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#include <iostream>
#include <cmath>
#include <functional>
#include <random>
#include <vector>
#include <limits>
#include "randutils/randutils.hpp"
#include "pcg-cpp/include/pcg_random.hpp"
using Rng = randutils::random_generator<pcg32>;
class Edge;
class HalfEdge;
class Vertex {
public:
unsigned index;
std::vector<std::reference_wrapper<HalfEdge>> neighbors;
std::array<unsigned, 2> coordinate;
void addEdge(HalfEdge& e) {
neighbors.push_back(e);
}
};
class HalfEdge {
private:
Vertex* tail;
Vertex* head;
public:
const Edge& edge;
double oldX;
double X;
HalfEdge(const Edge& e) : edge(e), oldX(0) {}
void setVertices(Vertex& vt, Vertex& vh) {
tail = &vt;
head = &vh;
}
const Vertex& getHead() const {
return *head;
}
const Vertex& getTail() const {
return *tail;
}
};
class Edge {
public:
std::array<HalfEdge, 2> halfedges;
double weight;
Edge() : halfedges{*this, *this} {};
void setVertices(Vertex& red, Vertex& blue) {
halfedges[0].setVertices(red, blue);
halfedges[1].setVertices(blue, red);
red.addEdge(halfedges[0]);
blue.addEdge(halfedges[1]);
}
double belief() const {
return halfedges[0].X + halfedges[1].X;
}
bool active() const {
return belief() >= 0;
}
};
class Graph {
public:
std::vector<Vertex> vertices;
std::vector<Edge> edges;
Graph(unsigned n, Rng& r) : vertices(2 * n * (n + 1)), edges(pow(2 * n, 2)) {
unsigned M = vertices.size() / 2;
for (unsigned i = 0; i < M; i++) {
vertices[i].index = i;
vertices[i].coordinate = {2 * (i % (n + 1)), 2 * (i / (n + 1)) + 1};
vertices[M + i].index = M + i;
vertices[M + i].coordinate = {2 * (i % n) + 1, 2 * (i / n)};
}
for (unsigned i = 0; i < edges.size(); i++) {
Vertex& redVertex = vertices[(1 + (i % (2 * n))) / 2 + (n + 1) * ((i / 4) / n)];
Vertex& blueVertex = vertices[M + (i % (2 * n)) / 2 + n * (((i + 2 * n) / 4) / n)];
edges[i].setVertices(redVertex, blueVertex);
edges[i].weight = r.variate<double, std::exponential_distribution>(1);
}
}
double propagateBeliefs() {
for (Edge& e : edges) {
for (HalfEdge& h : e.halfedges) {
h.X = std::numeric_limits<double>::infinity();
for (const HalfEdge& hn : h.getHead().neighbors) {
if (h.getTail().index != hn.getHead().index) {
h.X = std::min(hn.edge.weight - hn.oldX, h.X);
}
}
}
}
double minBelief = std::numeric_limits<double>::infinity();
for (Edge& e : edges) {
minBelief = std::min(std::abs(e.belief()), minBelief);
for (HalfEdge& he : e.halfedges) {
he.oldX = he.X;
}
}
return minBelief;
}
};
int main() {
unsigned n = 100;
unsigned maxSteps = 1e8;
double beliefThreshold = 1;
Rng r;
Graph G(n, r);
unsigned steps = 0;
double minBelief = 0;
while (minBelief < beliefThreshold && steps < maxSteps) {
minBelief = G.propagateBeliefs();
steps++;
}
for (const Edge& e : G.edges) {
if (e.active()) {
std::cout
<< e.halfedges[0].getTail().coordinate[0] << " "
<< e.halfedges[0].getTail().coordinate[1] << " "
<< e.halfedges[0].getHead().coordinate[0] << " "
<< e.halfedges[0].getHead().coordinate[1] << std::endl;
}
}
return 0;
}
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