/// <summary>
/// グラフを連結成分分解する
/// </summary>
/// <param name="graph"></param>
/// <param name="ids"></param>
/// <param name="edgeUsed">その辺を使うか否かを表す配列．nullの場合は全部使う．</param>
/// <returns>
/// グラフの連結成分数を返す
/// また，ids[v]にvが属する連結成分のIDを格納する
/// </returns>
public static int WeaklyConnectedComponents(DirectedGraph graph, out int[] ids, bool[] edgeUsed = null)
{
int n = graph.Vertices.Count;
ids = new int[n];
for (int i = 0; i < n; ++i) { ids[i] = -1; }
int currId = 0;
var stack = new Stack<int>();
for (int i = 0; i < n; ++i) {
if (ids[i] != -1) { continue; }
stack.Push(i);
ids[i] = currId;
while (stack.Count > 0) {
int v = stack.Pop();
foreach (Edge e in graph.OutEdges[v]) {
if (edgeUsed != null && !edgeUsed[e.Index]) { continue; }
int w = e.Dst;
if (ids[w] == -1) {
ids[w] = currId;
stack.Push(w);
}
}
foreach (Edge e in graph.InEdges[v]) {
if (edgeUsed != null && !edgeUsed[e.Index]) { continue; }
int w = e.Src;
if (ids[w] == -1) {
ids[w] = currId;
stack.Push(w);
}
}
}
currId += 1;
}
return currId;
}
private static double Augment(DirectedGraph graph, double[] cap, double[] flow, int[] level, bool[] finished, int u, int t, double cur)
{
if (u == t || cur < SMALL) return cur;
if (finished[u]) return 0;
finished[u] = true;
foreach (var e in graph.OutEdges[u]) {
if (level[e.Dst] > level[u]) {
double f = Augment(graph, cap, flow, level, finished, e.Dst, t, Math.Min(cur, cap[e.Index] - flow[e.Index]));
if (f >= SMALL) {
flow[e.Index] += f;
finished[u] = false;
return f;
}
}
}
foreach (var e in graph.InEdges[u]) {
if (level[e.Dst] > level[u]) {
double f = Augment(graph, cap, flow, level, finished, e.Dst, t, Math.Min(cur, flow[e.Index]));
if (f >= SMALL) {
flow[e.Index] -= f;
finished[u] = false;
return f;
}
}
}
return 0;
}
// グラフをCSVから読み込む
public static DirectedGraph LoadCSV(string fileName)
{
using (var reader = new StreamReader(fileName)) {
string line;
var id2index = new Dictionary<int, int>();
var g = new DirectedGraph();
for (int lineNo = 1; (line = reader.ReadLine()) != null; ++lineNo) {
if (line.Length == 0) { continue; }
string[] fields = line.Split(',');
if (fields.Length < 2) { throw new Exception(string.Format("{0}:{1} Fields Too Few", fileName, lineNo)); }
int src = int.Parse(fields[0]);
int dst = int.Parse(fields[1]);
if (!id2index.ContainsKey(src)) {
id2index.Add(src, g.Vertices.Count);
g.AddVertex(new Vertex(src));
}
if (!id2index.ContainsKey(dst)) {
id2index.Add(dst, g.Vertices.Count);
g.AddVertex(new Vertex(dst));
}
g.AddEdge(new Edge(id2index[src], id2index[dst]));
}
return g;
}
}
// グラフをCSVに書きこむ
public static void SaveCSV(DirectedGraph g, string fileName)
{
using (var writer = new StreamWriter(fileName)) {
foreach (Edge e in g.Edges) {
writer.WriteLine("{0},{1}", g.Vertices[e.Src].OriginalId, g.Vertices[e.Dst].OriginalId);
}
}
}
private static void OutputFlow(StreamWriter writer, DirectedGraph graph, double[] cap, double[] gain, double[] flow)
{
for (int e = 0; e < graph.Edges.Count; ++e) {
writer.WriteLine("{0},{1},{2},{3},{4}",
graph.Vertices[graph.Edges[e].Src].OriginalId,
graph.Vertices[graph.Edges[e].Dst].OriginalId,
cap[e], gain[e], flow[e]);
}
}
public static void Run(DirectedGraph graph, long graphLoadTime, int s, int t, double[] cap, double[] gain, double prob, string output, double eps)
{
int n = graph.Vertices.Count, m = graph.Edges.Count;
Stopwatch stopwatch = new Stopwatch();
long compressionTime = 0;
long gmfTime = 0;
double minValue = 1e10;
double[] minFlow = null;
DirectedGraph minGraph = null;
for (int i = 0; i < 4; ++i) {
Trace.WriteLine("Compressing the given graph...");
stopwatch.Restart();
Compressor compressor = new Compressor(graph, prob, new Random());
compressionTime += stopwatch.ElapsedMilliseconds;
var compressedGraph = compressor.CompressedGraph;
var mapping = compressor.Mapping;
Trace.WriteLine("Compressed Vertex Count: " + compressedGraph.Vertices.Count);
Trace.WriteLine("Compressed Edge Count: " + compressedGraph.Edges.Count);
Trace.WriteLine("Calculating the generalized maximum flow...");
stopwatch.Restart();
double[] flow;
double value = FleischerWayne.GeneralizedMaximumFlow(compressor.CompressedGraph, cap, gain, mapping[s], mapping[t], eps, out flow);
gmfTime += stopwatch.ElapsedMilliseconds;
if (value < minValue) {
minValue = value;
minFlow = flow;
minGraph = compressor.CompressedGraph;
}
}
Trace.WriteLine("Writing the results");
Utility.CreateDirectoryIfNotExists(output);
using (var writer1 = new StreamWriter(output + "/Flow.csv")) {
OutputFlow(writer1, minGraph, cap, gain, minFlow);
}
using (var writer2 = new StreamWriter(output + "/Value.txt")) {
writer2.WriteLine(minValue);
}
using (var writer3 = new StreamWriter(output + "/Sunnary.txt")) {
writer3.WriteLine("VertexCount: " + n);
writer3.WriteLine("EdgeCount: " + m);
writer3.WriteLine("Source: " + graph.Vertices[s].OriginalId);
writer3.WriteLine("Sink: " + graph.Vertices[t].OriginalId);
writer3.WriteLine("Prob: " + prob);
writer3.WriteLine("Compressed Vertex Count: " + minGraph.Vertices.Count);
writer3.WriteLine("Compressed Edge Count: " + minGraph.Edges.Count);
writer3.WriteLine("Graph Load Time [ms]: " + graphLoadTime);
writer3.WriteLine("Compression Time [ms]: " + compressionTime);
writer3.WriteLine("GMF Time [ms]: " + gmfTime);
}
}
private bool[] RandomSample(DirectedGraph graph, double prob, Random random)
{
int m = graph.Edges.Count;
var result = new bool[m];
for (int i = 0; i < m; ++i) {
if (random.NextDouble() < prob) {
result[i] = true;
}
}
return result;
}
public static void FindSourceAndSink(int source, int sink, DirectedGraph graph, out int s, out int t)
{
s = -1;
t = -1;
for (int i = 0; i < graph.Vertices.Count; ++i) {
if (graph.Vertices[i].OriginalId == source) { s = i; }
if (graph.Vertices[i].OriginalId == sink) { t = i; }
}
if (s == -1 || t == -1 || s == t) {
Console.Error.WriteLine("Error: 始点または終点が不正です．");
Environment.Exit(1);
}
}
public static double MaximumFlow(
DirectedGraph graph, double[] cap, int s, int t, out double[] flow)
{
if (s == t) {
throw new ArgumentException("始点と終点が同じ頂点です.");
}
int n = graph.Vertices.Count;
int m = graph.Edges.Count;
flow = new double[m];
double total = 0;
for (bool cont = true; cont; ) {
cont = false;
var level = new int[n];
for (int i = 0; i < n; ++i)
level[i] = -1;
level[s] = 0;
var Q = new Queue<int>();
Q.Enqueue(s);
for (int d = n; Q.Count > 0 && level[Q.Peek()] < d; ) {
int u = Q.Dequeue();
if (u == t) d = level[u];
foreach (var e in graph.OutEdges[u]) {
if (cap[e.Index] - flow[e.Index] >= SMALL && level[e.Dst] == -1) {
Q.Enqueue(e.Dst);
level[e.Dst] = level[u] + 1;
}
}
foreach (var e in graph.InEdges[u]) {
if (flow[e.Index] >= SMALL && level[e.Dst] == -1) {
Q.Enqueue(e.Dst);
level[e.Dst] = level[u] + 1;
}
}
}
var finished = new bool[n];
for (double f = 1; f > 0; ) {
f = Augment(graph, cap, flow, level, finished, s, t, double.PositiveInfinity);
if (f < SMALL) break;
total += f;
cont = true;
}
}
return total;
}
/// <summary>
/// graphからk個の頂点をランダムに選択し，選ばれた頂点と，それらが誘導する辺のみを持つグラフを返す
/// </summary>
public DirectedGraph Sample(DirectedGraph graph, int sampledVertexCount, Random random)
{
var choice = new HashSet<int>();
for (int i = 0; i < sampledVertexCount; ++i) {
for (; ; ) {
int n = random.Next(graph.Vertices.Count);
if (!choice.Contains(n)) {
Trace.WriteLine("Choose: " + graph.Vertices[n].OriginalId.ToString());
choice.Add(n);
break;
}
}
}
return graph.Induce(choice);
}
public DirectedGraph Sample(DirectedGraph graph, int sampledVertexCount, double burningProbability, Random random)
{
var result = new DirectedGraph();
var index2index = new Dictionary<int, int>();
var visit = new bool[graph.Vertices.Count];
while (result.Vertices.Count < sampledVertexCount) {
// 開始点を決める
int start;
do { start = random.Next(graph.Vertices.Count); } while (visit[start]);
var stack = new Stack<int>();
stack.Push(start);
AddVertexToResultGraph(start, graph, result, index2index);
visit[start] = true;
while (stack.Count > 0 && result.Vertices.Count < sampledVertexCount) {
int v = stack.Pop();
var outEdges = graph.OutEdges[v];
for (int i = 0; i < outEdges.Count; ++i) {
if (random.NextDouble() >= burningProbability) { break; }
// i番目以降の辺を一つ選んでi番目と入れ替える
int j = random.Next(i, outEdges.Count);
Edge t = outEdges[i];
outEdges[i] = outEdges[j];
outEdges[j] = t;
// 結果に追加
int dst = outEdges[i].Dst;
if (!visit[dst]) { AddVertexToResultGraph(dst, graph, result, index2index); }
result.AddEdge(new Edge(index2index[v], index2index[dst]));
// 再帰的に探索
if (!visit[dst]) {
visit[dst] = true;
stack.Push(dst);
}
}
}
}
return result;
}
static void Main(string[] args)
{
DirectedGraph graph = new DirectedGraph();
for (int i = 0; i < 6; ++i)
graph.AddVertex(new Vertex());
double[] cap = new double[8];
int m = 0;
graph.AddEdge(new Edge(0, 1));
cap[m++] = 1;
graph.AddEdge(new Edge(0, 2));
cap[m++] = 1;
graph.AddEdge(new Edge(1, 2));
cap[m++] = 1;
graph.AddEdge(new Edge(1, 3));
cap[m++] = 1;
graph.AddEdge(new Edge(2, 4));
cap[m++] = 0.8;
graph.AddEdge(new Edge(3, 5));
cap[m++] = 1;
graph.AddEdge(new Edge(4, 3));
cap[m++] = 1;
graph.AddEdge(new Edge(4, 5));
cap[m++] = 0.5;
double[] flow;
double value = Dinic.MaximumFlow(graph, cap, 0, 5, out flow);
Console.WriteLine("|f| = {0}", value);
foreach (var e in graph.Edges) {
Console.WriteLine("f({0}, {1}) = {2}", e.Src, e.Dst, flow[e.Index]);
}
}
/// <summary>
/// GMFを計算して結果を出力する
/// </summary>
/// <param name="input"></param>
/// <param name="output"></param>
/// <param name="graphLoadTime"></param>
/// <param name="graph"></param>
/// <param name="cap"></param>
/// <param name="gain"></param>
/// <param name="s"></param>
/// <param name="t"></param>
/// <param name="eps"></param>
public static void Run(string input, string output, long graphLoadTime, DirectedGraph graph, double[] cap, double[] gain,
int s, int t, double eps, string method = "FleischerWayne")
{
var stopwatch = new Stopwatch();
stopwatch.Start();
double[] flow = null;
double value;
if (method == "FleischerWayne") {
value = FleischerWayne.GeneralizedMaximumFlow(graph, cap, gain, s, t, eps, out flow);
} else if (method == "Greedy") {
value = GreedyGMF.GeneralizedMaximumFlow(graph, cap, gain, s, t, ref flow);
} else if (method == "GreedyImproved") {
GreedyGMF.ConstructInitialFlow(graph, cap, gain, s, t, out flow);
value = GreedyGMF.GeneralizedMaximumFlow(graph, cap, gain, s, t, ref flow);
} else {
throw new ArgumentException("method " + method + " は定義されていません．");
}
var gmfTime = stopwatch.ElapsedMilliseconds;
stopwatch.Stop();
Trace.WriteLine("Writing the results");
Utility.CreateDirectoryIfNotExists(output);
using (var writer1 = new StreamWriter(output + "/Flow.csv")) {
OutputFlow(writer1, graph, cap, gain, flow);
}
using (var writer2 = new StreamWriter(output + "/Value.txt")) {
writer2.WriteLine(value);
}
using (var writer3 = new StreamWriter(output + "/Summary.txt")) {
writer3.WriteLine("Input: " + input);
writer3.WriteLine("Vertex Count: " + graph.Vertices.Count);
writer3.WriteLine("Edge Count: " + graph.Edges.Count);
writer3.WriteLine("Source: " + graph.Vertices[s].OriginalId);
writer3.WriteLine("Sink: " + graph.Vertices[t].OriginalId);
writer3.WriteLine("Method: " + method);
writer3.WriteLine("Eps: " + eps);
writer3.WriteLine("Graph Load Time [ms]: " + graphLoadTime);
writer3.WriteLine("GMF Time [ms]: " + gmfTime);
writer3.WriteLine("Value: " + value);
}
}
/// <summary>
/// グラフを mapping に従って縮約したものを返す．
/// </summary>
/// <param name="graph">縮約するグラフ</param>
/// <param name="mapping">mapping[i] は 縮約元のグラフのi番目の頂点の縮約先の頂点</param>
/// <returns>縮約されたグラフ</returns>
public static DirectedGraph Contract(DirectedGraph graph, int[] mapping)
{
var result = new DirectedGraph();
int nVertices = mapping.Max() + 1;
for (int i = 0; i < nVertices; ++i) {
result.AddVertex(new Vertex());
}
for (int i = 0; i < mapping.Length; ++i) {
result.Vertices[mapping[i]] = graph.Vertices[i]; // copy vertex
}
for (int u = 0; u < graph.Vertices.Count; ++u) {
int src = mapping[u];
foreach (Edge e in graph.OutEdges[u]) {
int dst = mapping[e.Dst];
if (src != dst) {
result.AddEdge(new Edge(src, dst));
}
}
}
return result;
}
/// <summary>
/// Random Walk Sampling という手法を用いてサンプリングを行う
/// </summary>
/// <param name="graph"></param>
/// <param name="sampledVertexCount"></param>
/// <param name="random"></param>
/// <returns></returns>
public DirectedGraph Sample(DirectedGraph graph, int sampledVertexCount, Random random)
{
int n = graph.Vertices.Count;
int m = graph.Edges.Count;
var result = new DirectedGraph();
var visit = new bool[n];
var used = new bool[m];
var index2index = new Dictionary<int, int>();
while (result.Vertices.Count < sampledVertexCount) {
int start = random.Next(graph.Vertices.Count);
if (!visit[start]) {
AddVertexToResultGraph(start, graph, result, index2index);
visit[start] = true;
}
int v = start;
for (int step = 0; step < n && result.Vertices.Count < sampledVertexCount; ++step) {
if (graph.OutDegree(v) == 0 || random.NextDouble() < 0.15) {
v = start;
} else {
int choice = random.Next(graph.OutDegree(v));
Edge e = graph.OutEdges[v][choice];
v = e.Dst;
if (!visit[v]) {
AddVertexToResultGraph(v, graph, result, index2index);
visit[v] = true;
}
if (!used[e.Index]) {
result.AddEdge(new Edge(index2index[e.Src], index2index[e.Dst]));
used[e.Index] = true;
}
}
}
}
return result;
}
static void Main(string[] args)
{
UndirectedGraph <int> undirected = new UndirectedGraph <int>();
for (int i = 0; i < 7; i++)
{
undirected.AddVertex(new Vertex <int>(i));
}
undirected.AddEdge(undirected[0], undirected[1]);
undirected.AddEdge(undirected[1], undirected[2]);
undirected.AddEdge(undirected[1], undirected[3]);
undirected.AddEdge(undirected[2], undirected[3]);
undirected.AddEdge(undirected[2], undirected[4]);
undirected.AddEdge(undirected[4], undirected[6]);
undirected.AddEdge(undirected[6], undirected[5]);
Console.WriteLine("Undirected Depth-First Search:");
undirected.DepthFirstSearch(undirected[0]);
Console.WriteLine("\nUndirected Breadth-First Traversal:");
undirected.BreadthFirstTraversal(undirected[0]);
DirectedGraph <int> directed = new DirectedGraph <int>();
directed.AddVertex(new DVertex <int>(0)); //0
directed.AddVertex(new DVertex <int>(8)); //1
directed.AddVertex(new DVertex <int>(5)); //2
directed.AddVertex(new DVertex <int>(9)); //3
directed.AddVertex(new DVertex <int>(7)); //4
directed.AddEdge(directed[0], directed[1], 10); //0->8
directed.AddEdge(directed[0], directed[2], 5); //0->5
directed.AddEdge(directed[1], directed[2], 2); //8->5
directed.AddEdge(directed[1], directed[3], 1); //8->9
directed.AddEdge(directed[2], directed[1], 3); //5->8
directed.AddEdge(directed[2], directed[3], 9); //5->9
directed.AddEdge(directed[2], directed[4], 2); //5->7
directed.AddEdge(directed[3], directed[4], 4); //9->7
directed.AddEdge(directed[4], directed[3], 6); //7->9
directed.AddEdge(directed[4], directed[0], 7); //7->0
Console.WriteLine("\nDirected Depth-First Search:");
directed.DepthFirstSearch(directed[0]);
Console.WriteLine("\nDirected Breadth-First Traversal:");
directed.BreadthFirstTraversal(directed[0]);
PriorityQueue <int> queue = new PriorityQueue <int>(Comparer <int> .Create((a, b) => a.CompareTo(b)));
for (int i = 10; i > 0; i--)
{
queue.Enqueue(i);
Console.WriteLine(queue.ToString());
}
Console.WriteLine();
for (int i = 0; i < 10; i++)
{
queue.Dequeue();
Console.WriteLine(queue.ToString());
}
var vertices = (Stack <DVertex <int> >)directed.Dijkstra(directed[0], directed[4]);
int count = vertices.Count;
for (int i = 0; i < count; i++)
{
Console.Write($"{vertices.Pop().Value}{(i == count - 1 ? "\n" : "->") }");
}
DirectedGraph <string> houseThing = new DirectedGraph <string>();
//https://brilliant.org/wiki/dijkstras-short-path-finder/
houseThing.AddVertex(new DVertex <string>("Home")); //0
houseThing.AddVertex(new DVertex <string>("A")); //1
houseThing.AddVertex(new DVertex <string>("B")); //2
houseThing.AddVertex(new DVertex <string>("C")); //3
houseThing.AddVertex(new DVertex <string>("D")); //4
houseThing.AddVertex(new DVertex <string>("E")); //5
houseThing.AddVertex(new DVertex <string>("F")); //6
houseThing.AddVertex(new DVertex <string>("School")); //7
houseThing.AddEdge(houseThing[0], houseThing[1], 3);
houseThing.AddEdge(houseThing[0], houseThing[2], 2);
houseThing.AddEdge(houseThing[0], houseThing[3], 5);
houseThing.AddEdge(houseThing[1], houseThing[4], 3);
houseThing.AddEdge(houseThing[2], houseThing[4], 1);
houseThing.AddEdge(houseThing[2], houseThing[5], 6);
houseThing.AddEdge(houseThing[3], houseThing[5], 2);
houseThing.AddEdge(houseThing[4], houseThing[6], 4);
houseThing.AddEdge(houseThing[5], houseThing[6], 1);
houseThing.AddEdge(houseThing[5], houseThing[7], 4);
houseThing.AddEdge(houseThing[6], houseThing[7], 2);
var housePath = (Stack <DVertex <string> >)houseThing.Dijkstra(houseThing[0], houseThing[7]);
count = housePath.Count;
for (int i = 0; i < count; i++)
{
Console.Write($"{housePath.Pop().Value}{(i == count - 1 ? "\n" : "->") }");
}
Console.ReadKey();
}
public Compressor(DirectedGraph graph, double prob, Random random)
{
int[] mapping;
CompressedGraph = Compress(graph, prob, random, out mapping);
Mapping = mapping;
}
private DirectedGraph Compress(DirectedGraph graph, double prob, Random random, out int[] mapping)
{
bool[] selected = RandomSample(graph, prob, random);
Graph.Algorithms.WeaklyConnectedComponents(graph, out mapping, selected);
return Graph.Algorithms.Contract(graph, mapping);
}
private void AddVertexToResultGraph(int v, DirectedGraph graph, DirectedGraph result, Dictionary<int, int> index2index)
{
index2index.Add(v, result.Vertices.Count);
result.AddVertex(graph.Vertices[v]);
}
public void CopyTo(DirectedGraph other)
{
for (int i = 0; i < other.Vertices.Count; ++i) {
other.InEdges[i].Clear();
other.OutEdges[i].Clear();
}
other.Vertices.Clear();
other.Edges.Clear();
other.Vertices.AddRange(this.Vertices);
other.Edges.AddRange(this.Edges);
for (int i = 0; i < Vertices.Count; ++i) {
other.InEdges[i].AddRange(this.InEdges[i]);
other.OutEdges[i].AddRange(this.OutEdges[i]);
}
}
/// <summary>
/// 指定された頂点集合から誘導される部分グラフを返す
/// </summary>
/// <param name="vertices"></param>
/// <returns></returns>
public DirectedGraph Induce(IEnumerable<int> vertices)
{
var g = new DirectedGraph();
var index2index = new Dictionary<int, int>();
foreach (int v in vertices) {
index2index.Add(v, g.Vertices.Count);
g.AddVertex(Vertices[v]);
}
foreach (Edge e in Edges) {
if (index2index.ContainsKey(e.Src) && index2index.ContainsKey(e.Dst)) {
g.AddEdge(new Edge(index2index[e.Src], index2index[e.Dst]));
}
}
return g;
}
