an applicationpartial ordering (topological sortingan appropriate example of the use of flexibledynamic data structure is the process of topological sorting this is sorting process of items over which partial ordering is definedi where an ordering is given over some pairs of items but not between all of them the following are examples of partial orderings in dictionary or glossarywords are defined in terms of other words if word is defined in terms of word wwe denote this by topological sorting of the words in dictionary means arranging them in an order such that there will be no forward references task ( an engineering projectis broken up into subtasks completion of certain subtasks must usually precede the execution of other subtasks if subtask must precede subtask wwe write topological sorting means their arrangement in an order such that upon initiation of each subtask all its prerequisite subtasks have been completed in university curriculumcertain courses must be taken before others since they rely on the material presented in their prerequisites if course is prerequisite for course wwe write topological sorting means arranging the courses in such an order that no course lists later course as prerequisite in programsome procedures may contain calls of other procedures if procedure is called by procedure wwe write topological sorting implies the arrangement of procedure declarations in such way that there are no forward references in generala partial ordering of set is relation between the elements of it is denoted by the symbol "<"verbalized by precedesand satisfies the following three properties (axiomsfor any distinct elements xyz of if and zthen (transitivity if ythen not (asymmetry not (irreflexivityfor evident reasonswe will assume that the sets to be topologically sorted by an algorithm are finite hencea partial ordering can be illustrated by drawing diagram or graph in which the vertices denote the elements of and the directed edges represent ordering relationships an example is shown in fig fig partially ordered set the problem of topological sorting is to embed the partial order in linear order graphicallythis implies the arrangement of the vertices of the graph in rowsuch that all arrows point to the rightas shown in fig properties ( and ( of partial orderings ensure that the graph contains no loops this is exactly the prerequisite condition under which such an embedding in linear order is possible