A Set is an unordered collection data type that is iterable, mutable, and has no duplicate elements. Python’s set class represents the mathematical notion of a set. The major advantage of using a set, as opposed to a list, is that it has a highly optimized method for checking whether a speci?c element is contained in the set. This is based on a data structure known as a hash table.

**Frozen Sets** Frozen sets are immutable objects that only support methods and operators that produce a result without a?ecting the frozen set or sets to which they are applied.

# Python program to demonstrate differences # between normal and frozen set # Same as {"a", "b","c"} normal_set = set(["a", "b","c"]) # Adding an element to normal set is fine normal_set.add("d") print("Normal Set") print(normal_set) # A frozen set frozen_set = frozenset(["e", "f", "g"]) print("Frozen Set") print(frozen_set) # Uncommenting below line would cause error as # we are trying to add element to a frozen set # frozen_set.add("h")

Output:

Normal Set set(['a', 'c', 'b', 'd']) Frozen Set frozenset(['e', 'g', 'f'])

**Methods for Sets**

**1. add(x) Method: **Adds the item x to set if it is not already present in the set.

people = {"Jay", "Idrish", "Archil"} people.add("Daxit")

-> This will add Daxit in people set.

2. **union(s) Method**: Returns a union of two set.Using the ‘|’ operator between 2 sets is the same as writing set1.union(set2)

people = {"Jay", "Idrish", "Archil"} vampires = {"Karan", "Arjun"} population = people.union(vampires)

OR

population = people|vampires

-> Set population set will have components of both people and vampire

3.** intersect(s) Method: **Returns an intersection of two sets.The ‘&’ operator comes can also be used in this case.

victims = people.intersection(vampires)

-> Set victims will contain the common element of people and vampire

**4. difference(s) Method: **Returns a set containing all the elements of invoking set but not of the second set. We can use ‘-‘ operator here.

safe = people.difference(vampires)

OR

safe = people – vampires

-> Set safe will have all the elements that are in people but not vampire

**5. clear() Method: **Empties the whole set.

victims.clear()

-> Clears victim set

However there are two major pitfalls in Python sets:

- The set doesn’t maintain elements in any particular order.
- Only instances of immutable types can be added to a Python set.

**Operators for Sets**

Sets and frozen sets support the following operators:

key in s # containment check

key not in s # non-containment check

s1 == s2 # s1 is equivalent to s2

s1 != s2 # s1 is not equivalent to s2

s1 <= s2 # s1is subset of s2

s1 < s2 # s1 is proper subset of s2

s1 >= s2 # s1is superset of s2

s1 > s2 # s1 is proper superset of s2

s1 | s2 # the union of s1 and s2

s1 & s2 # the intersection of s1 and s2

s1 – s2 # the set of elements in s1 but not s2

s1 ˆ s2 # the set of elements in precisely one of s1 or s2

Code Snippet to illustrate all Set operations in Python

# Python program to demonstrate working# of # Set in Python # Creating two sets set1 = set() set2 = set() # Adding elements to set1 for i in range(1, 6): set1.add(i) # Adding elements to set2 for i in range(3, 8): set2.add(i) print("Set1 = ", set1) print("Set2 = ", set2) print("\n") # Union of set1 and set2 set3 = set1 | set2# set1.union(set2) print("Union of Set1 & Set2: Set3 = ", set3) # Intersection of set1 and set2 set4 = set1 & set2# set1.intersection(set2) print("Intersection of Set1 & Set2: Set4 = ", set4) print("\n") # Checking relation between set3 and set4 if set3 > set4: # set3.issuperset(set4) print("Set3 is superset of Set4") elif set3 < set4: # set3.issubset(set4) print("Set3 is subset of Set4") else : # set3 == set4 print("Set3 is same as Set4") # displaying relation between set4 and set3 if set4 < set3: # set4.issubset(set3) print("Set4 is subset of Set3") print("\n") # difference between set3 and set4 set5 = set3 - set4 print("Elements in Set3 and not in Set4: Set5 = ", set5) print("\n") # checkv if set4 and set5 are disjoint sets if set4.isdisjoint(set5): print("Set4 and Set5 have nothing in common\n") # Removing all the values of set5 set5.clear() print("After applying clear on sets Set5: ") print("Set5 = ", set5)

Output:

('Set1 = ', set([1, 2, 3, 4, 5])) ('Set2 = ', set([3, 4, 5, 6, 7])) ('Union of Set1 & Set2: Set3 = ', set([1, 2, 3, 4, 5, 6, 7])) ('Intersection of Set1 & Set2: Set4 = ', set([3, 4, 5])) Set3 is superset of Set4 Set4 is subset of Set3 ('Elements in Set3 and not in Set4: Set5 = ', set([1, 2, 6, 7])) Set4 and Set5 have nothing in common After applying clear on sets Set5: ('Set5 = ', set([]))

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