algorithm priorityqueuesort note that the elements of the input sequence serve as keys of the priority queue implementing priority queue with list in this sectionwe show how to implement priority queue by storing its entries in list (see we provide two realizationsdepending on whether or not we keep the entries in sorted by key when analyzing the running time of the methods of priority queue implemented with listwe will assume that comparison of two keys takes ( time implementation with an unsorted list as our first implementation of priority queue plet us consider storing the entries of in list swhere is implemented with doubly linked list thusthe elements of are entries ( , )where is the key and is the value fast insertions and slow removals simple way of performing operation insert( ,xon is to create new entry object ( ,xand add it at the end of list sby executing method addlast(eon this implementation of method insert takes ( time the above insertion algorithm implies that will be unsortedfor always inserting entries at the end of does not take into account the ordering of the keys as consequenceto perform operation min or removemin on pwe must inspect all the elements of list to find an entry (kxof with minimum thusmethods min and removemin take (ntime eachwhere is the number of entries in