結果
| 問題 |
No.5007 Steiner Space Travel
|
| コンテスト | |
| ユーザー |
 komori3
|
| 提出日時 | 2022-07-30 16:17:47 |
| 言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 525 ms / 1,000 ms |
| コード長 | 12,911 bytes |
| コンパイル時間 | 3,905 ms |
| 実行使用メモリ | 5,164 KB |
| スコア | 7,689,261 |
| 最終ジャッジ日時 | 2022-07-30 16:18:11 |
| 合計ジャッジ時間 | 20,954 ms |
|
ジャッジサーバーID （参考情報） |
judge12 / judge13 |
| 純コード判定しない問題か言語 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 30 |
ソースコード
#define _CRT_NONSTDC_NO_WARNINGS
#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
#include <random>
#include <unordered_set>
#include <atcoder/all>
//#include <boost/rational.hpp>
//#include <boost/multiprecision/cpp_int.hpp>
//#include <boost/multiprecision/cpp_bin_float.hpp>
#ifdef _MSC_VER
#include <conio.h>
#include <ppl.h>
#include <filesystem>
#include <opencv2/core.hpp>
#include <opencv2/highgui.hpp>
#include <opencv2/imgproc.hpp>
#include <intrin.h>
int __builtin_clz(unsigned int n)
{
unsigned long index;
_BitScanReverse(&index, n);
return 31 - index;
}
int __builtin_ctz(unsigned int n)
{
unsigned long index;
_BitScanForward(&index, n);
return index;
}
namespace std {
inline int __lg(int __n) { return sizeof(int) * 8 - 1 - __builtin_clz(__n); }
}
#else
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
/** compro_io **/
/* tuple */
// out
namespace aux {
template<typename T, unsigned N, unsigned L>
struct tp {
static void output(std::ostream& os, const T& v) {
os << std::get<N>(v) << ", ";
tp<T, N + 1, L>::output(os, v);
}
};
template<typename T, unsigned N>
struct tp<T, N, N> {
static void output(std::ostream& os, const T& v) { os << std::get<N>(v); }
};
}
template<typename... Ts>
std::ostream& operator<<(std::ostream& os, const std::tuple<Ts...>& t) {
os << '[';
aux::tp<std::tuple<Ts...>, 0, sizeof...(Ts) - 1>::output(os, t);
return os << ']';
}
template<class Ch, class Tr, class Container>
std::basic_ostream<Ch, Tr>& operator<<(std::basic_ostream<Ch, Tr>& os, const Container& x);
/* pair */
// out
template<class S, class T>
std::ostream& operator<<(std::ostream& os, const std::pair<S, T>& p) {
return os << "[" << p.first << ", " << p.second << "]";
}
// in
template<class S, class T>
std::istream& operator>>(std::istream& is, std::pair<S, T>& p) {
return is >> p.first >> p.second;
}
/* container */
// out
template<class Ch, class Tr, class Container>
std::basic_ostream<Ch, Tr>& operator<<(std::basic_ostream<Ch, Tr>& os, const Container& x) {
bool f = true;
os << "[";
for (auto& y : x) {
os << (f ? "" : ", ") << y;
f = false;
}
return os << "]";
}
// in
template <
class T,
class = decltype(std::begin(std::declval<T&>())),
class = typename std::enable_if<!std::is_same<T, std::string>::value>::type
>
std::istream& operator>>(std::istream& is, T& a) {
for (auto& x : a) is >> x;
return is;
}
std::ostream& operator<<(std::ostream& os, const std::vector<bool>& v) {
std::string s(v.size(), ' ');
for (int i = 0; i < v.size(); i++) s[i] = v[i] + '0';
os << s;
return os;
}
std::ostream& operator<<(std::ostream& os, const std::vector<std::vector<bool>>& m) {
for (const auto& v : m) os << v << '\n';
return os;
}
/* struct */
template<typename T>
auto operator<<(std::ostream& out, const T& t) -> decltype(out << t.stringify()) {
out << t.stringify();
return out;
}
/* setup */
struct IOSetup {
IOSetup(bool f) {
if (f) { std::cin.tie(nullptr); std::ios::sync_with_stdio(false); }
std::cout << std::fixed << std::setprecision(15);
}
} iosetup(true);
/** string formatter **/
template<typename... Ts>
std::string format(const std::string& f, Ts... t) {
size_t l = std::snprintf(nullptr, 0, f.c_str(), t...);
std::vector<char> b(l + 1);
std::snprintf(&b[0], l + 1, f.c_str(), t...);
return std::string(&b[0], &b[0] + l);
}
template<typename T>
std::string stringify(const T& x) {
std::ostringstream oss;
oss << x;
return oss.str();
}
/* dump */
#define DUMPOUT std::cerr
std::ostringstream DUMPBUF;
#define dump(...) do{DUMPBUF<<" ";DUMPBUF<<#__VA_ARGS__<<" :[DUMP - "<<__LINE__<<":"<<__FUNCTION__<<"]"<<std::endl;DUMPBUF<<" ";dump_func(__VA_ARGS__);DUMPOUT<<DUMPBUF.str();DUMPBUF.str("");DUMPBUF.clear();}while(0);
void dump_func() { DUMPBUF << std::endl; }
template <class Head, class... Tail> void dump_func(Head&& head, Tail&&... tail) { DUMPBUF << head; if (sizeof...(Tail) == 0) { DUMPBUF << " "; } else { DUMPBUF << ", "; } dump_func(std::move(tail)...); }
///* timer */
//class Timer {
// double t = 0, paused = 0, tmp;
//public:
// Timer() { reset(); }
// static double time() {
//#ifdef _MSC_VER
// return __rdtsc() / 3.0e9;
//#else
// unsigned long long a, d;
// __asm__ volatile("rdtsc"
// : "=a"(a), "=d"(d));
// return (d << 32 | a) / 3.0e9;
//#endif
// }
// void reset() { t = time(); }
// void pause() { tmp = time(); }
// void restart() { paused += time() - tmp; }
// double elapsed_ms() const { return (time() - t - paused) * 1000.0; }
//} timer;
/* rand */
struct Xorshift {
uint64_t x = 88172645463325252LL;
void set_seed(unsigned seed, int rep = 100) { x = uint64_t((seed + 1) * 10007); for (int i = 0; i < rep; i++) next_int(); }
unsigned next_int() { x = x ^ (x << 7); return x = x ^ (x >> 9); }
unsigned next_int(unsigned mod) { x = x ^ (x << 7); x = x ^ (x >> 9); return x % mod; }
unsigned next_int(unsigned l, unsigned r) { x = x ^ (x << 7); x = x ^ (x >> 9); return x % (r - l + 1) + l; } // inclusive
double next_double() { return double(next_int()) / UINT_MAX; }
} rnd;
/* shuffle */
template<typename T>
void shuffle_vector(std::vector<T>& v, Xorshift& rnd) {
int n = v.size();
for (int i = n - 1; i >= 1; i--) {
int r = rnd.next_int(i);
std::swap(v[i], v[r]);
}
}
/* split */
std::vector<std::string> split(std::string str, const std::string& delim) {
for (char& c : str) if (delim.find(c) != std::string::npos) c = ' ';
std::istringstream iss(str);
std::vector<std::string> parsed;
std::string buf;
while (iss >> buf) parsed.push_back(buf);
return parsed;
}
template<typename A, size_t N, typename T> inline void Fill(A(&array)[N], const T& val) {
std::fill((T*)array, (T*)(array + N), val);
}
template<typename T, typename ...Args> auto make_vector(T x, int arg, Args ...args) { if constexpr (sizeof...(args) == 0)return std::vector<T>(arg, x); else return std::vector(arg, make_vector<T>(x, args...)); }
template<typename T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } return false; }
template<typename T> bool chmin(T& a, const T& b) { if (a > b) { a = b; return true; } return false; }
using ll = long long;
using ull = unsigned long long;
using ld = double;
//using ld = boost::multiprecision::cpp_bin_float_quad;
using pii = std::pair<int, int>;
using pll = std::pair<ll, ll>;
using namespace std;
template<typename T>
void print_vector(const std::vector<T>& v) {
for (int i = 0; i < v.size(); i++) {
std::cout << (i ? " " : "") << v[i];
}
std::cout << '\n';
}
double lrnd[1 << 16];
void init() {
Xorshift rnd;
for (int i = 0; i < 100; i++) rnd.next_int();
for (int i = 0; i < (1 << 16); i++) lrnd[i] = log(rnd.next_double());
}
constexpr int N = 100;
constexpr int M = 8;
constexpr int alpha = 5;
constexpr int alpha2 = alpha * alpha;
int xs[N], ys[N];
int ds[N][N];
inline int dist2(int x1, int y1, int x2, int y2) {
return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
}
struct TSP {
Xorshift& rnd;
int score;
vector<int> p;
TSP(Xorshift& rnd) : rnd(rnd) {
score = 0;
p.resize(N);
for (int i = 0; i < N; i++) {
score += ds[i][(i + 1) % N];
p[i] = i;
}
}
inline int dist(int i1, int i2) {
return ds[i1][i2];
}
double calc_2opt_diff(int idx1, int idx2) {
int p1 = p[idx1], p2 = p[(idx1 + 1) % N], p3 = p[idx2], p4 = p[(idx2 + 1) % N];
return dist(p1, p3) + dist(p2, p4) - dist(p1, p2) - dist(p3, p4);
}
void solve_2opt_climbing() {
while (true) {
bool update = false;
for (int i1 = 0; i1 < N - 1; i1++) {
for (int i2 = i1 + 1; i2 < N; i2++) {
int diff = calc_2opt_diff(i1, i2);
if (diff < 0) {
reverse(p.begin() + i1 + 1, p.begin() + i2 + 1);
score += diff;
update = true;
}
}
}
if (!update) break;
}
}
double get_temp(double startTemp, double endTemp, int t, int T) {
return endTemp + (startTemp - endTemp) * (T - t) / T;
}
void solve_2opt_annealing(int numLoop) {
double bestScore = DBL_MAX;
vector<int> bp;
for (int n = 0; n < numLoop; n++) {
int i1 = rnd.next_int() % N;
int i2 = rnd.next_int() % (N - 1);
if (i2 >= i1) i2++;
if (i1 > i2) swap(i1, i2);
double diff = calc_2opt_diff(i1, i2);
double temp = get_temp(10000.0, 1.0, n, numLoop);
double x = -diff / temp;
if (-diff > temp * lrnd[n & 0xFFFF]) {
reverse(p.begin() + i1 + 1, p.begin() + i2 + 1);
score += diff;
if (score < bestScore) {
bestScore = score;
bp = p;
}
}
if (!(n & 0x3FFFFF)) {
dump(n, score);
}
}
score = bestScore;
dump(score);
p = bp;
}
};
struct KMeansRetVal {
int cxs[M];
int cys[M];
int cluster[N];
};
KMeansRetVal kmeans() {
int cxs[M] = {};
int cys[M] = {};
int nc = 0;
double prob[N]; Fill(prob, 1.0 / N);
double cumu[N];
auto sampling = [&]() {
memset(cumu, 0, sizeof(double) * N);
for (int i = 1; i < N; i++) cumu[i] = cumu[i - 1] + prob[i - 1];
double d = rnd.next_double() * cumu[N - 1];
int idx = distance(cumu, upper_bound(cumu, cumu + N, d)) - 1;
return idx;
};
auto nearest_centroid = [&](int x, int y) {
int mindist = INT_MAX;
int minidx = -1;
for (int i = 0; i < nc; i++) {
int dist = dist2(x, y, cxs[i], cys[i]);
if (chmin(mindist, dist)) {
minidx = i;
}
}
return minidx;
};
for (int i = 0; i < M; i++) {
int idx = sampling();
cxs[i] = xs[idx];
cys[i] = ys[idx];
nc++;
// update prob
int sum = 0;
for (int j = 0; j < N; j++) {
int nearest = nearest_centroid(xs[j], ys[j]);
int weight = dist2(xs[j], ys[j], cxs[nearest], cys[nearest]);
prob[j] = weight;
sum += weight;
}
for (int j = 0; j < N; j++) prob[j] /= sum;
}
int cluster[N];
for (int i = 0; i < N; i++) cluster[i] = nearest_centroid(xs[i], ys[i]);
while (true) {
int xmean[M] = {}, ymean[M] = {};
int ctr[M] = {};
for (int i = 0; i < N; i++) {
int c = cluster[i];
xmean[c] += xs[i];
ymean[c] += ys[i];
ctr[c]++;
}
for (int c = 0; c < M; c++) {
cxs[c] = xmean[c] / ctr[c];
cys[c] = ymean[c] / ctr[c];
}
bool update = false;
for (int i = 0; i < N; i++) {
int idx = nearest_centroid(xs[i], ys[i]);
if (cluster[i] != idx) update = true;
cluster[i] = idx;
}
if (!update) break;
}
KMeansRetVal res;
memcpy(res.cxs, cxs, sizeof(int) * M);
memcpy(res.cys, cys, sizeof(int) * M);
memcpy(res.cluster, cluster, sizeof(int) * N);
return std::move(res);
}
int main() {
init();
{ int buf; cin >> buf >> buf; }
for (int i = 0; i < N; i++) cin >> xs[i] >> ys[i];
for (int i = 1; i < N; i++) {
for (int j = 0; j < i; j++) {
ds[i][j] = ds[j][i] = dist2(xs[i], ys[i], xs[j], ys[j]);
}
}
TSP tsp(rnd);
tsp.solve_2opt_annealing(30000000);
auto [cxs, cys, cluster] = kmeans();
vector<pii> ans;
for (int i = 0; i < N; i++) {
// p[i], p[i+1] のクラスタが等しく c のとき、p[i] -> c -> p[i+1] としたときスコアが下がるなら採用
int u = tsp.p[i], v = tsp.p[(i + 1) % N];
int cu = cluster[u], cv = cluster[v];
ans.emplace_back(1, u + 1);
if (cu == cv) {
int cost1 = ds[u][v] * alpha2;
int cost2 = (dist2(xs[u], ys[u], cxs[cu], cys[cu]) + dist2(cxs[cu], cys[cu], xs[v], ys[v])) * alpha;
if (cost2 < cost1) {
ans.emplace_back(2, cu + 1);
}
}
}
ans.emplace_back(1, tsp.p[0] + 1);
for (int i = 0; i < M; i++) {
cout << format("%d %d\n", cxs[i], cys[i]);
}
cout << ans.size() << '\n';
for (const auto [t, r] : ans) {
cout << t << ' ' << r << '\n';
}
return 0;
}