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lp.cpp
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lp.cpp
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#include <algorithm>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <deque>
#include <iostream>
#include <iterator>
#include <limits>
#include <unordered_map>
#include <unordered_set>
#include <vector>
class Graph {
public:
using Vertex = size_t;
using VertexSet = std::unordered_set<Vertex>;
using AdjencyList = std::unordered_map<Vertex, VertexSet>;
void AddVertex(Vertex v) {
adjency_list_[v];
}
void AddEdge(Vertex u, Vertex v) {
adjency_list_[u].insert(v);
adjency_list_[v].insert(u);
}
const VertexSet& AdjecentVertices(Vertex v) const {
const auto it = adjency_list_.find(v);
if (it != adjency_list_.end()) {
return it->second;
} else {
return empty_set_;
}
}
VertexSet AllVertices() const {
VertexSet vs;
vs.reserve(adjency_list_.size());
for (const auto& pair : adjency_list_) {
const auto& vertex = pair.first;
vs.insert(vertex);
}
return vs;
}
Vertex RandVertex() const {
return rand() % AllVertices().size();
}
const AdjencyList& AsAdjencyList() const {
return adjency_list_;
}
private:
AdjencyList adjency_list_;
static const VertexSet empty_set_;
};
const Graph::VertexSet Graph::empty_set_;
class Path {
private:
std::deque<Graph::Vertex> path_;
Graph graph_;
public:
explicit Path(const Graph& graph)
: graph_(graph), path_(std::deque<Graph::Vertex>(1, rand() % graph.AllVertices().size() + 1)) {}
void Add(Graph::Vertex v) {
Graph::VertexSet front_adjescent = graph_.AdjecentVertices(path_.front());
Graph::VertexSet back_adjescent = graph_.AdjecentVertices(path_.back());
bool is_front_adjescent = front_adjescent.find(v) != front_adjescent.end();
bool is_back_adjescent = back_adjescent.find(v) != back_adjescent.end();
if (is_front_adjescent && is_back_adjescent)
if (rand() % 2)
path_.push_front(v);
else
path_.push_back(v);
else if (is_front_adjescent)
path_.push_front(v);
else if (is_back_adjescent)
path_.push_back(v);
}
void Remove(Graph::Vertex v) {
if (path_.front() == v)
path_.pop_front();
else if (path_.back() == v)
path_.pop_back();
}
size_t Cost() const {
return path_.size();
}
Graph::Vertex front() {
return path_.front();
}
Graph::Vertex back() {
return path_.back();
}
std::deque<Graph::Vertex>::const_iterator begin() const {
return path_.begin();
}
std::deque<Graph::Vertex>::const_iterator end() const {
return path_.end();
}
std::deque<Graph::Vertex>::const_iterator find(Graph::Vertex v) {
return std::find(begin(), end(), v);
}
};
struct DebugInfo {
std::vector<size_t> costs;
};
std::ostream& operator<<(std::ostream& out, const DebugInfo& debug_info) {
for (size_t i = 0; i < debug_info.costs.size(); ++i) {
out << i << " " << debug_info.costs[i] << "\n";
}
return out;
}
class Metropolis {
private:
size_t max_iterations = 1000;
public:
Path Solve(const Graph& graph, double K, double T, bool fire, DebugInfo &debug_info) const {
Path path = Path(graph);
for (size_t i = 0; i != max_iterations; ++i) {
if (path.Cost() == 0) {
path = Path(graph);
}
Graph::VertexSet cands;
cands.insert(path.front());
cands.insert(path.back());
for (auto v : graph.AdjecentVertices(path.front())) {
if (path.find(v) == path.end()) {
cands.insert(v);
}
}
for (auto v : graph.AdjecentVertices(path.back())) {
if (path.find(v) == path.end())
cands.insert(v);
}
auto tempit = cands.begin();
std::advance(tempit, rand()%cands.size());
auto v = *tempit;
if (v != path.front() && v != path.back()) {
path.Add(v);
} else {
if (rand() / RAND_MAX < exp(- (1 / (K * T))))
path.Remove(v);
}
if (fire) {
T = sqrt(T);
}
debug_info.costs.push_back(path.Cost());
}
return path;
}
};
class GradientDescent {
private:
size_t max_iterations = 1000;
public:
Path Solve(const Graph& graph, DebugInfo &debug_info) const {
Path path = Path(graph);
for (size_t i = 0; i != max_iterations; ++i) {
if (path.Cost() == 0) {
path = Path(graph);
}
Graph::VertexSet cands;
for (auto v : graph.AdjecentVertices(path.front())) {
if (path.find(v) == path.end()) {
cands.insert(v);
}
}
for (auto v : graph.AdjecentVertices(path.back())) {
if (path.find(v) == path.end())
cands.insert(v);
}
if (cands.size() == 0)
break;
auto tempit = cands.begin();
std::advance(tempit, rand()%cands.size());
auto v = *tempit;
path.Add(v);
debug_info.costs.push_back(path.Cost());
}
return path;
}
};
Graph RandomGraph(size_t size, double edge_probability) {
Graph graph;
for (Graph::Vertex v = 1; v <= size; ++v) {
graph.AddVertex(v);
}
for (Graph::Vertex v = 1; v <= size; ++v) {
for (Graph::Vertex u = v + 1; u <= size; ++u) {
if (double(rand()) / RAND_MAX <= edge_probability) {
graph.AddEdge(v, u);
}
}
}
return graph;
}
Graph StarGraph(size_t size) {
Graph graph;
for (Graph::Vertex v = 2; v <= size; ++v) {
graph.AddEdge(1, v);
}
return graph;
}
int InitRandSeed(int argc, const char* argv[]) {
int rand_seed;
if (argc >= 2) {
rand_seed = atoi(argv[1]);
} else {
rand_seed = time(nullptr);
}
srand(rand_seed);
return rand_seed;
}
int main(int argc, const char* argv[]) {
std::cout << "Using rand seed: " << InitRandSeed(argc, argv) << "\n";
Metropolis metropolis;
GradientDescent descent;
DebugInfo debug_info_metropolis1, debug_info_metropolis2, debug_info_descent;
for (size_t i = 0; i != 1; ++i) {
const auto graph = RandomGraph(100, 0.1);
double average1 = 0, average2 = 0, average3 = 0;
for (size_t j = 0; j != 100; ++j) {
debug_info_metropolis1.costs.clear();
debug_info_metropolis2.costs.clear();
debug_info_descent.costs.clear();
Path path_metropolis1(graph), path_metropolis2(graph), path_descent(graph);
path_metropolis1 = metropolis.Solve(graph, 1, 1000, true, debug_info_metropolis1);
path_metropolis2 = metropolis.Solve(graph, 1, 1000, false, debug_info_metropolis2);
path_descent = descent.Solve(graph, debug_info_descent);
average1 += path_metropolis1.Cost();
average2 += path_metropolis2.Cost();
average3 += path_descent.Cost();
}
average1 /= 100;
average2 /= 100;
average3 /= 100;
std::cout << i << " " << average1 << " " << average2 << " " << average3 << '\n';
}
std::cout << "--------------------\n";
std::cout << debug_info_metropolis1 << '\n';
std::cout << "--------------------\n";
std::cout << debug_info_metropolis2 << '\n';
std::cout << "--------------------\n";
std::cout << debug_info_descent << '\n';
return 0;
}