Describe and analyze an algorithm to determine

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Question: Daneel Olivaw and Elijah Baley decide to play a game on a directed acyclic graph G, which has one source s and one sink t. Each player has a token on one of the vertices of G. At the start of the game, Daneel's token is on the source vertex s, and Elijah's token is on the sink vertex t. The players alternate turns, with Daneel moving first. On each of his turns, Daneel moves his token forward along a directed edge; on each of his turns, Elijah moves his token backward along a directed edge. If the two tokens ever meet on the same vertex, Elijah wins the game. If Daneel's token reaches t or Elijah's token reaches s before the two tokens meet, then Daneel wins the game.

Describe and analyze an algorithm to determine who wins this game, assuming both players play perfectly. That is, if Daneel can win no matter how Elijah moves, then your algorithm should output "Daneel", and if Elijah can win no matter how Daneel moves, your algorithm should output "Elijah". (Why are these the only two possibilities?) The input to your algorithm is the graph G.

Reference no: EM133626671

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