What Is Multiset in Data Structure?

A multiset, also known as a bag, is a data structure that allows for multiple occurrences of the same element. Unlike a set, which only allows for unique elements, a multiset can contain duplicate elements. It is an abstract data type that can be implemented in various ways, such as arrays, linked lists, or binary search trees.

Operations on Multisets

There are several standard operations that can be performed on multisets:

• Insertion: Elements can be added to the multiset. Unlike sets, duplicate elements are allowed.
• Deletion: Elements can be removed from the multiset. If there are multiple occurrences of an element, only one occurrence is removed at a time.
• Count: The number of occurrences of a specific element in the multiset can be determined.
• Search: The presence of an element in the multiset can be checked.

Use Cases for Multisets

Multisets have various applications and are useful in scenarios where duplicate elements need to be stored or counted. Some common use cases include:

• Text Analysis: Multisets can be used to analyze text documents by counting the frequency of words or characters.
• Scheduling: Multisets can represent schedules where multiple instances of an event or task need to be accounted for.
• Inventory Management: Multisets can keep track of available items with their quantities in stock.

Multiset Implementation Example

To illustrate the implementation of a multiset, let’s consider using an array. We can use the array to store elements along with their frequencies.

class Multiset {
    private int[] elements;
    private int[] frequencies;
    private int size;

    public Multiset() {
        elements = new int[100]; // Assuming a maximum of 100 elements
        frequencies = new int[100];
        size = 0;
    }

    public void insert(int element) {
        // Check if the element already exists in the multiset
        for (int i = 0; i < size; i++) {
            if (elements[i] == element) {
                frequencies[i]++;
                return;
            }
        }
        
        // If the element does not exist, add it to the multiset
        elements[size] = element;
        frequencies[size] = 1;
        size++;
    }

    public void delete(int element) {
        for (int i = 0; i < size; i++) {
            if (elements[i] == element) {
                frequencies[i]--;
                
                // Remove the element from the multiset if its frequency becomes zero
                if (frequencies[i] == 0) {
                    for (int j = i; j < size - 1; j++) {
                        elements[j] = elements[j + 1];
                        frequencies[j] = frequencies[j + 1];
                    }
                    size--;
                }
                
                return;
            }
        }
    }

    public int count(int element) {
        for (int i = 0; i < size; i++) {
            if (elements[i] == element) {
                return frequencies[i];
            }
        }
        
        return 0;
    }

    public boolean search(int element) {
        for (int i = 0; i < size; i++) {
            if (elements[i] == element) {
                return true;
            }
        }
        
        return false;
    }
}

In this implementation, we use two arrays: one to store the elements and another to store their frequencies. The insert method checks if the element already exists and increments its frequency if found.

If the element is not present, it adds it to the multiset. The delete method decrements the frequency of the element and removes it from the multiset if its frequency becomes zero. The count method returns the frequency of a given element, and the search method checks if an element is present in the multiset.

Multisets are a versatile data structure that can be used in various scenarios where duplicate elements need to be stored or counted. Understanding and implementing multisets can greatly enhance your ability to handle such scenarios effectively.