Question

A multiset is a collection in which each item occurs with a frequency. You might have a multiset with two bananas and three apples, for example. A multiset can be implemented as a dictionary in which the keys are the items and the values are the frequencies. Implement a class, Multiset, with the following.

Constructor
1) init (self)
Instance Variables
a) data dictionary which holds information about items and their frequency
Methods
i) addItem(key, value)
ii) adds a new key value pair to the dictionary
iii) union(mSet) -takes the MultiSet mSet and returns a multiset representing the multiset union. The union is the sum total of all the items in two multisets.
iv) intersection(mSet) - takes the MultiSet mSet and returns a multiset representing the multiset intersection. The intersection is the minimum of the frequencies between two multisets.
v) difference (mSet) - takes the MultiSet mSet and returns a multiset representing the multiset difference between itself and the mSet. The difference is the difference of the frequencies in both multisets, but not less than zero.

Answer 1

The 'Multiset' class is a data structure in Python that allows items to have frequencies, similar to sets but with counts for each element. It is implemented with a dictionary to hold the pairs and methods to perform union, intersection, and difference operations between multisets.

Step-by-step explanation:

The task involves implementing a class called Multiset to work with collections that allow multiple occurrences of elements. The class should have a constructor that initializes a data dictionary, and three methods for set operations: addItem, union, intersection, and difference. The addItem method will add a key-value pair to the dictionary. The union method computes the multiset union by summing the frequencies of items from both multisets. The intersection method finds the common elements and uses the minimum frequency of the item from both multisets. Lastly, the difference method calculates the difference in frequencies of items between two multisets, ensuring that the result does not include negative frequencies.

Below is the example implementation of the Multiset class:

class Multiset:
def __init__(self):
self.data = {}

def addItem(self, key, value):
if key in self.data:
self.data[key] += value
else:
self.data[key] = value

def union(self, mSet):
result = Multiset()
result.data = self.data.copy()
for key in mSet.data:
if key in result.data:
result.data[key] += mSet.data[key]
else:
result.data[key] = mSet.data[key]
return result

def intersection(self, mSet):
result = Multiset()
keys_intersection = set(self.data.keys()) & set(mSet.data.keys())
for key in keys_intersection:
result.data[key] = min(self.data[key], mSet.data[key])
return result

def difference(self, mSet):
result = Multiset()
result.data = self.data.copy()
for key in mSet.data:
if key in result.data:
result.data[key] = max(result.data[key] - mSet.data[key], 0)
# If key not in result, we skip it as it does not contribute to the difference.
return result