Python: The min method for the UnsortedPriorityQueue class executes in O(n) time, as analyzed in Table 9.2. Give a simple modification to the class so that min runs in O(1) time. Explain any necessary modifications to other methods of the class. Table 9.2 compares the running times of the methods of a priority queue realizedby means of a sorted and unsorted list, respectively. We see an interesting trade-off when we use a list to implement the priority queue ADT. An unsorted listsupports fast insertions but slow queries and deletions, whereas a sorted list allowsfast queries and deletions, but slow insertions.Operationlenis_emptyaddminremove_minUnsorted List Sorted ListO(1)O(1)0(1)0(1)0(1)O(n)O(n)O(n)O(1)O(1)Table 9.2: Worst-case running times of the methods of a priority queue of size n,realized by means of an unsorted or sorted list, respectively. We assume that thelist is implemented by a doubly linked list. The space requirement is O(n).

when we use priority queues then use key K and value V to be considered as a single object. The following code we defining the public Interface Entry as below. public interface Entry<K,V>{K getKey();V getValue();} The Entry Type in the interface for priority queue as below which indeed helps in returning key and value as single object from methods such as min and removeMin public interface PriorityQueue<K,V>{int size();boolean isEmpty();Entry<K,V> insert(K key, V value) throws IllegalArgumentException;Entry<K,V> min(); //provides the key stored in this entryEntry<K,V> removeMin(); //provides the value stored in this entry // returns and entry with minimal key. public Entry<K,V> min( ){if (list.isEmpty( )) return null;return findMin( ).getElement( ); } //removes and returns an entry with minimal key, public Entry<K,V> removeMin( ) {if (list.isEmpty( )) return null;return list.remove(findMin( )); } // Inserts a key-value pair and returns the entry created. public Entry<K,V> insert(K key, V value) throws IllegalArgumentException {checkKey(key); Entry<K,V> newest = new PQEntry<>(key, value);list.addLast(newest);return newest; }