II. Read each problem carefully and present an algorithm with the required running-time to solve each problem. 1. In class we discussed that directed acyclic graphs (DAG) can be used to represent dependency/precedence relations. One example is modeling task dependency where tasks are represented as vertices and edges represents direct dependencies between tasks, e.g., if task T; requires task I, then there is an edge from vertex i to vertex j. Arranging tasks with respect to their dependencies can easily be done by performing topological sort to the DAG. a. Describe an algorithm that runs in O(n + m) time that given two tasks, T, and I, determines if task T, can be performed without performing task T₁. Note that I, is not required if it is not a direct or indirect dependency of T. Task I, is an indirect dependency of task T: if there is no edge from T, to T, but I, must appear before 7, in the topological order. b. Describe an algorithm that runs in O(n + m) time that given a task T₁, outputs the minimum possible position of tasks T, in any topological order.

II. Read each problem carefully and present an algorithm with the required running-time to solve each problem. 1. In class we discussed that directed acyclic graphs (DAG) can be used to represent dependency/precedence relations. One example is modeling task dependency where tasks are represented as vertices and edges represents direct dependencies between tasks, e.g., if task T; requires task I, then there is an edge from vertex i to vertex j. Arranging tasks with respect to their dependencies can easily be done by performing topological sort to the DAG. a. Describe an algorithm that runs in O(n + m) time that given two tasks, T, and I, determines if task T, can be performed without performing task T₁. Note that I, is not required if it is not a direct or indirect dependency of T. Task I, is an indirect dependency of task T: if there is no edge from T, to T, but I, must appear before 7, in the topological order. b. Describe an algorithm that runs in O(n + m) time that given a task T₁, outputs the minimum possible position of tasks T, in any topological order.

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter17: Linked Lists

Section: Chapter Questions

Problem 2PE

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