Professor Adam has two children who, unfortunately, dislike each other. The prob-lem is so severe that not only do they refuse to walk to school together, but in facteach one refuses to walk on any block that the other child has stepped on that day.The children have no problem with their paths crossing at a corner. Fortunatelyboth the professor’s house and the school are on corners, but beyond that he is notsure if it is going to be possible to send both of his children to the same school.The professor has a map of his town. Show how to formulate the problem of de-termining whether both his children can go to the same school as a maximum-flowproblem.
Question
Professor Adam has two children who, unfortunately, dislike each other. The prob-lem is so severe that not only do they refuse to walk to school together, but in facteach one refuses to walk on any block that the other child has stepped on that day.The children have no problem with their paths crossing at a corner. Fortunatelyboth the professor’s house and the school are on corners, but beyond that he is notsure if it is going to be possible to send both of his children to the same school.The professor has a map of his town. Show how to formulate the problem of de-termining whether both his children can go to the same school as a maximum-flowproblem.
Solution
To formulate this problem as a maximum-flow problem, we can consider the town as a directed graph where each block is a node and each corner is a directed edge connecting two nodes.
Step 1: Define the Graph Each block in the town is represented as a node in the graph. The corners where blocks meet are represented as directed edges between the nodes. The professor's house and the school are also nodes in the graph.
Step 2: Define the Source and Sink The source of the graph is the professor's house and the sink is the school.
Step 3: Assign Capacities Each edge in the graph has a capacity of 1, representing one child's ability to walk along that block.
Step 4: Find Maximum Flow The goal is to find a maximum flow from the source to the sink that respects the capacities of the edges.
Step 5: Interpret the Result If the maximum flow is 2, then it is possible for both children to walk to school without walking on the same block. If the maximum flow is less than 2, then it is not possible for both children to walk to school without walking on the same block.
This formulation allows us to use maximum-flow algorithms to solve the problem.
Similar Questions
Which problem solving strategy would be best to solve this problem?Your friend’s house is 12 miles from your home. Your school isone-third the way from your friend’s house and your home. Thepark is one-fourth the way from the school to your friend’s house.How far is the park from your home? A. guess, check and revise B. write an equation C. make a table, chart or list D. make a model or diagram
A boy was misdirected from his way while returning to his home from his school. In order to reach his home, he first moved 3 km in south direction and then turned to his left and moved 2 km in straight direction on the road leading to the east. From there, he moved to his left and walked 3 km. After this, he again turned to his left and moved 1 km. Finally he reached his home. The home of the boy was in which direction from his school?North
'Z' starts walking from his home andwalks 5m in the east direction, then he turns 900 in theanti-clockwise direction and walks 10m and then he takes a right turn and walks15m. Then he turns 900 in the clockwise direction and walks 2m toreach his school. From his school, he walks 8m in the East direction and thentakes a right turn and walks 3m, then he walks 9m after turning 900in the anti-clockwise direction, then he finally takes a right turn and walks5m to reach the playground.In which direction is Z's school with respect to his home?North-EastSouth-EastSouth-WestNorth-WestSubject: Reasoning Ability
Select the right option from the given alternatives. A child walks 4 kms towards east, then 8 kms towards north and from there he goes 2 kms towards west. In which direction is he from his starting point? Options East North-east North-west west
'Z' starts walking from his home andwalks 5m in the east direction, then he turns 900 in theanti-clockwise direction and walks 10m and then he takes a right turn and walks15m. Then he turns 900 in the clockwise direction and walks 2m to reachhis school. From his school, he walks 8m in the East direction and then takes aright turn and walks 3m, then he walks 9m after turning 900 in theanti-clockwise direction, then he finally takes a right turn and walks 5m toreach the playground.In which direction is Z's home with respect to the playground?North West South East
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.