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а. Give two different topological sorts of G. b. Is each of the following orderings a topological sort of G? Justify your answer. Cs111, CS141, CS261, CS362, CS211, CS251, CS361, CS401, CS342, CS151, CS301. Cs111, CS141, CS151, CS301, Cs211, CS261, CS361, CS362, CS251, CS342, CS401. 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.

а. Give two different topological sorts of G. b. Is each of the following orderings a topological sort of G? Justify your answer. Cs111, CS141, CS261, CS362, CS211, CS251, CS361, CS401, CS342, CS151, CS301. Cs111, CS141, CS151, CS301, Cs211, CS261, CS361, CS362, CS251, CS342, CS401. 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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 362 CS 141 CS 11 CS 211 Cs 361 CS 401 CS 151 CS 251 CS 342 CS 301 Answer the following questions: Give two different topological sorts of G. а. b. Is each of the following orderings a topological sort of G? Justify your answer. CS111, CS141, CS261, CS362, CS211, CS251, CS361, CS401, CS342, Cs151, CS301. Cs111, CS141, Cs151, CS301, CS211, CS261, CS361, CS362, CS251, CS342, CS401. 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. C.
Transcribed Image Text: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 362 CS 141 CS 11 CS 211 Cs 361 CS 401 CS 151 CS 251 CS 342 CS 301 Answer the following questions: Give two different topological sorts of G. а. b. Is each of the following orderings a topological sort of G? Justify your answer. CS111, CS141, CS261, CS362, CS211, CS251, CS361, CS401, CS342, Cs151, CS301. Cs111, CS141, Cs151, CS301, CS211, CS261, CS361, CS362, CS251, CS342, CS401. 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. C.
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