1 Hello friends and welcome to the tutorial on Sets

     2 

     3 {{{ Show the slide containing title }}}

     4 

     5 {{{ Show the slide containing the outline slide }}}

     6 

     7 In this tutorial, we shall learn

     8 

     9  * sets

    10  * operations on sets

    11 

    12 Sets are data structures which contain unique elements. In other words,

    13 duplicates are not allowed in sets.

    14 

    15 Lets look at how to input sets.

    16 type

    17 ::

    18  

    19     a_list = [1, 2, 1, 4, 5, 6, 7]

    20     a = set(a_list)

    21     a

    22      

    23 We can see that duplicates are removed and the set contains only unique

    24 elements. 

    25 ::

    26 

    27     f10 = set([1, 2, 3, 5, 8])

    28     p10 = set([2, 3, 5, 7])

    29 

    30 f10 is the set of fibonacci numbers from 1 to 10.

    31 p10 is the set of prime numbers from 1 to 10.

    32 

    33 Various operations that we do on sets are possible here also.

    34 The | character stands for union

    35 ::

    36 

    37     f10 | p10

    38 

    39 gives us the union of f10 and p10

    40 

    41 The & character stands for intersection.

    42 ::

    43 

    44     f10 & p10

    45 

    46 gives the intersection

    47 

    48 similarly,

    49 ::

    50 

    51     f10 - p10

    52 

    53 gives all the elements that are in f10 but not in p10

    54 

    55 ::

    56 

    57     f10 ^ p10

    58 

    59 is all the elements in f10 union p10 but not in f10 intersection p10. In

    60 mathematical terms, it gives the symmectric difference.

    61 

    62 Sets also support checking of subsets.

    63 ::

    64 

    65     b = set([1, 2])

    66     b < f10

    67 

    68 gives a True since b is a proper subset of f10.

    69 Similarly,

    70 ::

    71 

    72     f10 < f10

    73 

    74 gives a False since f10 is not a proper subset.

    75 hence the right way to do would be

    76 ::

    77 

    78     f10 <= f10

    79 

    80 and we get a True since every set is a subset of itself.

    81 

    82 Sets can be iterated upon just like lists and tuples. 

    83 ::

    84 

    85     for i in f10:

    86         print i,

    87 

    88 prints the elements of f10.

    89 

    90 The length and containership check on sets is similar as in lists and tuples.

    91 ::

    92 

    93     len(f10)

    94 

    95 shows 5. And

    96 ::

    97     

    98     1 in f10

    99     2 in f10

   100 

   101 prints True and False respectively

   102 

   103 The order in which elements are organised in a set is not to be relied upon 

   104 since sets do not support indexing. Hence, slicing and striding are not valid

   105 on sets.

   106 

   107 {{{ Pause here and try out the following exercises }}}

   108 

   109 %% 1 %% Given a list of marks, marks = [20, 23, 22, 23, 20, 21, 23] 

   110         list all the duplicates

   111 

   112 {{{ continue from paused state }}}

   113 

   114 Duplicates marks are the marks left out when we remove each element of the 

   115 list exactly one time.

   116 

   117 ::

   118 

   119     marks = [20, 23, 22, 23, 20, 21, 23] 

   120     marks_set = set(marks)

   121     for mark in marks_set:

   122         marks.remove(mark)

   123 

   124     # we are now left with only duplicates in the list marks

   125     duplicates = set(marks)

   126 

   127 {{{ Show summary slide }}}

   128 

   129 This brings us to the end of the tutorial.

   130 we have learnt

   131 

   132  * How to make sets from lists

   133  * How to input sets

   134  * How to perform union, intersection and symmectric difference operations

   135  * How to check if a set is a subset of other

   136  * The various similarities with lists like length and containership

   137 

   138 {{{ Show the "sponsored by FOSSEE" slide }}}

   139 

   140 #[Nishanth]: Will add this line after all of us fix on one.

   141 This tutorial was created as a part of FOSSEE project, NME ICT, MHRD India

   142 

   143 Hope you have enjoyed and found it useful.

   144 Thankyou

   145  

   146 .. Author              : Nishanth

   147    Internal Reviewer 1 : 

   148    Internal Reviewer 2 : 

   149    External Reviewer   :

   150 

   151 

   152 Questions

   153 =========

   154 

   155  1. If ``a = [1, 1, 2, 3, 3, 5, 5, 8]``. What is set(a)

   156 

   157    a. set([1, 1, 2, 3, 3, 5, 5, 8])

   158    #. set([1, 2, 3, 5, 8])

   159    #. set([1, 2, 3, 3, 5, 5])

   160    #. Error

   161 

   162    Answer: set([1, 2, 3, 5, 8])

   163 

   164  2. ``a = set([1, 3, 5])``. How do you find the length of a?

   165 

   166    Answer: len(a)

   167 

   168  3. ``a = set([1, 3, 5])``. What does a[2] produce?

   169 

   170    a. 1

   171    #. 3

   172    #. 5

   173    #. Error

   174 

   175    Answer: Error

   176 

   177  4. ``odd = set([1, 3, 5, 7, 9])`` and ``squares = set([1, 4, 9, 16])``. What

   178     is the value of ``odd | squares``?

   179 

   180    Answer: set([1, 3, 4, 5, 7, 9, 16])

   181 

   182  5. ``odd = set([1, 3, 5, 7, 9])`` and ``squares = set([1, 4, 9, 16])``. What

   183     is the value of ``odd - squares``?

   184 

   185    Answer: set([3, 5, 7])

   186 

   187  6. ``odd = set([1, 3, 5, 7, 9])`` and ``squares = set([1, 4, 9, 16])``. What

   188     is the value of ``odd ^ squares``?

   189 

   190    Answer: set([3, 4, 5, 7, 16])

   191 

   192  7. ``odd = set([1, 3, 5, 7, 9])`` and ``squares = set([1, 4, 9, 16])``. What

   193     does ``odd * squares`` give?

   194 

   195    a. set([1, 12, 45, 112, 9])

   196    #. set([1, 3, 4, 5, 7, 9, 16])

   197    #. set([])

   198    #. Error

   199 

   200    Answer: Error

   201 

   202  8. ``a = set([1, 2, 3, 4])`` and ``b = set([5, 6, 7, 8])``. What is ``a + b``

   203 

   204    a. set([1, 2, 3, 4, 5, 6, 7, 8])

   205    #. set([6, 8, 10, 12])

   206    #. set([5, 12, 21, 32])

   207    #. Error

   208 

   209  9. ``a`` is a set. how do you check if if a varaible ``b`` exists in ``a``?

   210 

   211    Answer: b in a

   212 

   213  10. ``a`` and ``b`` are two sets. What is ``a ^ b == (a - b) | (b - a)``?

   214 

   215    a. True

   216    #. False

   217 

   218    Answer: False

   219 

   220 

   221 Problems

   222 ========

   223 

   224  1. Given that mat_marks is a list of maths marks of a class. Find out the

   225     no.of duplicates marks in the list.

   226 

   227    Answer::

   228 

   229      unique_marks = set(mat_marks)

   230      no_of_duplicates = len(mat_marks) - len(unique_marks)

   231 

   232  2. Given that mat_marks is a list of maths marks of a class. Find how many

   233     duplicates of each mark exist.

   234 

   235    Answer::

   236 

   237      marks_set = set(mat_marks)

   238      for mark in marks_set:

   239          occurences = mat_marks.count(mark)

   240          print occurences - 1, "duplicates of", mark, "exist"