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Set is another collection data type in Python. However, it is not sequence, such as List or Tuple. It is an unordered collection of items. Hence, its constituent items don’t follow zero based positional index. Set also doesn’t allow duplicate objects to be stored, where as in List and Tuple, same object can appear more than once.

Set theory is an Important branch of Mathematics. Set data type is a Python implementation of set as defined in Mathematics. The built-in Set class has defined in it lot of suitable methods to perform mathematical set operations like union, intersection, difference etc.

A Set object contains one or more items, which may be of same or different type, separated by comma and enclosed in curly brackets {}. As mentioned earlier, Set doesn’t store duplicate objects. So, even if same object is put more than once inside curly brackets, only one copy appears in the object.

In [1]: s1={10,34,32,11,25} s1 Out[1]: {10, 11, 25, 32, 34} In [2]: s1={100, "Hundred", 10.25, 10.100+5j} s1 Out[2]: {(10.1+5j), 10.25, 100, 'Hundred'}

The set object can store a collection of only immutable objects such as number, string and tuple. If we try to include a list or dict object in curly brackets, Python raises TypeError saying that these are unhashable.

Hashing is a mechanism in computer science which enables quicker searching of objects in computer’s memory. Python interpreter uses its own hashing algorithm to store items in set. As a result, items may not appear in the same sequence as used in its literal representation. Python optimizes the structure for improved performance of set operations.

In [3]: s2={{1:11,2:22},(10,20),{1,2,3}} s2 --------------------------------------------------------------------------- TypeError Traceback (most recent call last) <ipython-input-3-1ae95440415b> in <module>() ----> 1 s2={{1:11,2:22},(10,20),{1,2,3}} 2 s2 TypeError: unhashable type: 'dict'

Python has an in-built function set() using which set object can be constructed out of any sequence like string, list or tuple object. In fact this function acts as constructor of built-in set class.When used without arguments, set() produces empty set.

In [4]: s2=tuple(range(5)) s2 Out[4]: (0, 1, 2, 3, 4) In [5]: s2=set() s2 Out[5]: set() In [6]: s3=set("Hello World") s3 Out[6]: {' ', 'H', 'W', 'd', 'e', 'l', 'o', 'r'} In [7]: s4=set([54,23,45,11,23,76,11]) s4 Out[7]: {11, 23, 45, 54, 76}

Even though mutable objects are not stored in a set, set itself is a mutable object. A set object can be modified by add(), update(), remove() and discard() methods.

add() | Add an element to a set.This has no effect if the element is already present. |

pop() | Remove and return an arbitrary set element.RaisesKeyError if the set is empty. |

remove() | Remove an element from a set.If the element is not a member, raise a KeyError. |

discard() | Remove an element from a set if it is a member.If the element is not a member, do nothing. |

update() | Update a set with the union of itself and others. |

In [8]: s1={"Django", "Flask", "Pyramid"} s1 Out[8]: {'Django', 'Flask', 'Pyramid'} In [9]: s1.add("Turbogears") s1 Out[9]: {'Django', 'Flask', 'Pyramid', 'Turbogears'} In [10]: s2={"NumPy", "SciPy","IPython"} s1.update(s2) s1 Out[10]: {'Django', 'Flask', 'IPython', 'NumPy', 'Pyramid', 'SciPy', 'Turbogears'}

The remove(), pop() and discard() methods drop an item from the set. pop() method drops a random item whereas remove() and discard() need an item to be dropped as argument. If not present in the set, remove() method raises KeyError exception.

In [11]: s1.remove('SciPy') s1 Out[11]: {'Django', 'Flask', 'IPython', 'NumPy', 'Pyramid', 'Turbogears'} In [12]: s1.remove("Kivy") --------------------------------------------------------------------------- KeyError Traceback (most recent call last) <ipython-input-12-29217ddff50a> in <module>() ----> 1 s1.remove("Kivy") KeyError: 'Kivy' In [13]: s1.pop() Out[13]: 'Flask' In [14]: s1 Out[14]: {'Django', 'IPython', 'NumPy', 'Pyramid', 'Turbogears'} In [15]: s1.discard("Flask") In [16]: s1 Out[16]: {'Django', 'IPython', 'NumPy', 'Pyramid', 'Turbogears'}

As mentioned earlier, set data type in Python implements set as defined in mathematics. Various Set operations like union, intersection, difference and symmetric difference can be performed using Python’s set object.

Set operations can be summarized by following table:

Union | Union of two sets is a set of all elements in both. |

Intersection | Intersection of two sets is a set containing elements common to both |

Difference | Difference of two sets results in a set containing elements only in first but not in second set. |

Symmetric difference | Result of Symmetric difference is a set consisting of elements in both sets excluding common elements |

Following methods in set class perform above operations:

difference() | Return the difference of two or more sets as a new set. |

difference_update() | Remove all elements of another set from this set. |

intersection() | Return the intersection of two sets as a new set. |

intersection_update() | Update a set with the intersection of itself and another. |

symmetric_difference() | Return the symmetric difference of two sets as a new set. |

symmetric_difference_update() | Update a set with the symmetric difference of itself and another. |

union() | Return the union of sets as a new set |

In [30]: s1={10,20,30,40,50} s2=set('abcde') s3=s1.union(s2) s3 Out[30]: {10, 20, 30, 40, 50, 'a', 'b', 'c', 'd', 'e'} In [31]: s1={10,20,30,40,50} s2={0,20,40,60} s3=s1.intersection(s2) s3 Out[31]: {20, 40} In [32]: s1={10,20,30,40,50} s2={0,20,40,60} s3=s1.difference(s2) s3 Out[32]: {10, 30, 50} In [33]: s1={10,20,30,40,50} s2={0,20,40,60} s3=s1.symmetric_difference(s2) s3 Out[33]: {0, 10, 30, 50, 60}

Above methods (union, intersection, difference and symmetric_difference) return a new set object. As against these methods intersection_update, difference_update and symmetric_difference_update perform their respective operations in place. It means s1.intersection_update(s2) will change s1 to the result of intersection with s2.

In [34]: s1={10,20,30,40,50} s2={20,40} s1.difference_update(s2) s1 Out[34]: {10, 30, 50} In [35]: s1={10,20,30,40,50} s2={0,20,40,60} s1.symmetric_difference_update(s2) s1 Out[35]: {0, 10, 30, 50, 60} In [36]: s1={10,20,30,40,50} s2={0,20,40,60} s1.intersection_update(s2) s1 Out[36]: {20, 40}

Following methods decide whether a set is a super set, sub set or two are disjoint.

isdisjoint() | Return True if two sets have a null intersection. |

issubset() | Report whether another set contains this set. |

issuperset() | Report whether this set contains another set. |

In [37]: s1={10,20,30,40,50} s2={20,40} s2.issubset(s1) Out[37]: True In [38]: s1.issuperset(s2) Out[38]: True In [39]: s1.isdisjoint(s2) Out[39]: False In [40]: s2.isdisjoint(s1) Out[40]: False

clear() method drops all items in the set keeping object intact. The del keyword on the other hand removes object from memory.

In [41]: s1.clear() s1 Out[41]: set() In [42]: del s2 s2 --------------------------------------------------------------------------- NameError Traceback (most recent call last) <ipython-input-42-9b4ca538b1cf> in <module>() 1 del s2 ----> 2 s2 NameError: name 's2' is not defined

A frozenset is different from set in the sense that it is immutable. It means that any operations that change the composition of frozenset object will raise exception.

In [46]: s1=frozenset(["Django", "Flask", "Pyramid"]) s1.add("TurboGears") --------------------------------------------------------------------------- AttributeError Traceback (most recent call last) <ipython-input-46-bfd9ac8ee662> in <module>() 1 s1=frozenset(["Django", "Flask", "Pyramid"]) ----> 2 s1.add("TurboGears") AttributeError: 'frozenset' object has no attribute 'add' In [47]: s1.pop() --------------------------------------------------------------------------- AttributeError Traceback (most recent call last) <ipython-input-47-095118de218b> in <module>() ----> 1 s1.pop() AttributeError: 'frozenset' object has no attribute 'pop'

However, set operations such as union, intersection etc. can be performed on frozenset object.

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