Additional Topics: Topological Sort A strict order relation can be represented by a directed acyclic graph (or DAG), which is a directed graph with no cycles. For example, the following directed graph is a DAG: A topological sort of a DAG is an ordering of the vertices that is consistent with the edges of the graph. That is, if there is an edge (u, v) in the graph, then u should appear before v in the topological sort. For example, 1, 2, 3 and 1,3, 2 are topological sorts of the DAG shown above, but 2, 1,3 is not a topological sort because 2 cannot be listed before 1. 7. Given the following DAG G representing UIC's Computer Science courses and prerequisites (note that edges implied by the transitive property are omitted): Cs 261 Cs 302 Cs 141 CS 111 CS 211 Cs 361 CS 401 CS 151 CS 251 CS 342 Cs 301 Answer the following questions: а. Give two different topological sorts of G. b. Is each of the following orderings a topological sort of G? Justify your answer. Cs111, CS151, CS301, CS251, CS342, CS141, CS211, cS261, CS361, CS362, CS401. Cs111, CS141, CS211, CS261, CS361, CS362, CS151, CS251, CS342, cs401, CS301. If a student can take an unlimited number of courses per semester, what is the fewest number of semesters required to complete these courses? Justify your answer.

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Types of trees

A tree data structure is a non–linear structure that stores data hierarchically. It can be defined as a group of objects, called nodes. The nodes are linked with edges. Trees begin with a root node which leads to children nodes. The last children nodes (endpoints) are called leaf nodes, and they do not have children nodes.