Ayush-Kaushal / Among-Us-AGT

Among Us made simple using Graph theory

Among Us and Graph Theory

We are analysing the AMONG US game using 3 different tasks:-

• Task 1: Possible Imposters
• Task 2: Shortest Path between two rooms
  • Shortest Path for Crewmates
  • Shortest Path for Imposters
• Task 3: Secure last task for Crewmates

Task 1: Possible Imposters

• 10 players (8 crewmates + 2 imposters)
• Condition – Both the imposters can’t move together
• The model for the graph will be an undirected and unweighted graph
  • Node will be the players
  • Edges will represent if players have seen each other.
• We can list out all the possible imposters using the GRAPH COLORING technique

Task 2: Shortest Path between two rooms

• The model of the map will be an undirected and weighted graph
  • Nodes will be the rooms
  • Weight will be the distance between two rooms
• Using Floyd–Warshall algorithm to compute minimum distance and path between two rooms

Task 3: Secure the last Task (Hamiltonian Path)

• To secure the last task crewmates will want to form a pack
• For this the model of the map will be an undirected and unweighted graph
  • Nodes will be the rooms
  • Edges will be the path between the rooms
• To solve this problem, we choose to implement the Hamiltonian path as we want a path where each room is visited exactly once