remove each element of the
list exactly one time.
::
marks = [20, 23, 22, 23, 20, 21, 23]
marks_set = set(marks)
for mark in marks_set:
marks.remove(mark)
# we are now left with only duplicates in the list marks
duplicates = set(marks)
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This brings us to the end of the tutorial.
we have learnt
* How to make sets from lists
* How to input sets
* How to perform union, intersection and symmectric difference operations
* How to check if a set is a subset of other
* The various similarities with lists like length and containership
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#[Nishanth]: Will add this line after all of us fix on one.
This tutorial was created as a part of FOSSEE project, NME ICT, MHRD India
Hope you have enjoyed and found it useful.
Thankyou
.. Author : Nishanth
Internal Reviewer 1 :
Internal Reviewer 2 :
External Reviewer :
Questions
=========
1. If ``a = [1, 1, 2, 3, 3, 5, 5, 8]``. What is set(a)
a. set([1, 1, 2, 3, 3, 5, 5, 8])
#. set([1, 2, 3, 5, 8])
#. set([1, 2, 3, 3, 5, 5])
#. Error
Answer: set([1, 2, 3, 5, 8])
2. ``a = set([1, 3, 5])``. How do you find the length of a?
Answer: len(a)
3. ``a = set([1, 3, 5])``. What does a[2] produce?
a. 1
#. 3
#. 5
#. Error
Answer: Error
4. ``odd = set([1, 3, 5, 7, 9])`` and ``squares = set([1, 4, 9, 16])``. What
is the value of ``odd | squares``?
Answer: set([1, 3, 4, 5, 7, 9, 16])
5. ``odd = set([1, 3, 5, 7, 9])`` and ``squares = set([1, 4, 9, 16])``. What
is the value of ``odd - squares``?
Answer: set([3, 5, 7])
6. ``odd = set([1, 3, 5, 7, 9])`` and ``squares = set([1, 4, 9, 16])``. What
is the value of ``odd ^ squares``?
Answer: set([3, 4, 5, 7, 16])
7. ``odd = set([1, 3, 5, 7, 9])`` and ``squares = set([1, 4, 9, 16])``. What
does ``odd * squares`` give?
a. set([1, 12, 45, 112, 9])
#. set([1, 3, 4, 5, 7, 9, 16])
#. set([])
#. Error
Answer: Error
8. ``a = set([1, 2, 3, 4])`` and ``b = set([5, 6, 7, 8])``. What is ``a + b``
a. set([1, 2, 3, 4, 5, 6, 7, 8])
#. set([6, 8, 10, 12])
#. set([5, 12, 21, 32])
#. Error
9. ``a`` is a set. how do you check if if a varaible ``b`` exists in ``a``?
Answer: b in a
10. ``a`` and ``b`` are two sets. What is ``a ^ b == (a - b) | (b - a)``?
a. True
#. False
Answer: False
Problems
========
1. Given that mat_marks is a list of maths marks of a class. Find out the
no.of duplicates marks in the list.
Answer::
unique_marks = set(mat_marks)
no_of_duplicates = len(mat_marks) - len(unique_marks)
2. Given that mat_marks is a list of maths marks of a class. Find how many
duplicates of each mark exist.
Answer::
marks_set = set(mat_marks)
for mark in marks_set:
occurences = mat_marks.count(mark)
print occurences - 1, "duplicates of", mark, "exist"