MaximumBipartiteMatching.cpp

Author: lxylxy123456

MaximumBipartiteMatching.cpp

@@ -0,0 +1,155 @@
+//  
+//  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_MaximumBipartiteMatching
+#endif
+
+#ifndef FUNC_MaximumBipartiteMatching
+#define FUNC_MaximumBipartiteMatching
+
+#include "utils.h"
+
+#include "FordFulkerson.cpp"
+
+template <typename GT>
+class Bipartite: public GT {
+	public:
+		using T = typename GT::vertix_type; 
+		Bipartite(bool direction): GT(direction) {}
+		template <typename F1, typename F2>
+		void graphviz(F1 f1, F2 f2) {
+			if (GT::dir)
+				std::cout << "digraph G {" << std::endl; 
+			else
+				std::cout << "graph G {" << std::endl; 
+			std::cout << '\t'; 
+			std::cout << "subgraph clusterL {\n\t"; 
+			bool newline = true; 
+			for (auto i = L.begin(); i != L.end(); i++) {
+				if (newline)
+					std::cout << '\t'; 
+				std::cout << *i; 
+				if (f1(*i)) {
+					std::cout << "; \n\t"; 
+					newline = true; 
+				} else {
+					std::cout << "; "; 
+					newline = false; 
+				}
+			}
+			if (!newline)
+				std::cout << "\n\t"; 
+			std::cout << '}' << std::endl; 
+			std::cout << '\t'; 
+			std::cout << "subgraph clusterR {\n\t"; 
+			newline = true; 
+			for (auto i = R.begin(); i != R.end(); i++) {
+				if (newline)
+					std::cout << '\t'; 
+				std::cout << *i; 
+				if (f1(*i)) {
+					std::cout << "; \n\t"; 
+					newline = true; 
+				} else {
+					std::cout << "; "; 
+					newline = false; 
+				}
+			}
+			if (!newline)
+				std::cout << "\n\t"; 
+			std::cout << '}' << std::endl; 
+			for (auto i = GT::all_edges(); !i.end(); i++) {
+				std::cout << '\t' << *i; 
+				f2(*i); 
+				std::cout << "; " << std::endl; 
+			}
+			std::cout << "}" << std::endl; 
+		}
+		void graphviz() {
+			auto f1 = [](T v) { return false; }; 
+			auto f2 = [](Edge<T> e) {}; 
+			graphviz(f1, f2); 
+		}
+		uset<T> L, R; 
+}; 
+
+template <typename GT, typename T>
+void random_bipartite(Bipartite<GT>& G, T vl, T vr, size_t e) {
+	for (T i = 0; i < vl; i++) {
+		G.add_vertex(i); 
+		G.L.insert(i); 
+	}
+	for (T i = vl; i < vl + vr; i++) {
+		G.add_vertex(i); 
+		G.R.insert(i); 
+	}
+	std::vector<T> dl, dr; 
+	random_integers<T>(dl, 0, vl - 1, e); 
+	random_integers<T>(dr, vl, vl + vr - 1, e); 
+	for (size_t i = 0; i < e; i++)
+		G.add_edge(dl[i], dr[i]); 
+}
+
+
+template <typename GT, typename T>
+void MaximumBipartiteMatching(GT& G, uset<Edge<T>, EdgeHash<T>>& ans) {
+	GraphAdjList<T> GF(true); 
+	umap<Edge<T>, T, EdgeHash<size_t>> c, f; 
+	T s = G.V.size(), t = s + 1; 
+	assert(G.V.find(s) == G.V.end() && G.V.find(t) == G.V.end()); 
+	for (auto i = G.L.begin(); i != G.L.end(); i++) {
+		GF.add_edge(s, *i); 
+		c[Edge<T>(s, *i, true)] = 1; 
+	}
+	for (auto i = G.R.begin(); i != G.R.end(); i++) {
+		GF.add_edge(*i, t); 
+		c[Edge<T>(*i, t, true)] = 1; 
+	}
+	for (auto i = G.all_edges(); !i.end(); i++) {
+		GF.add_edge(i.s(), i.d()); 
+		c[Edge<T>(i.s(), i.d(), true)] = 1; 
+	}
+	FordFulkerson(GF, c, s, t, f); 
+	for (auto i = G.all_edges(); !i.end(); i++)
+		if (f[Edge<T>(i.s(), i.d(), true)])
+			ans.insert(*i); 
+}
+#endif
+
+#ifdef MAIN_MaximumBipartiteMatching
+int main(int argc, char *argv[]) {
+	const size_t vl = get_argv(argc, argv, 1, 5); 
+	const size_t vr = get_argv(argc, argv, 2, 5); 
+	const size_t e = get_argv(argc, argv, 3, 10); 
+	const bool dir = false; 
+	Bipartite<GraphAdjList<size_t>> G(dir); 
+	random_bipartite(G, vl, vr, e); 
+	uset<Edge<size_t>, EdgeHash<size_t>> ans; 
+	MaximumBipartiteMatching(G, ans); 
+	auto f1 = [](size_t v) { return false; }; 
+	auto f2 = [ans](Edge<size_t> e) mutable {
+		if (ans.find(e) != ans.end())
+			std::cout << " [style=bold]"; 
+	}; 
+	G.graphviz(f1, f2); 
+	return 0; 
+}
+#endif
+

README.md

@@ -165,6 +165,7 @@
 | 25 | TransitiveClosure.cpp		| Transitive Closure					|  698 |
 | 25 | Johnson.cpp					| Johnson								|  704 |
 | 26 | FordFulkerson.cpp			| Ford Fulkerson						|  724 |
+| 26 | MaximumBipartiteMatching.cpp	| Maximum Bipartite Matching			|  733 |
 
 # Supplementary Files
 * `utils.h`: Utils