ApproxMinWeightVC.cpp

Author: lxylxy123456

ApproxMinWeightVC.cpp

@@ -0,0 +1,87 @@
+//  
+//  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_ApproxMinWeightVC
+#endif
+
+#ifndef FUNC_ApproxMinWeightVC
+#define FUNC_ApproxMinWeightVC
+
+#include "utils.h"
+
+#include "Graph.cpp"
+#include "Simplex.cpp"
+
+template <typename GT, typename T, typename WT>
+void ApproxMinWeightVC(GT& G, umap<T, WT>& w, uset<T>& C) {
+	umap<size_t, umap<size_t, WT>> A; 
+	umap<size_t, WT> b, c; 
+	for (auto i = G.V.begin(); i != G.V.end(); i++)
+		c[*i + 1] = -w[*i]; 
+	const size_t n = G.V.size(); 
+	size_t e = n + 1; 
+	for (auto i = G.all_edges(); !i.end(); i++, e++) {
+		for (auto j = G.V.begin(); j != G.V.end(); j++)
+			A[e][*j + 1] = 0; 
+		A[e][i.s() + 1] = -1; 
+		A[e][i.d() + 1] = -1; 
+		b[e] = -1; 
+	}
+	for (auto i = G.V.begin(); i != G.V.end(); i++, e++) {
+		for (auto j = G.V.begin(); j != G.V.end(); j++)
+			A[e][*j + 1] = 0; 
+		A[e][*i + 1] = 1; 
+		b[e] = 1; 
+	}
+	umap<size_t, WT> x = Simplex(A, b, c); 
+	for (auto i = G.V.begin(); i != G.V.end(); i++)
+		if (x[*i + 1] >= (WT) 1 / (WT) 2)
+			C.insert(*i); 
+}
+#endif
+
+#ifdef MAIN_ApproxMinWeightVC
+int main(int argc, char *argv[]) {
+	const size_t v = get_argv(argc, argv, 1, 10); 
+	const size_t e = get_argv(argc, argv, 2, 20); 
+	const bool dir = 0; 
+	GraphAdjList<size_t> G(dir); 
+	random_graph(G, v, e); 
+	uset<size_t> ans; 
+	std::vector<int> weight; 
+	random_integers(weight, 1, v, v); 
+	using WT = double; 
+	umap<size_t, WT> w; 
+	for (size_t i = 0; i < v; i++)
+		w[i] = weight[i]; 
+	ApproxMinWeightVC(G, w, ans); 
+	auto f1 = [w, ans](size_t v) mutable {
+		std::cout << " [label=" << w[v]; 
+		if (ans.find(v) != ans.end())
+			std::cout << " color=green"; 
+		std::cout << "]"; 
+		return true; 
+	}; 
+	auto f2 = [](Edge<size_t>) mutable {}; 
+	graphviz(G, f1, f2); 
+	return 0; 
+}
+#endif
+

README.md

@@ -225,6 +225,7 @@
 | 35 | ApproxVertexCover.cpp		| Approx Vertex Cover					| 1109 |
 | 35 | ApproxTSPTour.cpp			| Approx TSP Tour						| 1112 |
 | 35 | GreedySetCover.cpp			| Greedy Set Cover						| 1119 |
+| 35 | ApproxMinWeightVC.cpp		| Approx Min Weight VC					| 1126 |
 
 # Supplementary Files
 * `utils.h`: Utils

Simplex.cpp

@@ -84,7 +84,7 @@ void InitializeSimplex(usetst& N, usetst& B, matst& A, vectst& b, vectst& c,
 	vectst Lc; 
 	T Lv = 0; 
 	for (auto i = B.begin(); i != B.end(); i++)
-		A[*i][0] = 1; 
+		A[*i][0] = -1; 
 	Lc[0] = -1; 
 	for (auto j = N.begin(); j != N.end(); j++)
 		Lc[*j] = 0; 
@@ -130,9 +130,9 @@ void InitializeSimplex(usetst& N, usetst& B, matst& A, vectst& b, vectst& c,
 				c[*j] = 0; 
 		for (auto i = B.begin(); i != B.end(); i++) {
 			if (c.find(*i) != c.end()) {
-				v += b[*i]; 
+				v += b[*i] * c[*i]; 
 				for (auto j = N.begin(); j != N.end(); j++)
-					c[*j] -= A[*i][*j]; 
+					c[*j] -= A[*i][*j] * c[*i]; 
 				c.erase(*i); 
 			}
 		}
@@ -194,7 +194,6 @@ void main_T(const size_t n, const size_t m) {
 	for (size_t i = 1; i <= m; i++)
 		for (size_t j = 1; j <= n; j++)
 			A[n + i][j] = int_a[(i - 1) * n + (j - 1)]; 
-	vectst x = Simplex(A, b, c); 
 	for (size_t i = 1; i <= m; i++) {
 		for (size_t j = 1; j <= n; j++)
 			std::cout << A[n + i][j] << " "; 
@@ -207,15 +206,16 @@ void main_T(const size_t n, const size_t m) {
 	for (size_t i = 1; i <= n; i++)
 		std::cout << c[i] << " "; 
 	std::cout << std::endl; 
+	vectst x = Simplex(A, b, c); 
 	for (size_t i = 1; i <= n; i++)
 		std::cout << x[i] << " "; 
 	std::cout << std::endl; 
 }
 
 int main(int argc, char *argv[]) {
 	const size_t type = get_argv(argc, argv, 1, 0); 
-	const size_t m = get_argv(argc, argv, 2, 10); 
-	const size_t n = get_argv(argc, argv, 3, 5); 
+	const size_t m = get_argv(argc, argv, 2, 4); 
+	const size_t n = get_argv(argc, argv, 3, 2); 
 	if (!type)
 		main_T<double>(n, m); 
 	else