FloydWarshall.cpp

Author: lxylxy123456

FloydWarshall.cpp

@@ -0,0 +1,101 @@
+//  
+//  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_FloydWarshall
+#endif
+
+#ifndef FUNC_FloydWarshall
+#define FUNC_FloydWarshall
+
+#include "utils.h"
+
+#include "Graph.cpp"
+
+void PrintAllPairsShortestPath(Matrix<T_ptr<size_t>>& PI, size_t i, size_t j, 
+	std::vector<size_t>& ans) {
+	if (i == j)
+		ans.push_back(i); 
+	else if (!PI[i][j].nil) {
+		PrintAllPairsShortestPath(PI, i, PI[i][j].val, ans); 
+		ans.push_back(j); 
+	}
+}
+
+template <typename T>
+std::pair<Matrix<T>, Matrix<T_ptr<size_t>>> FloydWarshall(Matrix<T>& W) {
+	const size_t n = W.rows; 
+	Matrix<T> D = W; 
+	Matrix<T_ptr<size_t>> PI(n, n, T_ptr<size_t>()); 
+	for (size_t i = 0; i < n; i++)
+		for (size_t j = 0; j < n; j++)
+			if (i != j && !W[i][j].inf)
+				PI[i][j] = i; 
+	for (size_t k = 0; k < n; k++) {
+		Matrix<T> D_new = D; 
+		Matrix<T_ptr<size_t>> PI_new = PI; 
+		for (size_t i = 0; i < n; i++)
+			for (size_t j = 0; j < n; j++) {
+				T n = D[i][k] + D[k][j]; 
+				if (n < D_new[i][j]) {
+					D_new[i][j] = n; 
+					PI_new[i][j] = PI[k][j]; 
+				}
+			}
+		D = D_new; 
+		PI = PI_new; 
+	}
+	return std::pair<Matrix<T>, Matrix<T_ptr<size_t>>>(D, PI); 
+}
+#endif
+
+#ifdef MAIN_FloydWarshall
+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 = 1; 
+	const int weight_lower = get_argv<int>(argc, argv, 3, 0); 
+	const int weight_upper = get_argv<int>(argc, argv, 4, e); 
+	WeightedAdjMatrix<size_t, int> G(dir); 
+	G.random_graph(v, e, weight_lower, weight_upper); 
+	G.graphviz(); 
+	std::cout << std::endl; 
+	Matrix<Weight<int>> W(v, v); 
+	G.to_matrix(W); 
+	auto ans = FloydWarshall(W); 
+	Matrix<Weight<int>> D = ans.first; 
+	Matrix<T_ptr<size_t>> PI = ans.second; 
+	std::cout << D << std::endl; 
+	std::cout << PI << std::endl; 
+	for (size_t i = 0; i < v; i++)
+		for (size_t j = 0; j < v; j++)
+			if (i != j) {
+				std::cout << i << " ~> " << j << ": "; 
+				std::vector<size_t> ans; 
+				PrintAllPairsShortestPath(PI, i, j, ans); 
+				if (ans.size())
+					output_integers(ans); 
+				else 
+					std::cout << "no path from " << i << " to " << j
+							 << " exists" << std::endl; 
+			}
+	return 0; 
+}
+#endif
+

Graph.cpp

@@ -120,6 +120,21 @@ class Weight {
 		int inf; 
 }; 
 
+template <typename T>
+class T_ptr {
+	public:
+		T_ptr(): nil(true) {}
+		T_ptr(T v): val(v), nil(false) {}
+		friend std::ostream& operator<<(std::ostream& os, const T_ptr<T>& rhs) {
+			if (rhs.nil)
+				return os << "NIL"; 
+			else
+				return os << rhs.val; 
+		}
+		T val; 
+		bool nil; 
+}; 
+
 template <typename T>
 class EdgeIteratorAL1 {
 	public:

README.md

@@ -157,9 +157,11 @@
 | 24 | BellmanFord.cpp				| Bellman Ford							|  651 |
 | 24 | DagShortestPaths.cpp			| Dag Shortest Paths					|  655 |
 | 24 | Dijkstra.cpp					| Dijkstra								|  658 |
+| 25 | FloydWarshall.cpp			| Print All Pairs Shortest Path			|  685 |
 | 25 | AllPairsShortestPaths.cpp	| Extend Shortest Paths					|  688 |
 | 25 | AllPairsShortestPaths.cpp	| Slow All Pairs Shortest Paths			|  689 |
 | 25 | AllPairsShortestPaths.cpp	| Faster All Pairs Shortest Paths		|  691 |
+| 25 | FloydWarshall.cpp			| Floyd Warshall						|  695 |
 
 # Supplementary Files
 * `utils.h`: Utils