結果
| 問題 |
No.5007 Steiner Space Travel
|
| コンテスト | |
| ユーザー |
 hitonanode
|
| 提出日時 | 2023-08-23 00:31:46 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 862 ms / 1,000 ms |
| コード長 | 43,858 bytes |
| コンパイル時間 | 5,817 ms |
| コンパイル使用メモリ | 268,484 KB |
| 実行使用メモリ | 4,388 KB |
| スコア | 8,903,424 |
| 最終ジャッジ日時 | 2023-08-23 00:32:21 |
| 合計ジャッジ時間 | 34,499 ms |
|
ジャッジサーバーID （参考情報） |
judge14 / judge11 |
| 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
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#include <iostream>
#include <string>
#include <utility>
#include <vector>
class JsonDumper {
struct KeyValue {
std::string key;
std::string value;
};
std::vector<KeyValue> _items;
bool dump_at_end = false;
public:
JsonDumper(bool dump_at_end_ = false) : dump_at_end(dump_at_end_) {}
~JsonDumper() {
if (dump_at_end) std::cout << dump() << std::endl;
}
void set_dump_at_end() { dump_at_end = true; }
void operator()(const std::string &key, const std::string &value) {
_items.push_back(KeyValue{key, "\"" + value + "\""});
}
template <class T> void operator()(const std::string &key, T value) {
_items.push_back(KeyValue{key, std::to_string(value)});
}
std::string dump() const {
std::string ret = "{\n";
if (!_items.empty()) {
for (const auto &[k, v] : _items) ret += " \"" + k + "\": " + v + ",\n";
ret.erase(ret.end() - 2);
}
ret += "}";
return ret;
}
} jdump;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for (int i = (begin), i##_end_ = (end); i < i##_end_; i++)
#define IFOR(i, begin, end) for (int i = (end)-1, i##_begin_ = (begin); i >= i##_begin_; i--)
#define REP(i, n) FOR(i, 0, n)
#define IREP(i, n) IFOR(i, 0, n)
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) {
return (num > 0 ? num / den : -((-num + den - 1) / den));
}
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) {
return std::make_pair(l.first + r.first, l.second + r.second);
}
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) {
return std::make_pair(l.first - r.first, l.second - r.second);
}
template <class T> std::vector<T> sort_unique(std::vector<T> vec) {
sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end());
return vec;
}
template <class T> int arglb(const std::vector<T> &v, const T &x) {
return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x));
}
template <class T> int argub(const std::vector<T> &v, const T &x) {
return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x));
}
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) {
for (auto &v : vec) is >> v;
return is;
}
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH>
OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) {
os << '[';
for (auto v : vec) os << v << ',';
os << ']';
return os;
}
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) {
os << '[';
for (auto v : arr) os << v << ',';
os << ']';
return os;
}
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) {
std::apply([&is](auto &&...args) { ((is >> args), ...); }, tpl);
return is;
}
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) {
os << '(';
std::apply([&os](auto &&...args) { ((os << args << ','), ...); }, tpl);
return os << ')';
}
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) {
os << '{';
for (auto v : vec) os << v << ',';
os << '}';
return os;
}
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) {
os << "deq[";
for (auto v : vec) os << v << ',';
os << ']';
return os;
}
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) {
os << '{';
for (auto v : vec) os << v << ',';
os << '}';
return os;
}
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) {
os << '{';
for (auto v : vec) os << v << ',';
os << '}';
return os;
}
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) {
os << '{';
for (auto v : vec) os << v << ',';
os << '}';
return os;
}
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) {
return os << '(' << pa.first << ',' << pa.second << ')';
}
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) {
os << '{';
for (auto v : mp) os << v.first << "=>" << v.second << ',';
os << '}';
return os;
}
template <class OStream, class TK, class TV, class TH>
OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) {
os << '{';
for (auto v : mp) os << v.first << "=>" << v.second << ',';
os << '}';
return os;
}
#ifdef HITONANODE_LOCAL
const std::string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m",
BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m",
NORMAL_FAINT = "\033[0;2m";
#define dbg(x) \
std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " \
<< __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) \
((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ \
<< ") " << __FILE__ << COLOR_RESET << std::endl \
: std::cerr)
#else
#define dbg(x) 0
#define dbgif(cond, x) 0
#endif
#ifdef BENCHMARK
#define dump_onlinejudge(x) 0
struct setenv {
setenv() { jdump.set_dump_at_end(); }
} setenv_;
#else
#define dump_onlinejudge(x) (std::cout << (x) << std::endl)
#endif
#include <vector>
#include <cstdint>
uint32_t rand_int() // XorShift random integer generator
{
static uint32_t x = 123456789, y = 362436069, z = 521288629, w = 88675123;
uint32_t t = x ^ (x << 11);
x = y;
y = z;
z = w;
return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));
}
double rand_double() { return (double)rand_int() / UINT32_MAX; }
#include <algorithm>
#include <cassert>
#include <deque>
#include <fstream>
#include <functional>
#include <limits>
#include <queue>
#include <string>
#include <tuple>
#include <utility>
#include <vector>
template <typename T, T INF = std::numeric_limits<T>::max() / 2, int INVALID = -1>
struct shortest_path {
int V, E;
bool single_positive_weight;
T wmin, wmax;
std::vector<std::pair<int, T>> tos;
std::vector<int> head;
std::vector<std::tuple<int, int, T>> edges;
void build_() {
if (int(tos.size()) == E and int(head.size()) == V + 1) return;
tos.resize(E);
head.assign(V + 1, 0);
for (const auto &e : edges) ++head[std::get<0>(e) + 1];
for (int i = 0; i < V; ++i) head[i + 1] += head[i];
auto cur = head;
for (const auto &e : edges) {
tos[cur[std::get<0>(e)]++] = std::make_pair(std::get<1>(e), std::get<2>(e));
}
}
shortest_path(int V = 0) : V(V), E(0), single_positive_weight(true), wmin(0), wmax(0) {}
void add_edge(int s, int t, T w) {
assert(0 <= s and s < V);
assert(0 <= t and t < V);
edges.emplace_back(s, t, w);
++E;
if (w > 0 and wmax > 0 and wmax != w) single_positive_weight = false;
wmin = std::min(wmin, w);
wmax = std::max(wmax, w);
}
void add_bi_edge(int u, int v, T w) {
add_edge(u, v, w);
add_edge(v, u, w);
}
std::vector<T> dist;
std::vector<int> prev;
using Pque = std::priority_queue<std::pair<T, int>, std::vector<std::pair<T, int>>,
std::greater<std::pair<T, int>>>;
template <class Heap = Pque> void dijkstra(int s, int t = INVALID) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF);
prev.assign(V, INVALID);
dist[s] = 0;
Heap pq;
pq.emplace(0, s);
while (!pq.empty()) {
T d;
int v;
std::tie(d, v) = pq.top();
pq.pop();
if (t == v) return;
if (dist[v] < d) continue;
for (int e = head[v]; e < head[v + 1]; ++e) {
const auto &nx = tos[e];
T dnx = d + nx.second;
if (dist[nx.first] > dnx) {
dist[nx.first] = dnx, prev[nx.first] = v;
pq.emplace(dnx, nx.first);
}
}
}
}
void dijkstra_vquad(int s, int t = INVALID) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF);
prev.assign(V, INVALID);
dist[s] = 0;
std::vector<char> fixed(V, false);
while (true) {
int r = INVALID;
T dr = INF;
for (int i = 0; i < V; i++) {
if (!fixed[i] and dist[i] < dr) r = i, dr = dist[i];
}
if (r == INVALID or r == t) break;
fixed[r] = true;
int nxt;
T dx;
for (int e = head[r]; e < head[r + 1]; ++e) {
std::tie(nxt, dx) = tos[e];
if (dist[nxt] > dist[r] + dx) dist[nxt] = dist[r] + dx, prev[nxt] = r;
}
}
}
bool bellman_ford(int s, int nb_loop) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF), prev.assign(V, INVALID);
dist[s] = 0;
for (int l = 0; l < nb_loop; l++) {
bool upd = false;
for (int v = 0; v < V; v++) {
if (dist[v] == INF) continue;
for (int e = head[v]; e < head[v + 1]; ++e) {
const auto &nx = tos[e];
T dnx = dist[v] + nx.second;
if (dist[nx.first] > dnx) dist[nx.first] = dnx, prev[nx.first] = v, upd = true;
}
}
if (!upd) return true;
}
return false;
}
void spfa(int s) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF);
prev.assign(V, INVALID);
dist[s] = 0;
std::deque<int> q;
std::vector<char> in_queue(V);
q.push_back(s), in_queue[s] = 1;
while (!q.empty()) {
int now = q.front();
q.pop_front(), in_queue[now] = 0;
for (int e = head[now]; e < head[now + 1]; ++e) {
const auto &nx = tos[e];
T dnx = dist[now] + nx.second;
int nxt = nx.first;
if (dist[nxt] > dnx) {
dist[nxt] = dnx;
if (!in_queue[nxt]) {
if (q.size() and dnx < dist[q.front()]) { // Small label first optimization
q.push_front(nxt);
} else {
q.push_back(nxt);
}
prev[nxt] = now, in_queue[nxt] = 1;
}
}
}
}
}
void zero_one_bfs(int s, int t = INVALID) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF), prev.assign(V, INVALID);
dist[s] = 0;
std::vector<int> q(V * 4);
int ql = V * 2, qr = V * 2;
q[qr++] = s;
while (ql < qr) {
int v = q[ql++];
if (v == t) return;
for (int e = head[v]; e < head[v + 1]; ++e) {
const auto &nx = tos[e];
T dnx = dist[v] + nx.second;
if (dist[nx.first] > dnx) {
dist[nx.first] = dnx, prev[nx.first] = v;
if (nx.second) {
q[qr++] = nx.first;
} else {
q[--ql] = nx.first;
}
}
}
}
}
void dial(int s, int t = INVALID) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF), prev.assign(V, INVALID);
dist[s] = 0;
std::vector<std::vector<std::pair<int, T>>> q(wmax + 1);
q[0].emplace_back(s, dist[s]);
int ninq = 1;
int cur = 0;
T dcur = 0;
for (; ninq; ++cur, ++dcur) {
if (cur == wmax + 1) cur = 0;
while (!q[cur].empty()) {
int v = q[cur].back().first;
T dnow = q[cur].back().second;
q[cur].pop_back(), --ninq;
if (v == t) return;
if (dist[v] < dnow) continue;
for (int e = head[v]; e < head[v + 1]; ++e) {
const auto &nx = tos[e];
T dnx = dist[v] + nx.second;
if (dist[nx.first] > dnx) {
dist[nx.first] = dnx, prev[nx.first] = v;
int nxtcur = cur + int(nx.second);
if (nxtcur >= int(q.size())) nxtcur -= q.size();
q[nxtcur].emplace_back(nx.first, dnx), ++ninq;
}
}
}
}
}
bool dag_solver(int s) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF), prev.assign(V, INVALID);
dist[s] = 0;
std::vector<int> indeg(V, 0);
std::vector<int> q(V * 2);
int ql = 0, qr = 0;
q[qr++] = s;
while (ql < qr) {
int now = q[ql++];
for (int e = head[now]; e < head[now + 1]; ++e) {
const auto &nx = tos[e];
++indeg[nx.first];
if (indeg[nx.first] == 1) q[qr++] = nx.first;
}
}
ql = qr = 0;
q[qr++] = s;
while (ql < qr) {
int now = q[ql++];
for (int e = head[now]; e < head[now + 1]; ++e) {
const auto &nx = tos[e];
--indeg[nx.first];
if (dist[nx.first] > dist[now] + nx.second)
dist[nx.first] = dist[now] + nx.second, prev[nx.first] = now;
if (indeg[nx.first] == 0) q[qr++] = nx.first;
}
}
return *max_element(indeg.begin(), indeg.end()) == 0;
}
std::vector<int> retrieve_path(int goal) const {
assert(int(prev.size()) == V);
assert(0 <= goal and goal < V);
if (dist[goal] == INF) return {};
std::vector<int> ret{goal};
while (prev[goal] != INVALID) {
goal = prev[goal];
ret.push_back(goal);
}
std::reverse(ret.begin(), ret.end());
return ret;
}
void solve(int s, int t = INVALID) {
if (wmin >= 0) {
if (single_positive_weight) {
zero_one_bfs(s, t);
} else if (wmax <= 10) {
dial(s, t);
} else {
if ((long long)V * V < (E << 4)) {
dijkstra_vquad(s, t);
} else {
dijkstra(s, t);
}
}
} else {
bellman_ford(s, V);
}
}
std::vector<std::vector<T>> floyd_warshall() {
build_();
std::vector<std::vector<T>> dist2d(V, std::vector<T>(V, INF));
for (int i = 0; i < V; i++) {
dist2d[i][i] = 0;
for (const auto &e : edges) {
int s = std::get<0>(e), t = std::get<1>(e);
dist2d[s][t] = std::min(dist2d[s][t], std::get<2>(e));
}
}
for (int k = 0; k < V; k++) {
for (int i = 0; i < V; i++) {
if (dist2d[i][k] == INF) continue;
for (int j = 0; j < V; j++) {
if (dist2d[k][j] == INF) continue;
dist2d[i][j] = std::min(dist2d[i][j], dist2d[i][k] + dist2d[k][j]);
}
}
}
return dist2d;
}
void to_dot(std::string filename = "shortest_path") const {
std::ofstream ss(filename + ".DOT");
ss << "digraph{\n";
build_();
for (int i = 0; i < V; i++) {
for (int e = head[i]; e < head[i + 1]; ++e) {
ss << i << "->" << tos[e].first << "[label=" << tos[e].second << "];\n";
}
}
ss << "}\n";
ss.close();
return;
}
};
#include <algorithm>
#include <utility>
#include <vector>
#include <vector>
#include <algorithm>
#include <limits>
#include <utility>
#include <vector>
template <class DistanceMatrix>
std::vector<std::pair<int, int>> mst_edges(const DistanceMatrix &dist) {
using T = decltype((*dist.adjacents(0).begin()).second);
if (dist.n() <= 1) return {};
std::vector<T> dp(dist.n(), std::numeric_limits<T>::max());
std::vector<int> prv(dist.n(), -1);
std::vector<int> used(dist.n());
std::vector<std::pair<int, int>> ret(dist.n() - 1);
for (int t = 0; t < dist.n(); ++t) {
int x = std::min_element(dp.cbegin(), dp.cend()) - dp.cbegin();
dp.at(x) = std::numeric_limits<T>::max();
used.at(x) = 1;
if (t > 0) ret.at(t - 1) = {prv.at(x), x};
for (auto [y, len] : dist.adjacents(x)) {
if (!used.at(y) and len < dp.at(y)) dp.at(y) = len, prv.at(y) = x;
}
}
return ret;
}
template <class DistanceMatrix> auto calc_lkh_alpha(const DistanceMatrix &dist) {
using T = decltype((*dist.adjacents(0).begin()).second);
std::vector<std::vector<int>> to(dist.n());
for (auto [s, t] : mst_edges(dist)) {
to.at(s).push_back(t);
to.at(t).push_back(s);
}
std::vector ret(dist.n(), std::vector<T>(dist.n()));
for (int s = 0; s < dist.n(); ++s) {
auto rec = [&](auto &&self, int now, int prv, T hi) -> void {
ret.at(s).at(now) = dist(s, now) - hi;
for (int nxt : to.at(now)) {
if (nxt == prv) continue;
self(self, nxt, now, std::max(hi, dist(now, nxt)));
}
};
rec(rec, s, -1, T());
}
int best_one = -1;
T longest_2nd_nearest = T();
for (int one = 0; one < dist.n(); ++one) {
if (to.at(one).size() != 1) continue;
const int ng = to.at(one).front();
bool found = false;
T second_nearest = T();
for (auto [v, len] : dist.adjacents(one)) {
if (v == ng) continue;
if (!found) {
found = true, second_nearest = len;
} else if (len < second_nearest) {
second_nearest = len;
}
}
if (found and (best_one < 0 or second_nearest > longest_2nd_nearest))
best_one = one, longest_2nd_nearest = second_nearest;
}
if (best_one != -1) {
for (auto [v, len] : dist.adjacents(best_one)) {
if (v == to.at(best_one).front()) continue;
ret.at(best_one).at(v) = ret.at(v).at(best_one) = len - longest_2nd_nearest;
}
}
return ret;
}
template <class T> class csr_distance_matrix {
int _rows = 0;
std::vector<int> begins;
std::vector<std::pair<int, T>> vals;
public:
csr_distance_matrix() : csr_distance_matrix({}, 0) {}
csr_distance_matrix(const std::vector<std::tuple<int, int, T>> &init, int rows)
: _rows(rows), begins(rows + 1) {
std::vector<int> degs(rows);
for (const auto &p : init) ++degs.at(std::get<0>(p));
for (int i = 0; i < rows; ++i) begins.at(i + 1) = begins.at(i) + degs.at(i);
vals.resize(init.size(), std::make_pair(-1, T()));
for (auto [i, j, w] : init) vals.at(begins.at(i + 1) - (degs.at(i)--)) = {j, w};
}
void apply_pi(const std::vector<T> &pi) {
for (int i = 0; i < n(); ++i) {
for (auto &[j, d] : adjacents(i)) d += pi.at(i) + pi.at(j);
}
}
int n() const noexcept { return _rows; }
struct adjacents_sequence {
csr_distance_matrix *ptr;
int from;
using iterator = typename std::vector<std::pair<int, T>>::iterator;
iterator begin() { return std::next(ptr->vals.begin(), ptr->begins.at(from)); }
iterator end() { return std::next(ptr->vals.begin(), ptr->begins.at(from + 1)); }
};
struct const_adjacents_sequence {
const csr_distance_matrix *ptr;
const int from;
using const_iterator = typename std::vector<std::pair<int, T>>::const_iterator;
const_iterator begin() const {
return std::next(ptr->vals.cbegin(), ptr->begins.at(from));
}
const_iterator end() const {
return std::next(ptr->vals.cbegin(), ptr->begins.at(from + 1));
}
};
adjacents_sequence adjacents(int from) { return {this, from}; }
const_adjacents_sequence adjacents(int from) const { return {this, from}; }
const_adjacents_sequence operator()(int from) const { return {this, from}; }
};
template <class DistanceMatrix> auto build_adjacent_info(const DistanceMatrix &dist, int sz) {
using T = decltype((*dist.adjacents(0).begin()).second);
const std::vector<std::vector<T>> alpha = calc_lkh_alpha(dist);
std::vector<std::tuple<int, int, T>> adjacent_edges;
std::vector<std::tuple<T, T, int>> candidates;
for (int i = 0; i < dist.n(); ++i) {
candidates.clear();
for (auto [j, d] : dist.adjacents(i)) {
if (i != j) candidates.emplace_back(alpha.at(i).at(j), d, j);
}
const int final_sz = std::min<int>(sz, candidates.size());
std::nth_element(candidates.begin(), candidates.begin() + final_sz, candidates.end());
candidates.resize(final_sz);
std::sort(candidates.begin(), candidates.end(),
[&](const auto &l, const auto &r) { return std::get<1>(l) < std::get<1>(r); });
for (auto [alpha, dij, j] : candidates) adjacent_edges.emplace_back(i, j, dij);
}
return csr_distance_matrix(adjacent_edges, dist.n());
}
#include <algorithm>
#include <array>
#include <random>
#include <vector>
template <class DistanceMatrix, class Adjacents> struct SymmetricTSP {
DistanceMatrix dist;
Adjacents adjacents;
using T = decltype((*dist.adjacents(0).begin()).second);
struct Solution {
T cost;
std::vector<int> path;
template <class OStream> friend OStream &operator<<(OStream &os, const Solution &x) {
os << "[cost=" << x.cost << ", path=(";
for (int i : x.path) os << i << ",";
return os << x.path.front() << ")]";
}
};
T eval(const Solution &sol) const {
T ret = T();
int now = sol.path.back();
for (int nxt : sol.path) ret += dist(now, nxt), now = nxt;
return ret;
}
SymmetricTSP(const DistanceMatrix &distance_matrix, const Adjacents &adjacents)
: dist(distance_matrix), adjacents(adjacents) {}
Solution nearest_neighbor(int init) const {
if (n() == 0) return {T(), {}};
int now = init;
std::vector<int> ret{now}, alive(n(), 1);
T len = T();
ret.reserve(n());
alive.at(now) = 0;
while (int(ret.size()) < n()) {
int nxt = -1;
for (int i = 0; i < n(); ++i) {
if (alive.at(i) and (nxt < 0 or dist(now, i) < dist(now, nxt))) nxt = i;
}
ret.push_back(nxt);
alive.at(nxt) = 0;
len += dist(now, nxt);
now = nxt;
}
len += dist(ret.back(), ret.front());
return Solution{len, ret};
}
void two_opt(Solution &sol) const {
static std::vector<int> v_to_i;
v_to_i.resize(n());
for (int i = 0; i < n(); ++i) v_to_i.at(sol.path.at(i)) = i;
while (true) {
bool updated = false;
for (int i = 0; i < n() and !updated; ++i) {
const int u = sol.path.at(i), nxtu = sol.path.at(modn(i + 1));
const T dunxtu = dist(u, nxtu);
for (auto [v, duv] : adjacents(u)) {
if (duv >= dunxtu) break;
int j = v_to_i.at(v), nxtv = sol.path.at(modn(j + 1));
T diff = duv + dist(nxtu, nxtv) - dunxtu - dist(v, nxtv);
if (diff < 0) {
sol.cost += diff;
int l, r;
if (modn(j - i) < modn(i - j)) {
l = modn(i + 1), r = j;
} else {
l = modn(j + 1), r = i;
}
while (l != r) {
std::swap(sol.path.at(l), sol.path.at(r));
v_to_i.at(sol.path.at(l)) = l;
v_to_i.at(sol.path.at(r)) = r;
l = modn(l + 1);
if (l == r) break;
r = modn(r - 1);
}
updated = true;
break;
}
}
if (updated) break;
for (auto [nxtv, dnxtunxtv] : adjacents(nxtu)) {
if (dnxtunxtv >= dunxtu) break;
int j = modn(v_to_i.at(nxtv) - 1), v = sol.path.at(j);
T diff = dist(u, v) + dnxtunxtv - dunxtu - dist(v, nxtv);
if (diff < 0) {
sol.cost += diff;
int l, r;
if (modn(j - i) < modn(i - j)) {
l = modn(i + 1), r = j;
} else {
l = modn(j + 1), r = i;
}
while (l != r) {
std::swap(sol.path.at(l), sol.path.at(r));
v_to_i.at(sol.path.at(l)) = l;
v_to_i.at(sol.path.at(r)) = r;
l = modn(l + 1);
if (l == r) break;
r = modn(r - 1);
}
updated = true;
break;
}
}
}
if (!updated) break;
}
}
bool three_opt(Solution &sol) const {
static std::vector<int> v_to_i;
v_to_i.resize(n());
for (int i = 0; i < n(); ++i) v_to_i.at(sol.path.at(i)) = i;
auto check_uvw_order = [](int u, int v, int w) {
int i = v_to_i.at(u);
int j = v_to_i.at(v);
int k = v_to_i.at(w);
if (i < j and j < k) return true;
if (j < k and k < i) return true;
if (k < i and i < j) return true;
return false;
};
auto rev = [&](const int u, const int v) -> void {
int l = v_to_i.at(u), r = v_to_i.at(v);
while (l != r) {
std::swap(sol.path.at(l), sol.path.at(r));
l = modn(l + 1);
if (l == r) break;
r = modn(r - 1);
}
};
static int i = 0;
for (int nseen = 0; nseen < n(); ++nseen, i = modn(i + 1)) {
const int u = sol.path.at(modn(i - 1)), nxtu = sol.path.at(i);
const T dunxtu = dist(u, nxtu);
for (const auto &[nxtv, dunxtv] : adjacents(u)) {
if (dunxtv >= dunxtu) break;
const int v = sol.path.at(modn(v_to_i.at(nxtv) - 1));
const T dvnxtv = dist(v, nxtv);
for (const auto &[nxtw, dvnxtw] : adjacents(v)) {
if (nxtw == nxtv or nxtw == nxtu) continue;
if (dunxtv + dvnxtw >= dunxtu + dvnxtv) break;
const int w = sol.path.at(modn(v_to_i.at(nxtw) - 1));
if (!check_uvw_order(u, v, w)) continue;
const T current = dunxtu + dvnxtv + dist(w, nxtw);
if (T diff = dunxtv + dist(w, nxtu) + dvnxtw - current; diff < T()) {
sol.cost += diff;
rev(nxtu, v);
rev(nxtv, w);
rev(nxtw, u);
return true;
}
}
for (const auto &[w, dvw] : adjacents(v)) {
if (dunxtv + dvw >= dunxtu + dvnxtv) break;
if (!check_uvw_order(u, v, w)) continue;
const int nxtw = sol.path.at(modn(v_to_i.at(w) + 1));
const T current = dunxtu + dvnxtv + dist(w, nxtw);
if (T diff = dunxtv + dvw + dist(nxtu, nxtw) - current; diff < T()) {
sol.cost += diff;
rev(nxtw, u);
rev(nxtv, w);
return true;
}
}
}
for (const auto &[nxtv, dnxtunxtv] : adjacents(nxtu)) {
if (dnxtunxtv >= dunxtu) break;
const int v = sol.path.at(modn(v_to_i.at(nxtv) - 1));
const T dvnxtv = dist(v, nxtv);
for (const auto &[nxtw, dvnxtw] : adjacents(v)) {
const int w = sol.path.at(modn(v_to_i.at(nxtw) - 1));
if (dnxtunxtv + dvnxtw >= dunxtu + dvnxtv) break;
if (!check_uvw_order(u, v, w)) continue;
const T current = dunxtu + dvnxtv + dist(w, nxtw);
if (T diff = dist(u, w) + dnxtunxtv + dvnxtw - current; diff < T()) {
sol.cost += diff;
rev(nxtu, v);
rev(nxtw, u);
return true;
}
}
}
for (const auto &[v, duv] : adjacents(u)) {
if (duv >= dunxtu) break;
const int nxtv = sol.path.at(modn(v_to_i.at(v) + 1));
const T dvnxtv = dist(v, nxtv);
for (const auto &[nxtw, dnxtvnxtw] : adjacents(nxtv)) {
const int w = sol.path.at(modn(v_to_i.at(nxtw) - 1));
if (duv + dnxtvnxtw >= dunxtu + dvnxtv) break;
if (!check_uvw_order(u, v, w)) continue;
const T current = dunxtu + dvnxtv + dist(w, nxtw);
if (T diff = duv + dist(nxtu, w) + dnxtvnxtw - current; diff < T()) {
sol.cost += diff;
rev(nxtu, v);
rev(nxtv, w);
return true;
}
}
}
}
return false;
}
template <class Rng> bool double_bridge(Solution &sol, Rng &rng) const {
if (n() < 8) return false;
std::vector<int> &p = sol.path;
int rand_rot = std::uniform_int_distribution<int>(0, n() - 1)(rng);
std::rotate(p.begin(), p.begin() + rand_rot, p.end());
static std::array<int, 3> arr;
for (int &y : arr) y = std::uniform_int_distribution<int>(2, n() - 6)(rng);
std::sort(arr.begin(), arr.end());
const int i = arr.at(0), j = arr.at(1) + 2, k = arr.at(2) + 4;
static std::array<T, 2> diffs;
for (int d = 0; d < 2; ++d) {
int u = p.at(n() - 1), nxtu = p.at(0);
int v = p.at(i - 1), nxtv = p.at(i);
int w = p.at(j - 1), nxtw = p.at(j);
int x = p.at(k - 1), nxtx = p.at(k);
diffs.at(d) = dist(u, nxtu) + dist(v, nxtv) + dist(w, nxtw) + dist(x, nxtx);
if (d == 1) break;
std::reverse(p.begin(), p.begin() + i);
std::reverse(p.begin() + i, p.begin() + j);
std::reverse(p.begin() + j, p.begin() + k);
std::reverse(p.begin() + k, p.end());
}
sol.cost += diffs.at(1) - diffs.at(0);
return true;
}
int n() const noexcept { return dist.n(); }
int modn(int x) const noexcept {
if (x < 0) return x + n();
if (x >= n()) return x - n();
return x;
}
};
template <class T> class dense_distance_matrix {
int _n;
std::vector<T> _d;
public:
dense_distance_matrix(const std::vector<std::vector<T>> &distance_vecvec)
: _n(distance_vecvec.size()) {
_d.reserve(n() * n());
for (const auto &vec : distance_vecvec) _d.insert(end(_d), begin(vec), end(vec));
}
template <class U> void apply_pi(const std::vector<U> &pi) {
for (int i = 0; i < n(); ++i) {
for (int j = 0; j < n(); ++j) _d.at(i * n() + j) += pi.at(i) + pi.at(j);
}
}
int n() const noexcept { return _n; }
T dist(int s, int t) const { return _d.at(s * n() + t); }
T operator()(int s, int t) const { return dist(s, t); }
struct adjacents_sequence {
const dense_distance_matrix *ptr;
int from;
struct iterator {
const dense_distance_matrix *ptr;
int from;
int to;
iterator operator++() { return {ptr, from, to++}; }
std::pair<int, T> operator*() const { return {to, ptr->dist(from, to)}; }
bool operator!=(const iterator &rhs) const {
return to != rhs.to or ptr != rhs.ptr or from != rhs.from;
}
};
iterator begin() const { return iterator{ptr, from, 0}; }
iterator end() const { return iterator{ptr, from, ptr->n()}; }
};
adjacents_sequence adjacents(int from) const { return {this, from}; }
};
struct Solver {
static constexpr int N = 100, M = 8;
static constexpr int alpha = 5;
static constexpr int UB = 1000;
std::vector<int> X, Y;
std::vector<int> C, D;
std::vector<std::vector<long long>> direct_distances;
int calc_direct_dist(int i, int j) const {
int dx = X.at(i) - X.at(j);
int dy = Y.at(i) - Y.at(j);
return (dx * dx + dy * dy) * (alpha * alpha);
}
int calc_s2s_dist(int p, int q) const {
int dx = C.at(p) - C.at(q);
int dy = D.at(p) - D.at(q);
return (dx * dx + dy * dy);
}
int calc_p2s_dist(int i, int p) const {
int dx = X.at(i) - C.at(p);
int dy = Y.at(i) - D.at(p);
return (dx * dx + dy * dy) * alpha;
}
using Matrix = dense_distance_matrix<long long>;
using TSP = SymmetricTSP<Matrix, csr_distance_matrix<long long>>;
void three_opt(const TSP &tsp, TSP::Solution &sol) {
do {
tsp.two_opt(sol);
} while (tsp.three_opt(sol)); // three_opt() は一度 3-opt による改善に成功した時点で return
}
TSP::Solution sol;
Solver(const std::vector<int> &a, const std::vector<int> &b) : X(a), Y(b), C(M), D(M) {
direct_distances.assign(N, std::vector<long long>(N));
for (int i = 0; i < N; ++i) {
direct_distances.at(i).at(i) = 0;
for (int j = i + 1; j < N; ++j) {
direct_distances.at(i).at(j) = direct_distances.at(j).at(i) = calc_direct_dist(i, j);
}
}
for (int k = 0; k < N; ++k) {
for (int i = 0; i < N; ++i) {
for (int j = 0; j < N; ++j) {
direct_distances.at(i).at(j) = std::min(
direct_distances.at(i).at(j), direct_distances.at(i).at(k) + direct_distances.at(k).at(j));
}
}
}
for (int i = 0; i < M; ++i) {
C.at(i) = rand_int() % (UB + 1);
D.at(i) = rand_int() % (UB + 1);
}
auto best_mat = gen_best_mat();
csr_distance_matrix<long long> adj = build_adjacent_info(best_mat, 30);
auto tsp = SymmetricTSP(best_mat, adj);
sol = tsp.nearest_neighbor(0);
dbg(sol.cost);
three_opt(tsp, sol);
dbg(sol.cost);
}
Matrix gen_best_mat() const {
auto ret = direct_distances;
std::vector pqwf(M, std::vector<int>(M));
for (int p = 0; p < M; ++p) {
for (int q = 0; q < M; ++q) {
pqwf.at(p).at(q) = calc_s2s_dist(p, q);
}
}
for (int k = 0; k < M; ++k) {
for (int p = 0; p < M; ++p) {
for (int q = 0; q < M; ++q) {
pqwf.at(p).at(q) = std::min(pqwf.at(p).at(q), pqwf.at(p).at(k) + pqwf.at(k).at(q));
}
}
}
for (int i = 0; i < N; ++i) {
for (int j = 0; j < i; ++j) {
ret.at(i).at(j) = calc_direct_dist(i, j);
for (int p = 0; p < M; ++p) {
for (int q = 0; q < M; ++q) {
ret.at(i).at(j) = std::min<int>(
ret.at(i).at(j), calc_p2s_dist(i, p) + pqwf.at(p).at(q) + calc_p2s_dist(j, q));
}
}
ret.at(j).at(i) = ret.at(i).at(j);
assert(ret.at(i).at(j) >= 0);
}
}
return Matrix(ret);
}
void step(int m, int dmax) {
const int dx = rand_int() % (dmax * 2 + 1) - dmax;
const int dy = rand_int() % (dmax * 2 + 1) - dmax;
C.at(m) += dx;
D.at(m) += dy;
auto tmpsol = sol;
auto best_mat = gen_best_mat();
csr_distance_matrix<long long> adj = build_adjacent_info(best_mat, 30);
const auto tsp = SymmetricTSP(best_mat, adj);
tmpsol.cost = tsp.eval(tmpsol);
tsp.two_opt(tmpsol);
if (tmpsol.cost < sol.cost) {
dbg(tmpsol.cost);
sol = tmpsol;
} else {
C.at(m) -= dx;
D.at(m) -= dy;
}
}
void finalize() {
auto best_mat = gen_best_mat();
csr_distance_matrix<long long> adj = build_adjacent_info(best_mat, 30);
const auto tsp = SymmetricTSP(best_mat, adj);
three_opt(tsp, sol);
}
void exp_step() {
const int m = rand_int() % M;
const int cm = C.at(m), dm = D.at(m);
int dx = 0, dy = 0;
while (!dx and !dy) {
dx = rand_int() % 31 - 15;
dy = rand_int() % 31 - 15;
}
bool init = true;
while (true) {
C.at(m) += dx;
D.at(m) += dy;
auto tmpsol = sol;
auto best_mat = gen_best_mat();
csr_distance_matrix<long long> adj = build_adjacent_info(best_mat, 30);
const auto tsp = SymmetricTSP(best_mat, adj);
tmpsol.cost = tsp.eval(tmpsol);
tsp.two_opt(tmpsol);
if (tmpsol.cost < sol.cost) {
dbg(tmpsol.cost);
sol = tmpsol;
if (init) {
init = false;
} else {
dx *= 2;
dy *= 2;
}
} else {
C.at(m) -= dx;
D.at(m) -= dy;
dbg(std::make_tuple(m, dx, dy));
break;
}
}
}
int score() const { return round(1e9 / (1000 + sqrt(sol.cost))); }
std::vector<std::pair<int, int>> dump_solution() const {
shortest_path<long long> graph(N + M);
for (int i = 0; i < N; ++i) {
for (int j = i + 1; j < N; ++j) graph.add_bi_edge(i, j, calc_direct_dist(i, j));
for (int p = 0; p < M; ++p) graph.add_bi_edge(i, N + p, calc_p2s_dist(i, p));
}
for (int p = 0; p < M; ++p) {
for (int q = p + 1; q < M; ++q) graph.add_bi_edge(N + p, N + q, calc_s2s_dist(p, q));
}
auto path = sol.path;
std::rotate(path.begin(), std::find(path.begin(), path.end(), 0), path.end());
assert(path.front() == 0);
path.push_back(0);
dbg(path);
std::vector<std::pair<int, int>> ret;
ret.emplace_back(1, 0);
for (int c = 1; c < (int)path.size(); ++c) {
int prv = path.at(c - 1), cur = path.at(c);
graph.solve(prv, cur);
auto p = graph.retrieve_path(cur);
for (int d = 1; d < (int)p.size(); ++d) {
int v = p.at(d);
if (v < N) ret.emplace_back(1, v);
else ret.emplace_back(2, v - N);
}
}
return ret;
}
std::string build_dump_str() const {
std::string ret;
for (int p = 0; p < M; ++p) ret += std::to_string(C.at(p)) + " " + std::to_string(D.at(p)) + "\n";
auto vec = dump_solution();
ret += std::to_string(vec.size()) + "\n";
for (auto [k, v] : vec) {
ret += std::to_string(k) + " " + std::to_string(v + 1) + "\n";
}
return ret;
}
};
using namespace std;
using lint = long long;
using pint = std::pair<int, int>;
using plint = std::pair<lint, lint>;
struct fast_ios {
fast_ios() {
std::cin.tie(nullptr), std::ios::sync_with_stdio(false), std::cout << std::fixed << std::setprecision(20);
};
} fast_ios_;
int main(int argc, char *argv[]) {
int X = 0;
if (argc >= 2) { X = std::stoi(argv[1]); }
int N, M;
cin >> N >> M;
vector<int> A(N), B(N);
REP(i, N) cin >> A.at(i) >> B.at(i);
dbg(make_tuple(N, M, A, B));
dbg(A);
dbg(B);
Solver solver(A, B);
for (int d = 350; d > 0; d -= 8) {
for (int m = 0; m < M; ++m) solver.step(m, d);
}
solver.finalize();
dbg(solver.sol.cost);
dbg(solver.score());
// dump_onlinejudge("solution");
auto sol = solver.dump_solution();
dbg(sol);
dump_onlinejudge(solver.build_dump_str());
jdump("score", solver.score());
}