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/*
* vim: ts=4 sw=4 et tw=0 wm=0
*
* libcola - A library providing force-directed network layout using the
* stress-majorization method subject to separation constraints.
*
* Copyright (C) 2006-2014 Monash University
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
* See the file LICENSE.LGPL distributed with the library.
*
* This library 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.
*
* Author(s): Tim Dwyer
*/
#ifndef SHORTEST_PATHS_H
#define SHORTEST_PATHS_H
#include <vector>
#include <valarray>
#include <cfloat>
#include <cassert>
#include <algorithm>
#include <iostream>
#include <limits>
#include "libcola/commondefs.h"
#include <libvpsc/pairing_heap.h>
#include <libvpsc/assertions.h>
template <class T>
struct PairNode;
namespace shortest_paths {
template <typename T>
struct Node {
unsigned id;
T d;
Node* p; // predecessor
std::vector<Node<T>*> neighbours;
std::vector<T> nweights;
PairNode<Node<T>*>* qnode;
};
template <typename T>
struct CompareNodes {
bool operator() (Node<T> *const &u, Node<T> *const &v) const {
if(u==v) return false; // with g++ 4.1.2 unless I have this explicit check
// it returns true for this case when using -O3 optimization
// CRAZY!
if(u->d < v->d) {
return true;
}
return false;
}
};
typedef std::pair<unsigned,unsigned> Edge;
template <typename T>
/**
* returns the adjacency matrix, 0 entries for non-adjacent nodes
* @param n total number of nodes
* @param D n*n matrix of shortest paths
* @param es edge pairs
* @param eweights edge weights, if empty then all weights will be taken as 1
*/
void neighbours(unsigned const n, T** D, std::vector<Edge> const & es,
std::valarray<T> const & eweights = std::valarray<T>());
/**
* find all pairs shortest paths, n^3 dynamic programming approach
* @param n total number of nodes
* @param D n*n matrix of shortest paths
* @param es edge pairs
* @param eweights edge weights, if empty then all weights will be taken as 1
*/
template <typename T>
void floyd_warshall(unsigned const n, T** D, std::vector<Edge> const & es,
std::valarray<T> const & eweights = std::valarray<T>());
/**
* find all pairs shortest paths, faster, uses dijkstra
* @param n total number of nodes
* @param D n*n matrix of shortest paths
* @param es edge pairs
* @param eweights edge weights, if empty then all weights will be taken as 1
*/
template <typename T>
void johnsons(unsigned const n, T** D, std::vector<Edge> const & es,
std::valarray<T> const & eweights = std::valarray<T>());
/**
* find shortest path lengths from node s to all other nodes
* @param s starting node
* @param n total number of nodes
* @param d n vector of path lengths
* @param es edge pairs
* @param eweights edge weights, if empty then all weights will be taken as 1
*/
template <typename T>
void dijkstra(unsigned const s, unsigned const n, T* d,
std::vector<Edge> const & es,
std::valarray<T> const & eweights = std::valarray<T>());
//-----------------------------------------------------------------------------
// Implementation:
// O(n^3) time dynamic programming approach. Slow, but fool proof.
// Use for testing.
template <typename T>
void floyd_warshall(
unsigned const n,
T** D,
std::vector<Edge> const & es,
std::valarray<T> const & eweights)
{
COLA_ASSERT((eweights.size() == 0) || (eweights.size() == es.size()));
for(unsigned i=0;i<n;i++) {
for(unsigned j=0;j<n;j++) {
if(i==j) D[i][j]=0;
else D[i][j]=std::numeric_limits<T>::max();
}
}
for(unsigned i=0;i<es.size();i++) {
unsigned u=es[i].first, v=es[i].second;
COLA_ASSERT(u<n&&v<n);
D[u][v] = D[v][u] = (eweights.size() > 0) ? eweights[i] : 1;
}
for(unsigned k=0; k<n; k++) {
for(unsigned i=0; i<n; i++) {
for(unsigned j=0; j<n; j++) {
D[i][j]=std::min(D[i][j],D[i][k]+D[k][j]);
}
}
}
}
// Simply returns the adjacency graph
template <typename T>
void neighbours(
unsigned const n,
T** D,
std::vector<Edge> const & es,
std::valarray<T> const & eweights)
{
COLA_ASSERT((eweights.size() == 0) || (eweights.size() == es.size()));
for(unsigned i=0;i<n;i++) {
for(unsigned j=0;j<n;j++) {
D[i][j]=0;
}
}
for(unsigned i=0;i<es.size();i++) {
unsigned u=es[i].first, v=es[i].second;
COLA_ASSERT(u<n&&v<n);
D[u][v] = D[v][u] = (eweights.size() > 0) ? eweights[i] : 1;
}
}
template <typename T>
void dijkstra_init(
std::vector<Node<T> > & vs,
std::vector<Edge> const& es,
std::valarray<T> const & eweights) {
COLA_ASSERT((eweights.size() == 0) || (eweights.size() == es.size()));
#ifndef NDEBUG
const unsigned n=vs.size();
#endif
for(unsigned i=0;i<es.size();i++) {
unsigned u=es[i].first, v=es[i].second;
COLA_ASSERT(u<n);
COLA_ASSERT(v<n);
T w = (eweights.size() > 0) ? eweights[i] : 1;
vs[u].neighbours.push_back(&vs[v]);
vs[u].nweights.push_back(w);
vs[v].neighbours.push_back(&vs[u]);
vs[v].nweights.push_back(w);
}
}
template <typename T>
void dijkstra(
unsigned const s,
std::vector<Node<T> > & vs,
T* d)
{
const unsigned n=vs.size();
COLA_ASSERT(s<n);
for(unsigned i=0;i<n;i++) {
vs[i].id=i;
vs[i].d=std::numeric_limits<T>::max();
vs[i].p=nullptr;
}
vs[s].d=0;
PairingHeap<Node<T>*,CompareNodes<T> > Q;
for(unsigned i=0;i<n;i++) {
vs[i].qnode = Q.insert(&vs[i]);
}
while(!Q.isEmpty()) {
Node<T> *u=Q.extractMin();
d[u->id]=u->d;
for(unsigned i=0;i<u->neighbours.size();i++) {
Node<T> *v=u->neighbours[i];
T w=u->nweights[i];
if(u->d!=std::numeric_limits<T>::max()
&& v->d > u->d+w) {
v->p=u;
v->d=u->d+w;
Q.decreaseKey(v->qnode,v);
}
}
}
}
template <typename T>
void dijkstra(
unsigned const s,
unsigned const n,
T* d,
std::vector<Edge> const & es,
std::valarray<T> const & eweights)
{
COLA_ASSERT((eweights.size() == 0) || (eweights.size() == es.size()));
COLA_ASSERT(s<n);
std::vector<Node<T> > vs(n);
dijkstra_init(vs,es,eweights);
dijkstra(s,vs,d);
}
template <typename T>
void johnsons(
unsigned const n,
T** D,
std::vector<Edge> const & es,
std::valarray<T> const & eweights)
{
std::vector<Node<T> > vs(n);
dijkstra_init(vs,es,eweights);
for(unsigned k=0;k<n;k++) {
dijkstra(k,vs,D[k]);
}
}
} //namespace shortest_paths
#endif //SHORTEST_PATHS_H
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