linked structures earlier we were limited to the use of list or dictionary but with the introduction of the linked list in this we now have an additional option the linked list has the advantage of requiring fewer shifts and no underlying array management as is required with the python list this is especially important when working with dynamic polynomials linked list structure we are going to implement our polynomial adt using singly linked list given this choicewe must decide how the data should be stored and organized within the linked list since polynomial is constructed as the sum of one or more non-zero termswe can simply store an individual term in each node of the list as defined by the polytermnode classshown in lines - of listing nextwe must decide whether to order the nodes within the linked list upon analysis of the polynomial operationsit becomes clear an ordered list would be better since many of those operations are based on the degree of the terms for examplethe degree of the polynomial is the degree of the largest term if the list is orderedfinding the polynomial degree is rather simple likewiseyou will soon see that ordering the terms allows for more efficient implementation of the addition and multiplication operations unlike previous exampleswe are going to order the nodes in descending order based on degree since polynomials are typically written with the terms ordered from largest degree to smallest sample linked list structure for the polynomial is illustrated in figure polyhead - - polytail polynomial figure polynomial object for the polynomial finallywe need to decide whether our implementation can benefit from the use of tail pointer or if head pointer alone will suffice rule of thumb in making this decision is whether we will be appending nodes to the list or simply inserting them in their proper position if you need to append nodes to linked listyou should use tail pointer the implementation of some of our polynomial operations can be improved if we append nodes directly to the end of the linked list thuswe will use and manage tail pointer in our implementation of the polynomial adt