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BUGLIFE.cs
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using System;
using System.Collections.Generic;
using System.IO;
using System.Text;
// https://www.spoj.com/problems/BUGLIFE/ #dfs #graph-theory
// Determines if a set of bugs can be divided into two non-interacting groups.
public static class BUGLIFE
{
// Check to see if the ants can be divided into two groups, where members of one group
// group only interact with members of the other group: AKA check bipartiteness.
public static bool Solve(SimpleGraph interactionGraph)
=> interactionGraph.IsBipartite();
}
// Undirected, unweighted graph with no loops or multiple edges. The graph's vertices are stored
// in an array, with the ID of a vertex (from 0 to vertexCount - 1) corresponding to its index.
public sealed class SimpleGraph
{
public SimpleGraph(int vertexCount)
{
var vertices = new Vertex[vertexCount];
for (int id = 0; id < vertexCount; ++id)
{
vertices[id] = new Vertex(this, id);
}
Vertices = Array.AsReadOnly(vertices);
}
public IReadOnlyList<Vertex> Vertices { get; }
public int VertexCount => Vertices.Count;
public void AddEdge(int firstVertexID, int secondVertexID)
=> AddEdge(Vertices[firstVertexID], Vertices[secondVertexID]);
public void AddEdge(Vertex firstVertex, Vertex secondVertex)
{
firstVertex.AddNeighbor(secondVertex);
secondVertex.AddNeighbor(firstVertex);
}
public bool HasEdge(int firstVertexID, int secondVertexID)
=> HasEdge(Vertices[firstVertexID], Vertices[secondVertexID]);
public bool HasEdge(Vertex firstVertex, Vertex secondVertex)
=> firstVertex.HasNeighbor(secondVertex);
// Performs a DFS from some vertex in every connected component of the graph, while
// attempting a 2-coloring. Don't need the count property from a hash set, so using
// two parallel bool arrays, one for discovery, one for 2-coloring.
public bool IsBipartite()
{
bool[] discoveredVertexIDs = new bool[VertexCount];
bool[] discoveredVertexColors = new bool[VertexCount];
var verticesToVisit = new Stack<Vertex>();
for (int i = 0; i < VertexCount; ++i)
{
if (discoveredVertexIDs[i])
continue; // Already explored this component.
discoveredVertexIDs[i] = true;
discoveredVertexColors[i] = true;
verticesToVisit.Push(Vertices[i]);
while (verticesToVisit.Count > 0)
{
var vertex = verticesToVisit.Pop();
bool vertexColor = discoveredVertexColors[vertex.ID];
foreach (var neighbor in vertex.Neighbors)
{
// If undiscovered, discover it and color it opposite the vertex we're
// visiting from (put it in the other set).
if (!discoveredVertexIDs[neighbor.ID])
{
discoveredVertexIDs[neighbor.ID] = true;
discoveredVertexColors[neighbor.ID] = !vertexColor;
verticesToVisit.Push(neighbor);
}
// Else, make sure its color isn't the same as the vertex we're visting
// from (verify its not in the same set).
else if (discoveredVertexColors[neighbor.ID] == vertexColor)
return false;
}
}
}
return true;
}
public sealed class Vertex : IEquatable<Vertex>
{
private readonly SimpleGraph _graph;
private readonly HashSet<Vertex> _neighbors = new HashSet<Vertex>();
internal Vertex(SimpleGraph graph, int ID)
{
_graph = graph;
this.ID = ID;
}
public int ID { get; }
public IReadOnlyCollection<Vertex> Neighbors => _neighbors;
public int Degree => _neighbors.Count;
internal void AddNeighbor(int neighborID)
=> _neighbors.Add(_graph.Vertices[neighborID]);
internal void AddNeighbor(Vertex neighbor)
=> _neighbors.Add(neighbor);
public bool HasNeighbor(int neighborID)
=> _neighbors.Contains(_graph.Vertices[neighborID]);
public bool HasNeighbor(Vertex neighbor)
=> _neighbors.Contains(neighbor);
public override bool Equals(object obj)
=> (obj as Vertex)?.ID == ID;
public bool Equals(Vertex other)
=> other.ID == ID;
public override int GetHashCode()
=> ID;
}
}
public static class Program
{
private static void Main()
{
var output = new StringBuilder();
int testCount = FastIO.ReadNonNegativeInt();
for (int t = 1; t <= testCount; ++t)
{
int bugCount = FastIO.ReadNonNegativeInt();
int interactionCount = FastIO.ReadNonNegativeInt();
var interactionGraph = new SimpleGraph(bugCount);
for (int i = 0; i < interactionCount; ++i)
{
interactionGraph.AddEdge(
firstVertexID: FastIO.ReadNonNegativeInt() - 1,
secondVertexID: FastIO.ReadNonNegativeInt() - 1);
}
output.AppendLine($"Scenario #{t}:");
output.AppendLine(BUGLIFE.Solve(interactionGraph)
? "No suspicious bugs found!" : "Suspicious bugs found!");
}
Console.Write(output);
}
}
// This is based in part on submissions from https://www.codechef.com/status/INTEST.
// It's assumed the input is well-formed, so if you try to read an integer when no
// integers remain in the input, there's undefined behavior (infinite loop).
public static class FastIO
{
private const byte _null = (byte)'\0';
private const byte _newLine = (byte)'\n';
private const byte _minusSign = (byte)'-';
private const byte _zero = (byte)'0';
private const int _inputBufferLimit = 8192;
private static readonly Stream _inputStream = Console.OpenStandardInput();
private static readonly byte[] _inputBuffer = new byte[_inputBufferLimit];
private static int _inputBufferSize = 0;
private static int _inputBufferIndex = 0;
private static byte ReadByte()
{
if (_inputBufferIndex == _inputBufferSize)
{
_inputBufferIndex = 0;
_inputBufferSize = _inputStream.Read(_inputBuffer, 0, _inputBufferLimit);
if (_inputBufferSize == 0)
return _null; // All input has been read.
}
return _inputBuffer[_inputBufferIndex++];
}
public static int ReadNonNegativeInt()
{
byte digit;
// Consume and discard whitespace characters (their ASCII codes are all < _minusSign).
do
{
digit = ReadByte();
}
while (digit < _minusSign);
// Build up the integer from its digits, until we run into whitespace or the null byte.
int result = digit - _zero;
while (true)
{
digit = ReadByte();
if (digit < _zero) break;
result = result * 10 + (digit - _zero);
}
return result;
}
}