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Among Us - INOI 2021

INOI · 2021 · Indian National Olympiad in Informatics · AMONGUS2

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graphs · parity · bipartite

The organizer’s problem statement is available at the official source link.

truth parity graph

Statements become same/different constraints

An accusation requires opposite roles; a vouch requires equal roles, independent of whether the speaker is truthful or lying. Schematic structure only; vertices and edges represent the task relation, not an official sample. Schematic graph only; labels and edges show the task relation, not an official sample.

same / differentsame / differentPerson APerson BPerson C
  1. 1

    Encode each statement

    An accusation means the two astronauts have opposite roles; a vouch means they have the same role.
  2. 2

    Check consistency

    Propagate same/opposite constraints through each connected component; any contradiction makes the statements inconsistent.
  3. 3

    Maximize parasites

    Among consistent role assignments, report the largest possible number of parasites.
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