5. A construction company is contracted to build a new skyscraper. There are a number of...

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5. A construction company is contracted to build a new skyscraper. There are a number of tasks that need to be done throughout the planning and construction process. Certain tasks rely on previous tasks to be completed before they can be worked on. Each task has been designed to take one working day to complete. The company has a large crew, so any number of tasks can be completed in one day as long as the previous tasks they rely on have been completed. We will represent the tasks as nodes, and draw a directed edge from node u to v if task v requires task u to be completed first. Describe an O(m+ n) algorithm to compute the minimum number of working days needed to complete the entire project. 5. A construction company is contracted to build a new skyscraper. There are a number of tasks that need to be done throughout the planning and construction process. Certain tasks rely on previous tasks to be completed before they can be worked on. Each task has been designed to take one working day to complete. The company has a large crew, so any number of tasks can be completed in one day as long as the previous tasks they rely on have been completed. We will represent the tasks as nodes, and draw a directed edge from node u to v if task v requires task u to be completed first. Describe an O(m+ n) algorithm to compute the minimum number of working days needed to complete the entire project.

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