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cgal-kernels-lpqp.cpp
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cgal-kernels-lpqp.cpp
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#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
//#include <CGAL/Exact_predicates_exact_constructions_kernel_with_sqrt.h>
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Projection_traits_xy_3.h>
#include <CGAL/Delaunay_triangulation_2.h>
#include <CGAL/Triangulation_vertex_base_with_info_2.h>
#include <CGAL/Triangulation_face_base_with_info_2.h>
#include <CGAL/Triangulation_vertex_base_with_id_2.h>
#include <CGAL/Min_circle_2.h>
#include <CGAL/Min_circle_2_traits_2.h>
#include <CGAL/basic.h>
#include <CGAL/QP_models.h>
#include <CGAL/QP_functions.h>
#include <CGAL/Gmpz.h>
#include "UnionFind.h"
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/bipartite.hpp>
#include <boost/graph/connected_components.hpp>
#include <boost/graph/kruskal_min_spanning_tree.hpp>
#include <iostream>
#include <cassert>
#include <vector>
#include <queue>
#include <stack>
#include <cmath>
#include <valarray>
// LP/QP
typedef CGAL::Gmpq ET;
// program and solution types
typedef CGAL::Quadratic_program<ET> Program;
typedef CGAL::Quadratic_program_solution<ET> Solution;
// General CGAL
typedef CGAL::Exact_predicates_exact_constructions_kernel EK;
//typedef CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt KR;
typedef CGAL::Exact_predicates_inexact_constructions_kernel IK;
//typedef CGAL::Min_circle_2_traits_2<KR> Traits;
//typedef CGAL::Min_circle_2<Traits> Min_circle;
// Change when use different kernels!
typedef long long lint;
typedef IK::Point_2 Pt;
typedef IK::Point_3 Pt3;
typedef IK::Ray_2 Ray;
typedef IK::Vector_2 Vec;
typedef IK::Segment_2 Seg;
// Triangulation
typedef int ind_t; // not a good one...
//typedef CGAL::Triangulation_vertex_base_with_info_2<ind_t, IK> Vb;
//typedef CGAL::Triangulation_data_structure_2<Vb> Tds;
//typedef CGAL::Delaunay_triangulation_2<IK> Delaunay;
//typedef Delaunay::Finite_faces_iterator Face_iterator;
//typedef Delaunay::Finite_edges_iterator Edge_iterator;
//typedef Delaunay::Vertex_handle Vertex_handle;
//typedef Delaunay::Point DPt;
// Boost
typedef boost::adjacency_list < boost::vecS, boost::vecS, boost::undirectedS,
boost::no_property, boost::property < boost::edge_weight_t, lint > > Graph;
typedef boost::property_map < Graph, boost::edge_weight_t >::type WeightMap;
typedef boost::graph_traits < Graph >::edge_descriptor Edge;
typedef boost::graph_traits < Graph >::edge_iterator EdgeIt;
typedef boost::graph_traits < Graph >::out_edge_iterator OutEdgeIt;
typedef boost::graph_traits < Graph >::vertex_descriptor Vertex;
//typedef std::pair<int, int> E;
#define _o std::cout
#define _l std::endl
#define _i std::cin
#define _e std::cerr
double floor_to_double(const CGAL::Quotient<ET>& x)
{
double a = std::floor(CGAL::to_double(x));
while (a > x) a -= 1;
while (a + 1 <= x) a += 1;
return a;
}
double ceil_to_double(const CGAL::Quotient<ET>& x)
{
double a = std::ceil(CGAL::to_double(x));
while (a < x) a += 1;
while (a - 1 >= x) a -= 1;
return a;
}
struct MyRay {
Ray r;
int idx;
MyRay(Ray r=Ray(), int i=0):r(r),idx(i){}
MyRay(Pt src, Pt next, int i) {
r = Ray(src, next);
idx = i;
}
};
bool CompareRayByY0(const MyRay& r1, const MyRay& r2) {
return r1.r.source().y() > r2.r.source().y();
}
int whoWins(const std::vector<MyRay>& rays, int oldone, int newone) {
Vec vo = rays[oldone].r.to_vector();
Vec vn = rays[newone].r.to_vector();
if (vo.y() >= 0 && vn.y() >= 0) {
return oldone;
}
if (vo.y() < 0 && vn.y() < 0) {
return newone;
}
if (vo.y() >= 0 && vn.y() < 0) {
return (vo.y() * vn.x() + vo.x() * vn.y() > 0) ? newone : oldone;
}
if (vo.y() < 0 && vn.y() >= 0) {
return (vo.y() * vn.x() + vo.x() * vn.y() > 0) ? oldone : newone;
}
return -1;
}
int rayChallenge(Ray& rold, Ray& rnew) {
// rold.y0 > rnew.y0
// return 0 if old one wins
// return 1 if new one wins
Vec vo = rold.to_vector();
Vec vn = rnew.to_vector();
if (vo.y() >= 0 && vn.y() >= 0) {
return 0;
}
if (vo.y() < 0 && vn.y() < 0) {
return 1;
}
if (vo.y() >= 0 && vn.y() < 0) {
Seg so(rold.source(), rold.source() + vo);
Seg sn(rnew.source(), Pt(rnew.source().x() + vn.x(), rnew.source().y() - vn.y()));
CGAL::Comparison_result cr = CGAL::compare_slopes(so, sn);
//_e << " _" << cr << "_ ";
return (cr == CGAL::LARGER ? 1 : 0);
//return (vo.y() * vn.x() + vo.x() * vn.y() > 0) ? 1 : 0;
}
if (vo.y() < 0 && vn.y() >= 0) {
Seg so(rold.source(), Pt(rold.source().x() + vo.x(), rold.source().y() - vo.y()));
Seg sn(rnew.source(), rnew.source() + vn);
CGAL::Comparison_result cr = CGAL::compare_slopes(sn, so);
//_e << " _" << cr << "_ ";
return (cr == CGAL::LARGER ? 0 : 1);
}
return 0;
}
void Motorcycles() {
int n; _i >> n;
_e << n << _l;
std::vector<MyRay> rays(n);
for (int i = 0; i < n; i++) {
lint y0, x1, y1;
_i >> y0 >> x1 >> y1;
rays[i] = MyRay(Pt(0, y0), Pt(x1, y1), i);
}
std::sort(rays.begin(), rays.end(), CompareRayByY0);
std::stack<MyRay> st_rays;
st_rays.push(rays[0]);
for (int i = 1; i < n; i++) {
MyRay ray = rays[i];
while (!st_rays.empty()) {
MyRay topray = st_rays.top();
if (!CGAL::do_intersect(ray.r, topray.r)) {
st_rays.push(ray);
//_e << ray.idx << " in stack\n";
break;
}
else {
//_e << topray.idx << ":" << topray.r.to_vector() << "---" << ray.idx << ":" << ray.r.to_vector();
int who = rayChallenge(topray.r, ray.r);
//_e << " \twinner:" << ((who==0)?topray.idx:ray.idx) << _l;
if (who == 0) break;
else {
//_e << topray.idx << " out of stack\n";
st_rays.pop();
}
}
}
if (st_rays.empty()) {
st_rays.push(ray);
//_e << ray.idx << " in empty stack\n";
}
}
//_e << _l;
std::vector<int> alives;
while (!st_rays.empty()) {
alives.push_back(st_rays.top().idx);
st_rays.pop();
}
std::sort(alives.begin(), alives.end());
std::vector<int>::iterator ait = alives.begin();
for (; ait != alives.end(); ++ait) {
_o << *ait << " ";
}
_o << _l;
return;
}
void testUnionFind();
int main(int argc, char** argv) {
std::ios_base::sync_with_stdio(false);
if (argc > 1) {
std::string str("C:\\M.K.S.H\\ETH\\AlgoLab\\week6\\potw\\motorcycles\\");
str += std::string(argv[1]) + ".in";
freopen(str.c_str(), "r", stdin);
}
else freopen("C:\\M.K.S.H\\ETH\\AlgoLab\\week6\\potw\\motorcycles\\test1.in", "r", stdin);
freopen("C:\\M.K.S.H\\ETH\\AlgoLab\\week6\\potw\\motorcycles\\out_my.out", "w", stdout);
freopen("C:\\M.K.S.H\\ETH\\AlgoLab\\week6\\potw\\motorcycles\\err_my.out", "w", stderr);
int t;
_i >> t;
while (t--) {
Motorcycles();
}
return 0;
}
void testUnionFind() {
UnionFind uf(9);
uf.unionSets(1, 3);
uf.unionSets(1, 9);
uf.unionSets(5, 6);
uf.unionSets(8, 9);
uf.unionSets(7, 8);
uf.unionSets(5, 8);
_e << uf.toString() << _l;
return;
}
// Week 8: Germs / 100 pts
// Nearest neighbor
void Germs(int n) {
typedef CGAL::Triangulation_vertex_base_with_info_2<int, IK> Vb;
typedef CGAL::Triangulation_data_structure_2<Vb> Tds;
typedef CGAL::Delaunay_triangulation_2<IK, Tds> Delaunay;
typedef Delaunay::Finite_faces_iterator Face_iterator;
typedef Delaunay::Finite_edges_iterator Edge_iterator;
typedef Delaunay::Finite_vertices_iterator Vertex_iterator;
typedef Delaunay::Vertex_handle Vertex_handle;
typedef Delaunay::Point DPt;
typedef Delaunay::Vertex_circulator Vertex_circulator;
int l, b, r, t;
_i >> l >> b >> r >> t;
std::vector< std::pair<Pt, int> > pts(n);
std::vector<lint> mind2(n);
for (int i = 0; i < n; i++) {
int x, y;
_i >> x >> y;
lint dl = std::abs(x - l);
lint dr = std::abs(x - r);
lint db = std::abs(y - b);
lint dt = std::abs(y - t);
lint md = std::min(std::min(dl, dr), std::min(db, dt));
mind2[i] = md*md * 4;
pts[i] = std::make_pair(Pt(x, y), i);
}
lint fd2, md2, ld2;
if (n > 1) {
Delaunay D;
D.insert(pts.begin(), pts.end());
Vertex_iterator vit = D.finite_vertices_begin(), vend = D.finite_vertices_end();
for (; vit != vend; ++vit) {
int uind = vit->info();
Pt up = vit->point();
lint md2 = mind2[uind];
Vertex_circulator vc(D.incident_vertices(vit)), done(vc);
do {
if (D.is_infinite(vc)) continue;
Pt vp = vc->point();
lint d2 = CGAL::squared_distance(vp, up);
md2 = std::min(d2, md2);
} while (++vc != done);
mind2[uind] = md2;
}
std::sort(mind2.begin(), mind2.end());
}
fd2 = mind2[0], md2 = mind2[n / 2], ld2 = mind2[n - 1];
double tf = std::sqrt((std::sqrt(fd2) - 1) / 2);
double tm = std::sqrt((std::sqrt(md2) - 1) / 2);
double tl = std::sqrt((std::sqrt(ld2) - 1) / 2);
int tfi = std::ceil(tf);
int tmi = std::ceil(tm);
int tli = std::ceil(tl);
_o << tfi << " " << tmi << " " << tli << _l;
return;
}
// Week 8: H1N1 / incorrect 100pts?
// Find the maximum width of the path from outside to the vertex
void H1N1(int n) {
// Boost
typedef boost::adjacency_list < boost::vecS, boost::vecS, boost::undirectedS,
boost::no_property, boost::property < boost::edge_weight_t, long > > Graph;
typedef boost::property_map < Graph, boost::edge_weight_t >::type WeightMap;
typedef boost::graph_traits < Graph >::edge_descriptor Edge;
typedef boost::graph_traits < Graph >::edge_iterator EdgeIt;
typedef boost::graph_traits < Graph >::out_edge_iterator OutEdgeIt;
typedef boost::graph_traits < Graph >::vertex_descriptor Vertex;
// CGAL
typedef CGAL::Triangulation_vertex_base_2<IK> Vb;
typedef CGAL::Triangulation_face_base_with_info_2<int, IK> Fb;
typedef CGAL::Triangulation_data_structure_2<Vb, Fb> Tds;
typedef CGAL::Delaunay_triangulation_2<IK, Tds> Delaunay;
typedef Delaunay::Finite_faces_iterator Face_iterator;
typedef Delaunay::Face_handle Face_handle;
typedef Delaunay::Finite_edges_iterator Edge_iterator;
typedef Delaunay::Edge_circulator Edge_circulator;
typedef Delaunay::Finite_vertices_iterator Vertex_iterator;
typedef Delaunay::Vertex_handle Vertex_handle;
typedef Delaunay::Point DPt;
typedef Delaunay::Vertex_circulator Vertex_circulator;
int m;
std::vector<Pt> infected(n);
for (int i = 0; i < n; i++) {
int x, y;
_i >> x >> y;
infected[i] = Pt(x, y);
}
Delaunay D;
D.insert(infected.begin(), infected.end());
Graph G(1); // only infinite face
WeightMap wmap = boost::get(boost::edge_weight, G); // weight = width^2 = r^2*4
int newind = 1; // gradually add faces
Face_iterator fit = D.finite_faces_begin(), fend = D.finite_faces_end();
for (; fit != fend; ++fit) {
fit->info() = 0; // or it could be anything
}
fit = D.finite_faces_begin(), fend = D.finite_faces_end();
for (; fit != fend; ++fit) {
Vertex u;
if (!fit->info()) {
u = boost::add_vertex(G);
fit->info() = newind++;
}
else u = fit->info();
// circulate its 3 neighbors to add edges to the graph
for (int nb = 0; nb < 3; nb++) {
Face_handle fh = fit->neighbor(nb);
if (D.is_infinite(fh)) {
// infinite face: add edge to vertex 0
Vertex v = 0;
Edge e; bool su;
Vertex_handle vh1 = fit->vertex(fit->cw(nb)), vh2 = fit->vertex(fit->ccw(nb));
lint d2 = CGAL::squared_distance(vh1->point(), vh2->point());
boost::tie(e, su) = boost::add_edge(u, v, G);
wmap[e] = d2;
}
else {
// if the face hasn't been visited, add a new vertex and fill fh->info()
Vertex v;
if (!fh->info()) {
fh->info() = newind++;
v = boost::add_vertex(G);
}
else v = fh->info();
// continue if the edge already exists
Edge e; bool su;
boost::tie(e, su) = boost::edge(u, v, G);
if (su) continue;
Vertex_handle vh1 = fit->vertex(fit->cw(nb)), vh2 = fit->vertex(fit->ccw(nb));
lint d2 = CGAL::squared_distance(vh1->point(), vh2->point());
boost::tie(e, su) = boost::add_edge(u, v, G);
wmap[e] = d2;
}
}
}
const lint BIG = 10000000000000000;
typedef std::pair<lint, Vertex> DistV;
int nv = boost::num_vertices(G);
std::vector<DistV> vdist(nv);
for (int i = 0; i < nv; i++) vdist[i] = std::make_pair(-1, i);
std::vector<bool> selected(nv, false); // whether the width of a vertex has been optimized
std::vector<lint> distmap(nv, -1); // the maximum width towards each vertex
OutEdgeIt eit, eend;
for (boost::tie(eit, eend) = boost::out_edges(0, G); eit != eend; eit++) {
Vertex v = boost::target(*eit, G);
vdist[v].first = std::max(vdist[v].first, (lint)wmap[*eit]);
distmap[v] = std::max(distmap[v], (lint)wmap[*eit]);
}
vdist[0].first = 0;
_e << "BFS " << _l;
// BFS for max min edge
std::priority_queue < DistV > pq(vdist.begin(), vdist.end());
selected[0] = true;
distmap[0] = BIG;
while (!pq.empty()) {
DistV dv = pq.top();
pq.pop();
lint d = dv.first;
Vertex u = dv.second;
if (selected[u]) continue; // see the pq.push() below, one vertex could be pushed multiple times
OutEdgeIt eit, eend;
for (boost::tie(eit, eend) = boost::out_edges(u, G); eit != eend; eit++)
{
Vertex v = boost::target(*eit, G);
if (!selected[v]) {
// the updating rule: d[v] = max(d[v], min(w[e], d[u]))
lint curw = std::max((long)distmap[v], std::min(wmap[*eit], (long)distmap[u]));
distmap[v] = curw;
pq.push(std::make_pair(distmap[v], v));
}
}
selected[u] = true;
}
_i >> m;
for (int j = 0; j < m; j++) {
int x, y; lint r2;
_i >> x >> y >> r2;
Pt person(x, y);
Vertex_handle vh = D.nearest_vertex(person);
if (CGAL::squared_distance(person, vh->point()) < r2) {
_o << "n"; continue;
}
Face_handle fh = D.locate(person);
if (D.is_infinite(fh)) {
_o << "y"; continue;
}
Vertex u = fh->info();
if (r2 * 4 > distmap[u]) _o << "n";
else _o << "y";
}
_o << _l;
}
// Week 8: Graypes / 50->50->50->100
// Delaunay, find shortest edge
// Use Vertex_iterator to iterate through the vertices -> O(1)
// rather than nearest_vertex() -> O(log n)
// Tho I didn't they would kill an O(nlogn) algo..
// Don't play with constant when there is a method to improve asymptotic
void Graypes(int n) {
typedef CGAL::Triangulation_vertex_base_with_info_2<int, IK> Vb;
typedef CGAL::Triangulation_data_structure_2<Vb> Tds;
typedef CGAL::Delaunay_triangulation_2<IK, Tds> Delaunay;
typedef Delaunay::Finite_faces_iterator Face_iterator;
typedef Delaunay::Finite_edges_iterator Edge_iterator;
typedef Delaunay::Finite_vertices_iterator Vertex_iterator;
typedef Delaunay::Vertex_handle Vertex_handle;
typedef Delaunay::Point DPt;
typedef Delaunay::Vertex_circulator Vertex_circulator;
std::vector< std::pair<Pt, int> > apes(n);
for (int i = 0; i < n; i++) {
int x, y;
_i >> x >> y;
apes[i] = std::make_pair(Pt(x, y), i);
}
//std::random_shuffle(apes.begin(), apes.end());
Delaunay D;
D.insert(apes.begin(), apes.end());
const lint BIG = 10000000000000000;
//std::vector<int> runto(n, -1);
//std::vector<lint> d2runto(n, BIG);
lint totalmind2 = BIG;
Vertex_iterator vit = D.finite_vertices_begin(), vend = D.finite_vertices_end();
for (; vit != vend; ++vit) {
Pt p = vit->point();
Vertex_circulator vc = D.incident_vertices(vit), done(vc);
do {
if (D.is_infinite(vc))continue;
Pt q = vc->point();
lint d2pq = CGAL::squared_distance(p, q);
totalmind2 = std::min(totalmind2, d2pq);
} while (++vc != done);
}
/* O(nlogn) because of nearest_vertex()
for (int i = 0; i < n; i++) {
//lint mind2 = d2runto[i];
//int prunto = runto[i];
lint mind2 = BIG;
Pt p = apes[i].first;
int pind = apes[i].second;
Vertex_handle vh = D.nearest_vertex(p);
Vertex_circulator vc = D.incident_vertices(vh), done(vc);
do {
if (D.is_infinite(vc)) continue;
Pt q = vc->point();
int qind = vc->info();
if (qind < pind) continue;
lint d2pq = CGAL::squared_distance(p, q);
if (d2pq < mind2) {
mind2 = d2pq;
//prunto = qind;
}
//else if (d2pq == mind2) {
// Pt prevbest = apes[prunto].first;
// if (q.x() < prevbest.x() || (q.x() == prevbest.x() && q.y() < prevbest.y())) {
// prunto = qind;
// }
//}
} while (++vc != done);
//if (prunto != runto[i]) {
// runto[i] = prunto;
// d2runto[i] = mind2;
// if (mind2 < d2runto[prunto]) {
// runto[prunto] = i;
// d2runto[prunto] = mind2;
// }
// else if (mind2 == d2runto[prunto]) {
// Pt p2 = apes[runto[prunto]].first;
// if (p.x() < p2.x() || (p.x() == p2.x() && p.y() < p2.y())) {
// runto[prunto] = i;
// }
// }
//}
totalmind2 = std::min(totalmind2, mind2);
}
*/
lint time = std::ceil(50 * std::sqrt((double)(totalmind2)));
_o << time << _l;
return;
}
// Week 11 PotW: Sith / 25->50->100pts
// Delaunay + find connected components
// Update connected components: Union Find
int calcBiggestComponent(const std::vector<int>& comp, int ncomp) {
int n = comp.size();
std::vector<int> counter(ncomp);
for (int i = 0; i < n; i++) {
counter[comp[i]]++;
}
int largest = 0;
for (int j = 0; j < ncomp; j++) {
largest = std::max(largest, counter[j]);
}
return largest;
}
void Comp2Par(const std::vector<int>& comp, int ncomp, std::vector<int>& par) {
int n = comp.size();
std::vector<int> first(ncomp, -1);
for (int i = 0; i < n; i++) {
if (first[comp[i]] == -1)
first[comp[i]] = i;
par[i] = first[comp[i]];
}
}
void Sith() {
typedef CGAL::Triangulation_vertex_base_with_info_2<int, IK> Vb;
typedef CGAL::Triangulation_data_structure_2<Vb> Tds;
typedef CGAL::Delaunay_triangulation_2<IK, Tds> Delaunay;
typedef Delaunay::Finite_faces_iterator Face_iterator;
typedef Delaunay::Finite_edges_iterator Edge_iterator;
typedef Delaunay::Finite_vertices_iterator Vertex_iterator;
typedef Delaunay::Vertex_handle Vertex_handle;
typedef Delaunay::Point DPt;
typedef Delaunay::Vertex_circulator Vertex_circulator;
typedef boost::adjacency_list < boost::vecS, boost::vecS, boost::undirectedS,
boost::no_property, boost::property < boost::edge_weight_t, double > > Graph;
typedef boost::property_map < Graph, boost::edge_weight_t >::type WeightMap;
typedef boost::graph_traits < Graph >::edge_descriptor Edge;
typedef boost::graph_traits < Graph >::vertex_descriptor Vertex;
int n, r;
_i >> n >> r;
_e << "testcase: " << n << " " << r << _l;
lint r2 = (lint)r*r;
std::vector< std::pair<Pt, int> > p(n);
// invert the input
// so I choose planets [0, k) rather than [k, end)
for (int i = 0; i < n; i++) {
int x, y;
_i >> x >> y;
p[n - 1 - i] = std::make_pair(Pt(x, y), n - 1 - i);
}
Delaunay D;
int nv = n / 2;
D.insert(p.begin(), p.begin() + nv);
Graph G(nv);
for (int i = 0; i < nv; i++) {
Vertex_handle vh = D.nearest_vertex(p[i].first);
Pt pt = vh->point();
int ipt = vh->info();
Vertex_circulator vc = D.incident_vertices(vh), done(vc);
do {
if (D.is_infinite(vc)) continue;
Pt pin = vc->point();
int ipin = vc->info();
if (ipin < ipt) continue; // i --> j, add edge when i < j
lint d2 = CGAL::squared_distance(pt, pin);
if (d2 <= r2) {
boost::add_edge(ipt, ipin, G);
}
} while (++vc != done);
}
std::vector<int> comp(nv), par(nv);
int ncomp = boost::connected_components(G, &comp[0]);
int biggestComp = calcBiggestComponent(comp, ncomp);
Comp2Par(comp, ncomp, par);
UnionFind uf(par);
for (int last = nv; last < n; last++) {
int largestPossible = n - last - 1;
if (biggestComp >= largestPossible) break;
Vertex vlast = boost::add_vertex(G);
Pt plast = p[last].first; // p[last].second == last
D.insert(p.begin() + last, p.begin() + last + 1);
int ipt = last;
Vertex_handle vh = D.nearest_vertex(plast);
Vertex_circulator vc = D.incident_vertices(vh), done(vc);
uf.append();
do {
if (D.is_infinite(vc)) continue;
Pt pin = vc->point();
int ipin = vc->info();
lint d2 = CGAL::squared_distance(plast, pin);
if (d2 <= r2) {
boost::add_edge(ipt, ipin, G);
uf.unionSets(ipt, ipin);
}
} while (++vc != done);
//std::vector<int> ccomp(last+1);
//int nccomp = boost::connected_components(G, &ccomp[0]);
//int largest = calcBiggestComponent(ccomp, nccomp);
int largest = uf.getMaxSize();
largest = std::min(largest, largestPossible);
biggestComp = std::max(biggestComp, largest);
}
_e << "result: " << biggestComp << _l;
_o << biggestComp << _l;
return;
}
// Week 12: Radiation / 60->80->100
// LP + bin_search?? 2^300??
// LP (with Gmpz not Gmpq) + exp_search+bin_search
// they are exact number types and don't worry about 2^300
struct PolyTerm {
int xd;
int yd;
int zd;
int idx;
PolyTerm(int x = 0, int y = 0, int z = 0, int idx = 0) :xd(x), yd(y), zd(z), idx(idx) {}
};
void calcPolyTerm(int deg, std::vector<PolyTerm> &terms) {
//int balls = deg + 2;
terms.clear();
int idx = 0;
int d = deg;
for (int d = 0; d <= deg; d++) {
int balls = d + 2;
for (int i = 0; i < balls - 1; i++) {
for (int j = i + 1; j < balls; j++) {
PolyTerm pt(i, j - i - 1, d + 1 - j, idx);
terms.push_back(pt);
idx++;
}
}
}
return;
}
typedef CGAL::Gmpz ETZ;
typedef CGAL::Quadratic_program<ETZ> ProgramZ;
typedef CGAL::Quadratic_program_solution<ETZ> SolutionZ;
ETZ findPoly(int deg, std::vector<Pt3> &hcell, std::vector<Pt3> &tcell, std::vector< std::vector<ETZ> >& hpowers, std::vector< std::vector<ETZ> >& tpowers) {
ProgramZ lp(CGAL::SMALLER, false, 0, false, 0);
std::vector<PolyTerm> terms;
calcPolyTerm(deg, terms);
int h = hcell.size(), t = tcell.size();
int nterms = terms.size();
const int delta = nterms;
for (int j = 0; j < nterms; j++) {
//lp.set_c(j, 1);
int xind = terms[j].xd, yind = 31 + terms[j].yd, zind = 62 + terms[j].zd;
for (int i = 0; i < h; i++) {
ETZ xyz = hpowers[i][xind] * hpowers[i][yind] * hpowers[i][zind];
lp.set_a(j, i, xyz);
}
for (int i = 0; i < t; i++) {
ETZ xyz = tpowers[i][xind] * tpowers[i][yind] * tpowers[i][zind];
lp.set_a(j, h + i, -xyz);
}
}
lp.set_c(delta, -1);
//lp.set_l(delta, true, 0);
lp.set_u(delta, true, 1);
for (int i = 0; i < h; i++) {
lp.set_b(i, 0);
lp.set_a(delta, i, 0);
}
for (int i = 0; i < t; i++) {
lp.set_a(delta, h + i, 1);
lp.set_b(h + i, 0);
}
SolutionZ s = CGAL::solve_linear_program(lp, ETZ());
//if (s.is_optimal() && s.objective_value() < 0)
// return true;
//return false;
ETZ result = s.objective_value().numerator() / s.objective_value().denominator();
return result;
}
void calcPowers(std::vector<Pt3> & cell, std::vector< std::vector<ETZ> >& powers) {
int n = cell.size();
_e << "powers!" << _l;
for (int i = 0; i < n; i++) {
powers[i] = std::vector<ETZ>(93);
ETZ xp(1), yp(1), zp(1);
int cx = (int)cell[i].x();
int cy = (int)cell[i].y();
int cz = (int)cell[i].z();
for (int d = 0; d <= 30; d++) {
powers[i][d] = xp;
powers[i][31 + d] = yp;
powers[i][62 + d] = zp;
if (d == 30) break;
xp *= cx;
yp *= cy;
zp *= cz;
//_e << xp << " " << yp << " " << zp << _l;
}
}
}
void Radiation() {
int h, t; _i >> h >> t;
std::vector<Pt3> hcell(h), tcell(t);
for (int i = 0; i < h; i++) {
int x, y, z; _i >> x >> y >> z;
hcell[i] = Pt3(x, y, z);
//_e << hcell[i] << _l;
}
for (int j = 0; j < t; j++) {
int x, y, z; _i >> x >> y >> z;
tcell[j] = Pt3(x, y, z);
//_e << tcell[j] << _l;
}
if (h == 0 || t == 0) {
_o << 0 << _l;
return;
}
std::vector< std::vector<ETZ> > hpowers(h), tpowers(t);
calcPowers(hcell, hpowers);
calcPowers(tcell, tpowers);
_e << "calcpowers!" << _l;
//std::vector<bool> canFinds(31, false);
std::vector<ETZ> res(31, 0);
int st = 0, ed = 1;
int low, up, mid;
while (true) {
_e << "d=" << ed << _l;
//canFinds[ed] = canFindPoly(ed, hcell, tcell, hpowers, tpowers);
res[ed] = findPoly(ed, hcell, tcell, hpowers, tpowers);
if (res[ed] < 0) {
low = st;
up = ed;
mid = (low + up) / 2;
break;
}
else {
if (ed == 30) {
_o << "Impossible!\n";
return;
}
st = ed;
ed = std::min(30, ed * 2);
}
}
// binary search
while (true) {
_e << "d=" << mid << _l;
if (up - low <= 1) {
if (res[low]<0 || findPoly(low, hcell, tcell, hpowers, tpowers)<0) {
_o << low << _l;
return;
}
else if (res[up]<0 || findPoly(up, hcell, tcell, hpowers, tpowers)<0) {
_o << up << _l;
return;
}
}
res[mid] = findPoly(mid, hcell, tcell, hpowers, tpowers);
if (res[mid]<0) {
up = mid;
mid = (low + up) / 2;
}
else {
low = mid + 1;
mid = (low + up) / 2;
}
}
_e << _l;
_o << "Impossible!" << _l;
return;
}
// Week 13: Clues / 100pts
// Delaunay + is_bipartite + connected_components
void Clues() {
typedef CGAL::Triangulation_vertex_base_with_info_2<int, IK> Vb;
typedef CGAL::Triangulation_data_structure_2<Vb> Tds;
typedef CGAL::Delaunay_triangulation_2<IK, Tds> Delaunay;
typedef Delaunay::Finite_faces_iterator Face_iterator;
typedef Delaunay::Finite_edges_iterator Edge_iterator;
typedef Delaunay::Finite_vertices_iterator Vertex_iterator;
typedef Delaunay::Vertex_handle Vertex_handle;
typedef Delaunay::Point DPt;
typedef Delaunay::Vertex_circulator Vertex_circulator;
typedef boost::adjacency_list < boost::vecS, boost::vecS, boost::undirectedS,
boost::no_property, boost::property < boost::edge_weight_t, double > > Graph;
typedef boost::property_map < Graph, boost::edge_weight_t >::type WeightMap;
typedef boost::graph_traits < Graph >::edge_descriptor Edge;
typedef boost::graph_traits < Graph >::vertex_descriptor Vertex;
int n, m, r;
_i >> n >> m >> r;
lint r2 = (lint)r*r;
std::vector< std::pair<Pt, int> > stations(n);
std::vector< std::pair<Pt, Pt> > clues(m);
for (int i = 0; i < n; i++) {
int x, y; _i >> x >> y;
stations[i] = std::make_pair(Pt(x, y), i);
}
for (int j = 0; j < m; j++) {
int xa, ya, xb, yb; _i >> xa >> ya >> xb >> yb;
clues[j] = std::make_pair(Pt(xa, ya), Pt(xb, yb));
}
Graph G(n);
std::vector<int> components(n);
Delaunay D;
D.insert(stations.begin(), stations.end());
Vertex_iterator vit;
bool violated = false;
for (vit = D.finite_vertices_begin(); vit != D.finite_vertices_end(); ++vit) {
Vertex_circulator vc = D.incident_vertices(vit), done(vc);
int idx = vit->info();
std::vector< std::pair<Pt, int> > candidates;
candidates.push_back(std::make_pair(vit->point(), vit->info()));
do {
if (!D.is_infinite(vc)) {
int vcidx = vc->info();
//if (vcidx < idx) continue;
if (CGAL::squared_distance(vc->point(), vit->point()) > r2) continue;
//boost::add_edge(idx, vcidx, G);
candidates.push_back(std::make_pair(vc->point(), vcidx));
}
} while (++vc != done);
int ncand = candidates.size();
for (int i = 1; i < ncand; i++) {
Pt pi = candidates[i].first;
for (int j = i + 1; j < ncand; j++) {
Pt pj = candidates[j].first;
if (CGAL::squared_distance(pi, pj) <= r2) {
violated = true;
break;
}
}
}
if (violated) break;
for (int j = 1; j < ncand; j++) {
int idxj = candidates[j].second;
boost::add_edge(idx, idxj, G);
}
}
if (violated) {
for (int j = 0; j < m; j++) {
_o << "n";
}
_o << _l;
_e << "violated" << _l;
return;
}
bool isBipartite = boost::is_bipartite(G);
if (!isBipartite) {
for (int j = 0; j < m; j++) {
_o << "n";
}
_o << _l;
_e << "n" << _l;
return;
}
boost::connected_components(G, &components[0]);
for (int i = 0; i < n; i++) {
_e << components[i] << " ";
}_e << _l;
for (int j = 0; j < m; j++) {
Pt a = clues[j].first, b = clues[j].second;
if (CGAL::squared_distance(a, b) <= r2) {
_o << "y";
continue;
}
Vertex_handle vha = D.nearest_vertex(a);
Vertex_handle vhb = D.nearest_vertex(b);
// not reachable to any station
if (CGAL::squared_distance(vha->point(), a) > r2
|| CGAL::squared_distance(vhb->point(), b) > r2) {
_o << "n";
continue;
}
// not in the same component
int idxa = vha->info(), idxb = vhb->info();
if (components[idxa] == components[idxb]) {
_o << "y";
//_e << vha->point() << "|" << vhb->point() << _l;
//_e << components[idxa] << " " << components[idxb] << _l;
}
else _o << "n";
}
_o << _l;
return;
}
// Week 13: Goldfinger / 100 pts
// LP + Delaunay + bin_search
typedef CGAL::Delaunay_triangulation_2<IK> Delaunay;
typedef Delaunay::Finite_faces_iterator Face_iterator;
typedef Delaunay::Finite_edges_iterator Edge_iterator;
typedef Delaunay::Vertex_handle Vertex_handle;
typedef Delaunay::Point DPt;
bool isSolvable(int a, std::vector<Pt> &psensor, std::vector<int> &esensor,
std::vector<Pt> &pmpe, std::vector<lint> &r2mpe, int Imax, std::vector< std::vector<lint> >& d2) {
int n = psensor.size();
int m = pmpe.size();
bool isRestricted = r2mpe[0] > 0;
Program lp(CGAL::LARGER, true, 0, false);
for (int i = 0; i < n; i++) {
for (int j = 0; j < a; j++) {
//lint d2 = CGAL::squared_distance(pmpe[j], psensor[i]);
if (!isRestricted || d2[i][j] < r2mpe[j])
lp.set_a(j, i, (ET)1 / d2[i][j]);
}
lp.set_b(i, esensor[i]);
}
for (int j = 0; j < a; j++) {
lp.set_a(j, n, -1);
lp.set_c(j, 1);
}
lp.set_b(n, -Imax);
Solution s = CGAL::solve_linear_program(lp, ET());
if (s.is_optimal()) {
//_o << a << _l;
return true;
}
else {