AllPairsShortestPaths.cpp

//  
//  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_AllPairsShortestPaths
#endif

#ifndef FUNC_AllPairsShortestPaths
#define FUNC_AllPairsShortestPaths

#include "utils.h"

#include "Graph.cpp"

template <typename T>
Matrix<T> ExtendShortestPaths(Matrix<T>& L, Matrix<T>& W) {
	const size_t n = L.rows; 
	Matrix<T> ans(n, n, T()); 
	for (size_t i = 0; i < n; i++)
		for (size_t j = 0; j < n; j++)
			for (size_t k = 0; k < n; k++)
				ans[i][j] = std::min(ans[i][j], L[i][k] + W[k][j]); 
	return ans; 
}

template <typename T>
Matrix<T> SlowAllPairsShortestPaths(Matrix<T>& W) {
	const size_t n = W.rows; 
	Matrix<T> L = W; 
	for (size_t m = 2; m < n; m++)
		L = ExtendShortestPaths(L, W); 
	return L; 
}

template <typename T>
Matrix<T> FasterAllPairsShortestPaths(Matrix<T>& W) {
	const size_t n = W.rows; 
	Matrix<T> L = W; 
	for (size_t m = 1; m < n - 1; m *= 2)
		L = ExtendShortestPaths(L, L); 
	return L; 
}
#endif

#ifdef MAIN_AllPairsShortestPaths
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); 
	Matrix<Weight<int>> ans1 = SlowAllPairsShortestPaths(W); 
	std::cout << ans1 << std::endl; 
	Matrix<Weight<int>> ans2 = FasterAllPairsShortestPaths(W); 
	std::cout << ans2 << std::endl; 
	std::cout << std::boolalpha << (ans1 == ans2) << std::endl; 
	return 0; 
}
#endif