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A problem Four people come to a river in the night. There is a narrow bridge, but it can only hold two people at a time. They have one torch and, because it's night, the torch has to be used when crossing the bridge, meaning that the torch must travel back across the bridge. When two people cross the bridge together, they must move at the slower person's pace. If person A can cross the bridge in 1 minute, B in 2 minutes, C in 3 minutes, and D in 4 minutes, how fast do all four of the cross the river?

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**What if the times are A(1), B(2), C(4), D (5)**

A problem Four people come to a river in the night. There is a narrow bridge, but it can only hold two people at a time. They have one torch and, because it's night, the torch has to be used when crossing the bridge, meaning that the torch must travel back across the bridge. When two people cross the bridge together, they must move at the slower person's pace. If person A can cross the bridge in 1 minute, B in 2 minutes, C in 3 minutes, and D in 4 minutes, how fast do all four of the cross the river? What if the times are A(1), B(2), C(4), D (5)

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Hamiltonian Circuits Path through a circuit that touches every vertex once, not all edges must be used Must know by name Can be used to explain precedence Typically used to find most efficient route/order Edges are weighted (values assigned)

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**For Example BP Udall Mulvane Wellington 9 mi 16 mi 25 mi 9 mi 10 mi**

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**Traveling Salesman Problem**

20 A B 35 40 25 45 C D 30

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**ABCDA, ABDCA, ACBDA, ACDBA, ADBCA, ADCBA**

Similar: They touch each vertex once; Different: Some order just in different direction ABCDA (125), ABDCA (120), ACBDA (145), ACDBA (120), ADBCA (145), ADCBA (125) 120 mi or minutes Guess (4 city routes: ), 25 city routes: 6.24 x 1023 Answer

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VE Graph Test tomorrow

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**Test Prep Be able to explain what a vertex and an edge is**

Example of VE Graph A group of classmates convene in a room. They quickly realize that they’ve all met before. Julie’s boyfriend Bill is Tyrese’s roommate. Tyrese works with Shawnna and is related to Levi’s roommate. Shawnna went to high school with Chris, Levi’s brother. Levi’s other brother, Xander dated Julie before Bill. Draw a Vertex Edge Graph modeling this situation How many people are in the room?

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Test Prep

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Test Prep List all the different paths, and compute the length of each path. Find the critical path and the EFT. Earliest Finish Time What are the critical tasks? Are there any tasks that can have their task times increased by 3 units and yet not cause a change in the EFT for the whole project? If so, which tasks? If not, why not?

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Consider the school yearbook staff who has 16 days to complete the yearbook. They know what they have to do and how long it will take. (They can only use one camera, but everyone will cooperate). Do they make it? Task Time Prerequisite Start - A Buy film 1 None B Load Cameras C Take Photos of Clubs 3 D Take Sports Photos 2 E Take Teacher Photos F Develop Film D, E G Design Layout 5 H Print & Mail Pages G, F

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Test Prep

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MTH118 Sanchita Mal-Sarkar. Routing Problems The fundamental questions: Is there any proper route for the particular problem? If there are many possible.

MTH118 Sanchita Mal-Sarkar. Routing Problems The fundamental questions: Is there any proper route for the particular problem? If there are many possible.

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