SCC.cpp

Author: lxylxy123456

BFS.cpp

@@ -24,7 +24,6 @@
 #ifndef FUNC_BFS
 #define FUNC_BFS
 
-#include <cassert>
 #include "utils.h"
 
 #include "Queue.cpp"

DFS.cpp

@@ -118,9 +118,8 @@ void DFSVisit(GT& G, VT& ans, ET edge_ans, T u, size_t& time) {
 	info.set_color(black, time); 
 }
 
-template <typename GT, typename VT, typename ET>
-void DFS(GT& G, VT& ans, ET edge_ans) {
-	using T = typename GT::vertix_type; 
+template <typename T, typename GT, typename VT>
+void DFS(GT& G, VT& ans, umap<Edge<T>, DFSEdgeType, EdgeHash<T>>* edge_ans) {
 	for (auto i = G.V.begin(); i != G.V.end(); i++)
 		ans[*i] = DFSInfo<T>(); 
 	size_t time = 0; 

DisjointSet.cpp

@@ -24,20 +24,22 @@
 #ifndef FUNC_DisjointSet
 #define FUNC_DisjointSet
 
+#include <map>
 #include "utils.h"
 
 #include "Graph.cpp"
 
 const size_t NIL = -1; 
 
+template <typename T>
 class DisjointSetForest {
 	public:
-		DisjointSetForest(size_t n): p(n, NIL), rank(n, 0) {}
-		void MakeSet(size_t x) {
+		DisjointSetForest() {}
+		void MakeSet(T x) {
 			p[x] = x; 
 			rank[x] = 0; 
 		}
-		void Link(size_t x, size_t y) {
+		void Link(T x, T y) {
 			if (rank[x] > rank[y])
 				p[y] = x; 
 			else {
@@ -46,32 +48,34 @@ class DisjointSetForest {
 					rank[y]++; 
 			}
 		}
-		size_t FindSet(size_t x) {
+		T FindSet(T x) {
 			if (p[x] == NIL)
 				return x; 
 			if (x != p[x])
 				p[x] = FindSet(p[x]); 
 			return p[x]; 
 		}
-		void Union(size_t x, size_t y) {
+		void Union(T x, T y) {
 			Link(FindSet(x), FindSet(y)); 
 		}
-		std::vector<size_t> p, rank; 
+		std::map<T, T> p; 
+		std::map<T, size_t> rank; 
 }; 
 
+template <typename T>
 class ConnectedComponents {
 	public:
-		ConnectedComponents(size_t n, GraphAdjList<size_t>& G): F(n) {
+		ConnectedComponents(T n, GraphAdjList<T>& G) {
 			for (auto i = G.V.begin(); i != G.V.end(); i++)
 				F.MakeSet(*i); 
 			for (auto i = G.all_edges(); !i.end(); i++)
 				if (F.FindSet(i.s()) != F.FindSet(i.d()))
 					F.Union(i.s(), i.d()); 
 		}
-		bool SameComponent(size_t u, size_t v) {
+		bool SameComponent(T u, T v) {
 			return F.FindSet(u) == F.FindSet(v); 
 		}
-		DisjointSetForest F; 
+		DisjointSetForest<T> F; 
 }; 
 #endif
 
@@ -86,7 +90,7 @@ int main(int argc, char *argv[]) {
 	GraphAdjList<size_t> G(false); 
 	random_graph(G, v, e); 
 	graphviz(G); 
-	ConnectedComponents CC(n, G); 
+	ConnectedComponents<size_t> CC(n, G); 
 	for (size_t i = 0; i < n; i++) {
 		std::cout << c[i] << "\t" << d[i] << "\tconnected = " << std::boolalpha;
 		std::cout << CC.SameComponent(c[i], d[i]) << std::endl; 

Graph.cpp

@@ -24,6 +24,7 @@
 #ifndef FUNC_Graph
 #define FUNC_Graph
 
+#include <cassert>
 #include <unordered_set>
 #include <unordered_map>
 #include "utils.h"
@@ -147,7 +148,7 @@ class EdgeIteratorAM1 {
 		}
 		void next() {
 			if (mbegin != mend)
-				while (sbegin == send || !sbegin->second || !dir && s() > d()) {
+				while (sbegin == send || !sbegin->second || (!dir && s()>d())) {
 					if (sbegin == send) {
 						mbegin++; 
 						if (mbegin == mend)
@@ -217,6 +218,7 @@ class Graph {
 		}
 		virtual void add_edge(T, T) = 0; 
 		virtual bool is_edge(T u, T v) = 0; 
+		virtual void transpose() = 0; 
 		virtual ~Graph() {}
 		typedef T vertix_type; 
 		bool dir; 
@@ -243,6 +245,14 @@ class GraphAdjList: public Graph<T> {
 		EdgeIteratorAL2<T> edges_from(T s) {
 			return EdgeIteratorAL2<T>(s, E[s], this->dir); 
 		}
+		virtual void transpose() {
+			assert(this->dir); 
+			umap<T, uset<T>> old_E = E; 
+			E.clear(); 
+			for (auto i = old_E.begin(); i != old_E.end(); i++)
+				for (auto j = i->second.begin(); j != i->second.end(); j++)
+					E[*j].insert(i->first); 
+		}
 		virtual ~GraphAdjList() {}
 		umap<T, uset<T>> E; 
 }; 
@@ -277,6 +287,13 @@ class GraphAdjMatrix: public Graph<T> {
 		EdgeIteratorAM2<T> edges_from(T s) {
 			return EdgeIteratorAM2<T>(s, E[s], this->dir); 
 		}
+		virtual void transpose() {
+			assert(this->dir); 
+			for (auto i = this->V.begin(); i != this->V.end(); i++)
+				for (auto j = this->V.begin(); j != this->V.end(); j++)
+					if (*i < *j)
+						std::swap(E[*i][*j], E[*j][*i]); 
+		}
 		virtual ~GraphAdjMatrix() {}
 		umap<T, umap<T, bool>> E; 
 }; 
@@ -338,6 +355,10 @@ void graph_test(const size_t v, const size_t e) {
 		}
 		std::cout << std::endl; 
 		graphviz(G); 
+		if (dir) {
+			G.transpose(); 
+			graphviz(G); 
+		}
 		std::cout << std::endl; 
 	}
 }

README.md

@@ -149,6 +149,7 @@
 | 22 | DFS.cpp						| DFS									|  604 |
 | 22 | DFS.cpp						| DFS Visit								|  604 |
 | 22 | TopologicalSort.cpp			| Topological Sort						|  613 |
+| 23 | SCC.cpp						| Strongly Connected Components			|  617 |
 
 # Supplementary Files
 * `utils.h`: Utils

SCC.cpp

@@ -0,0 +1,98 @@
+//  
+//  algorithm - some algorithms in "Introduction to Algorithms", third edition
+//  Copyright (C) 2018  lxylxy123456
+//  
+//  This program is free software: you can redistribute it and/or modify
+//  it under the terms of the GNU Affero General Public License as
+//  published by the Free Software Foundation, either version 3 of the
+//  License, or (at your option) any later version.
+//  
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU Affero General Public License for more details.
+//  
+//  You should have received a copy of the GNU Affero General Public License
+//  along with this program.  If not, see <https://www.gnu.org/licenses/>.
+//  
+
+#ifndef MAIN
+#define MAIN
+#define MAIN_SCC
+#endif
+
+#ifndef FUNC_SCC
+#define FUNC_SCC
+
+#include <map>
+#include "utils.h"
+
+#include "DFS.cpp"
+#include "DisjointSet.cpp"
+
+template <typename GT, typename T, typename VT>
+void DFSVisit_SCC(GT& G, VT& inf, DisjointSetForest<T>& D, T u, size_t& time) {
+	DFSInfo<T>& info = inf[u]; 
+	info.set_color(gray, time); 
+	for (auto i = G.edges_from(u); !i.end(); i++) {
+		T v = i.d(); 
+		DFSInfo<T>& vinfo = inf[v]; 
+		if (vinfo.color == white) {
+			vinfo.set_pi(u); 
+			D.Union(u, v); 
+			DFSVisit_SCC(G, inf, D, v, time); 
+		}
+	}
+	info.set_color(black, time); 
+}
+
+template <typename GT, typename T>
+void DFS_SCC(GT& G, std::map<size_t, T>& f_order, DisjointSetForest<T>& D) {
+	umap<T, DFSInfo<T>> inf; 
+	for (auto i = G.V.begin(); i != G.V.end(); i++)
+		inf[*i] = DFSInfo<T>(); 
+	size_t time = 0; 
+	for (auto i = f_order.rbegin(); i != f_order.rend(); i++) {
+		T v = i->second; 
+		if (inf[v].color == white)
+			DFSVisit_SCC(G, inf, D, v, time); 
+	}
+}
+
+template <typename GT, typename T>
+void StronglyConnectedComponents(GT& G, DisjointSetForest<T>& D) {
+	umap<T, DFSInfo<T>> inf; 
+	DFS<T>(G, inf, nullptr); 
+	GT G_transpose = G; 
+	G_transpose.transpose(); 
+	std::map<size_t, T> f_order; 
+	for (auto i = inf.begin(); i != inf.end(); i++) {
+		f_order[i->second.f] = i->first; 
+		D.MakeSet(i->first); 
+	}
+	DFS_SCC(G_transpose, f_order, D); 
+}
+#endif
+
+#ifdef MAIN_SCC
+int main(int argc, char *argv[]) {
+	const size_t v = get_argv(argc, argv, 1, 5); 
+	const size_t e = get_argv(argc, argv, 2, 10); 
+	const bool dir = get_argv(argc, argv, 3, 1); 
+	GraphAdjList<size_t> G(dir); 
+	random_graph(G, v, e); 
+	DisjointSetForest<size_t> ans; 
+	StronglyConnectedComponents(G, ans); 
+	auto f1 = [](size_t v) { return false; }; 
+	auto f2 = [](Edge<size_t> e) {}; 
+	graphviz(G, f1, f2); 
+	// print ans
+	std::map<size_t, uset<size_t>> components; 
+	for (auto i = G.V.begin(); i != G.V.end(); i++)
+		components[ans.FindSet(*i)].insert(*i); 
+	for (auto i = components.begin(); i != components.end(); i++)
+		output_integers(i->second); 
+	return 0; 
+}
+#endif
+