advanced sorting this implementation of the radix sort algorithm is straightforwardbut it requires the use of multiple queues to result in an efficient implementationwe must use the queue adt implemented as linked list or have direct access to the underlying list in order to use the python list version efficiency analysis to evaluate the radix sort algorithmassume sequence of keys in which each key contains components in the largest key value and each component contains value between and - also assume we are using the linked list implementation of the queue adtwhich results in ( time queue operations the array used to store the queues and the creation of the queues themselves can be done in (ktime the distribution and gathering of the keys involves two stepswhich are performed timesone for each componentthe distribution of the keys across the queues requires (ntime since an individual queue can be accessed directly by subscript gathering the keys from the queues and placing them back into the sequence requires (ntime even though the keys have to be gathered from queuesthere are keys in total to be dequeued resulting in the dequeue(operation being performed times the distribution and gathering steps are performed timesresulting in time of (dncombining this with the initialization step we have an overall time of ( +dnthe radix sort is special purpose algorithm and in practice both and are constants specific to the given problemresulting in linear time algorithm for examplewhen sorting list of integersk and can vary but commonly thusthe sorting time depends only on the number of keys sorting linked lists the sorting algorithms introduced in the previous sections and earlier in can be used to sort keys stored in mutable sequence but what if we need to sort keys stored in an unsorted singly linked list such as the one shown in figure in this sectionwe explore that topic by reviewing two common algorithms that can be used to sort linked list by modifying the links to rearrange the existing nodes the techniques employed by any of the three quadratic sorting algorithms-bubbleselectionand insertion--presented in can be used to sort linked list instead of swapping or shifting the values within the sequencehoweverthe nodes are rearranged by unlinking each node from the list and then relinking them at different position linked list version of the bubble sort would rearrange the nodes within the same list by leap-frogging the nodes containing larger values over those with smaller values the selection and insertion sortson the other hand