結果
| 問題 | No.1777 万華鏡美術館 |
| ユーザー |
👑  emthrm
|
| 提出日時 | 2021-12-06 16:26:37 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 47 ms / 3,153 ms |
| コード長 | 18,385 bytes |
| コンパイル時間 | 3,829 ms |
| コンパイル使用メモリ | 266,804 KB |
| 実行使用メモリ | 7,936 KB |
| 最終ジャッジ日時 | 2024-07-07 20:21:48 |
| 合計ジャッジ時間 | 3,812 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,812 KB |
| testcase_01 | AC | 2 ms
6,940 KB |
| testcase_02 | AC | 2 ms
6,940 KB |
| testcase_03 | AC | 3 ms
6,944 KB |
| testcase_04 | AC | 34 ms
6,940 KB |
| testcase_05 | AC | 11 ms
6,940 KB |
| testcase_06 | AC | 14 ms
6,940 KB |
| testcase_07 | AC | 16 ms
6,940 KB |
| testcase_08 | AC | 31 ms
6,944 KB |
| testcase_09 | AC | 23 ms
6,940 KB |
| testcase_10 | AC | 2 ms
6,940 KB |
| testcase_11 | AC | 47 ms
7,936 KB |
| testcase_12 | AC | 2 ms
6,944 KB |
ソースコード
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
// constexpr double EPS = 1e-8;
constexpr int MOD = 1000000007;
// constexpr int MOD = 998244353;
constexpr int DY[]{1, 0, -1, 0}, DX[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1}, DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
IOSetup() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
std::cout << fixed << setprecision(20);
}
} iosetup;
// https://github.com/togatoga/togasat
#ifndef TOGASAT_HPP
#define TOGASAT_HPP
/************************************************************
MiniSat -- Copyright (c) 2003-2006, Niklas Een, Niklas Sorensson
Copyright (c) 2007-2010 Niklas Sorensson
Permission is hereby granted, free of charge, to any person obtaining a
copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:
The above copyright notice and this permission notice shall be included
in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
************************************************************/
#include <assert.h>
#include <math.h>
#include <stdio.h>
#include <algorithm>
#include <fstream>
#include <iostream>
#include <list>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <vector>
#include <unordered_map>
#include <unordered_set>
// SAT Solver
// CDCL Solver
// Author togatoga
// https://github.com/togatoga/togasat
namespace togasat {
using Var = int;
using CRef = int;
using lbool = int;
const CRef CRef_Undef = -1;
class Solver {
private:
const lbool l_True = 0;
const lbool l_False = 1;
const lbool l_Undef = 2;
const int var_Undef = -1;
// Literal
struct Lit {
int x;
inline bool operator==(Lit p) const { return x == p.x; }
inline bool operator!=(Lit p) const { return x != p.x; }
inline bool operator<(Lit p) const { return x < p.x; }
inline Lit operator~() {
Lit q;
q.x = x ^ 1;
return q;
}
};
inline Lit mkLit(Var var, bool sign) {
Lit p;
p.x = var + var + sign;
return p;
};
inline bool sign(Lit p) const { return p.x & 1; }
inline int var(Lit p) const { return p.x >> 1; }
inline int toInt(Var v) { return v; }
inline int toInt(Lit p) { return p.x; }
inline Lit toLit(int x) {
Lit p;
p.x = x;
return p;
}
const Lit lit_Undef = {-2};
const Lit lit_Error = {-1};
// lifted boolean
// VarData
struct VarData {
CRef reason;
int level;
};
inline VarData mkVarData(CRef cr, int l) {
VarData d = {cr, l};
return d;
}
// Watcher
struct Watcher {
CRef cref;
Lit blocker;
Watcher() {}
Watcher(CRef cr, Lit p) : cref(cr), blocker(p) {}
bool operator==(const Watcher &w) const { return cref == w.cref; }
bool operator!=(const Watcher &w) const { return cref != w.cref; }
};
// Clause
class Clause {
public:
struct {
bool learnt;
int size;
} header;
std::vector<Lit> data; //(x1 v x2 v not x3)
Clause() {}
Clause(const std::vector<Lit> &ps, bool learnt) {
header.learnt = learnt;
header.size = ps.size();
// data = move(ps);
data.resize(header.size);
for (int i = 0; i < ps.size(); i++) {
data[i] = ps[i];
// //data.emplace_back(ps[i]);
}
}
int size() const { return header.size; }
bool learnt() const { return header.learnt; }
Lit &operator[](int i) { return data[i]; }
Lit operator[](int i) const { return data[i]; }
};
CRef allocClause(std::vector<Lit> &ps, bool learnt = false) {
static CRef res = 0;
ca[res] = std::move(Clause(ps, learnt));
return res++;
}
Var newVar(bool sign = true, bool dvar = true) {
int v = nVars();
assigns.emplace_back(l_Undef);
vardata.emplace_back(mkVarData(CRef_Undef, 0));
activity.emplace_back(0.0);
seen.push_back(false);
polarity.push_back(sign);
decision.push_back(0);
setDecisionVar(v, dvar);
return v;
}
bool addClause_(std::vector<Lit> &ps) {
// std::sort(ps.begin(), ps.end());
// empty clause
if (ps.size() == 0) {
return false;
} else if (ps.size() == 1) {
uncheckedEnqueue(ps[0]);
} else {
CRef cr = allocClause(ps, false);
// clauses.insert(cr);
attachClause(cr);
}
return true;
}
void attachClause(CRef cr) {
const Clause &c = ca[cr];
assert(c.size() > 1);
watches[(~c[0]).x].emplace_back(Watcher(cr, c[1]));
watches[(~c[1]).x].emplace_back(Watcher(cr, c[0]));
}
// Input
void readClause(const std::string &line, std::vector<Lit> &lits) {
lits.clear();
int parsed_lit, var;
parsed_lit = var = 0;
bool neg = false;
std::stringstream ss(line);
while (ss) {
int val;
ss >> val;
if (val == 0) break;
var = abs(val) - 1;
while (var >= nVars()) {
newVar();
}
lits.emplace_back(val > 0 ? mkLit(var, false) : mkLit(var, true));
}
}
std::unordered_map<CRef, Clause> ca; // store clauses
std::unordered_set<CRef> clauses; // original problem;
std::unordered_set<CRef> learnts;
std::unordered_map<int, std::vector<Watcher>> watches;
std::vector<VarData> vardata; // store reason and level for each variable
std::vector<bool> polarity; // The preferred polarity of each variable
std::vector<bool> decision;
std::vector<bool> seen;
// Todo
int qhead;
std::vector<Lit> trail;
std::vector<int> trail_lim;
// Todo rename(not heap)
std::set<std::pair<double, Var>> order_heap;
std::vector<double> activity;
double var_inc;
std::vector<Lit> model;
std::vector<Lit> conflict;
int nVars() const { return vardata.size(); }
int decisionLevel() const { return trail_lim.size(); }
void newDecisionLevel() { trail_lim.emplace_back(trail.size()); }
inline CRef reason(Var x) const { return vardata[x].reason; }
inline int level(Var x) const { return vardata[x].level; }
inline void varBumpActivity(Var v) {
std::pair<double, Var> p = std::make_pair(activity[v], v);
activity[v] += var_inc;
if (order_heap.erase(p) == 1) {
order_heap.emplace(std::make_pair(activity[v], v));
}
if (activity[v] > 1e100) {
// Rescale
std::set<std::pair<double, Var>> tmp_order;
tmp_order = std::move(order_heap);
order_heap.clear();
for (int i = 0; i < nVars(); i++) {
activity[i] *= 1e-100;
}
for (auto &val : tmp_order) {
order_heap.emplace(std::make_pair(activity[val.second], val.second));
}
var_inc *= 1e-100;
}
}
bool satisfied(const Clause &c) const {
for (int i = 0; i < c.size(); i++) {
if (value(c[i]) == l_True) {
return true;
}
}
return false;
}
lbool value(Var p) const { return assigns[p]; }
lbool value(Lit p) const {
if (assigns[var(p)] == l_Undef) {
return l_Undef;
}
return assigns[var(p)] ^ sign(p);
}
void setDecisionVar(Var v, bool b) {
decision[v] = b;
order_heap.emplace(std::make_pair(0.0, v));
}
void uncheckedEnqueue(Lit p, CRef from = CRef_Undef) {
assert(value(p) == l_Undef);
assigns[var(p)] = sign(p);
vardata[var(p)] = std::move(mkVarData(from, decisionLevel()));
trail.emplace_back(p);
}
// decision
Lit pickBranchLit() {
Var next = var_Undef;
while (next == var_Undef or value(next) != l_Undef) {
if (order_heap.empty()) {
next = var_Undef;
break;
} else {
auto p = *order_heap.rbegin();
next = p.second;
order_heap.erase(p);
}
}
return next == var_Undef ? lit_Undef : mkLit(next, polarity[next]);
}
// clause learning
void analyze(CRef confl, std::vector<Lit> &out_learnt, int &out_btlevel) {
int pathC = 0;
Lit p = lit_Undef;
int index = trail.size() - 1;
out_learnt.emplace_back(mkLit(0, false));
do {
assert(confl != CRef_Undef);
Clause &c = ca[confl];
for (int j = (p == lit_Undef) ? 0 : 1; j < c.size(); j++) {
Lit q = c[j];
if (not seen[var(q)] and level(var(q)) > 0) {
varBumpActivity(var(q));
seen[var(q)] = 1;
if (level(var(q)) >= decisionLevel()) {
pathC++;
} else {
out_learnt.emplace_back(q);
}
}
}
while (not seen[var(trail[index--])])
;
p = trail[index + 1];
confl = reason(var(p));
seen[var(p)] = 0;
pathC--;
} while (pathC > 0);
out_learnt[0] = ~p;
// unit clause
if (out_learnt.size() == 1) {
out_btlevel = 0;
} else {
int max_i = 1;
for (int i = 2; i < out_learnt.size(); i++) {
if (level(var(out_learnt[i])) > level(var(out_learnt[max_i]))) {
max_i = i;
}
}
Lit p = out_learnt[max_i];
out_learnt[max_i] = out_learnt[1];
out_learnt[1] = p;
out_btlevel = level(var(p));
}
for (int i = 0; i < out_learnt.size(); i++) {
seen[var(out_learnt[i])] = false;
}
}
// backtrack
void cancelUntil(int level) {
if (decisionLevel() > level) {
for (int c = trail.size() - 1; c >= trail_lim[level]; c--) {
Var x = var(trail[c]);
assigns[x] = l_Undef;
polarity[x] = sign(trail[c]);
order_heap.emplace(std::make_pair(activity[x], x));
}
qhead = trail_lim[level];
trail.erase(trail.end() - (trail.size() - trail_lim[level]), trail.end());
trail_lim.erase(trail_lim.end() - (trail_lim.size() - level),
trail_lim.end());
}
}
CRef propagate() {
CRef confl = CRef_Undef;
int num_props = 0;
while (qhead < trail.size()) {
Lit p = trail[qhead++]; // 'p' is enqueued fact to propagate.
std::vector<Watcher> &ws = watches[p.x];
std::vector<Watcher>::iterator i, j, end;
num_props++;
for (i = j = ws.begin(), end = i + ws.size(); i != end;) {
// Try to avoid inspecting the clause:
Lit blocker = i->blocker;
if (value(blocker) == l_True) {
*j++ = *i++;
continue;
}
CRef cr = i->cref;
Clause &c = ca[cr];
Lit false_lit = ~p;
if (c[0] == false_lit) c[0] = c[1], c[1] = false_lit;
assert(c[1] == false_lit);
i++;
Lit first = c[0];
Watcher w = Watcher(cr, first);
if (first != blocker && value(first) == l_True) {
*j++ = w;
continue;
}
// Look for new watch:
for (int k = 2; k < c.size(); k++)
if (value(c[k]) != l_False) {
c[1] = c[k];
c[k] = false_lit;
watches[(~c[1]).x].emplace_back(w);
goto NextClause;
}
*j++ = w;
if (value(first) == l_False) { // conflict
confl = cr;
qhead = trail.size();
while (i < end) *j++ = *i++;
} else {
uncheckedEnqueue(first, cr);
}
NextClause:;
}
int size = i - j;
ws.erase(ws.end() - size, ws.end());
}
return confl;
}
static double luby(double y, int x) {
// Find the finite subsequence that contains index 'x', and the
// size of that subsequence:
int size, seq;
for (size = 1, seq = 0; size < x + 1; seq++, size = 2 * size + 1)
;
while (size - 1 != x) {
size = (size - 1) >> 1;
seq--;
x = x % size;
}
return pow(y, seq);
}
lbool search(int nof_conflicts) {
int backtrack_level;
std::vector<Lit> learnt_clause;
learnt_clause.emplace_back(mkLit(-1, false));
int conflictC = 0;
while (true) {
CRef confl = propagate();
if (confl != CRef_Undef) {
// CONFLICT
conflictC++;
if (decisionLevel() == 0) return l_False;
learnt_clause.clear();
analyze(confl, learnt_clause, backtrack_level);
cancelUntil(backtrack_level);
if (learnt_clause.size() == 1) {
uncheckedEnqueue(learnt_clause[0]);
} else {
CRef cr = allocClause(learnt_clause, true);
// learnts.insert(cr);
attachClause(cr);
uncheckedEnqueue(learnt_clause[0], cr);
}
// varDecay
var_inc *= 1.05;
} else {
// NO CONFLICT
if ((nof_conflicts >= 0 and conflictC >= nof_conflicts)) {
cancelUntil(0);
return l_Undef;
}
Lit next = pickBranchLit();
if (next == lit_Undef) {
return l_True;
}
newDecisionLevel();
uncheckedEnqueue(next);
}
}
};
public:
std::vector<lbool> assigns; // The current assignments (ex assigns[0] = 0 ->
// X1 = True, assigns[1] = 1 -> X2 = False)
lbool answer; // SATISFIABLE 0 UNSATISFIABLE 1 UNKNOWN 2
Solver() { qhead = 0; }
void parseDimacsProblem(std::string problem_name) {
std::vector<Lit> lits;
int vars = 0;
int clauses = 0;
std::string line;
std::ifstream ifs(problem_name, std::ios_base::in);
while (ifs.good()) {
getline(ifs, line);
if (line.size() > 0) {
if (line[0] == 'p') {
sscanf(line.c_str(), "p cnf %d %d", &vars, &clauses);
} else if (line[0] == 'c' or line[0] == 'p') {
continue;
} else {
readClause(line, lits);
if (lits.size() > 0) addClause_(lits);
}
}
}
ifs.close();
}
lbool solve() {
model.clear();
conflict.clear();
lbool status = l_Undef;
answer = l_Undef;
var_inc = 1.01;
int curr_restarts = 0;
double restart_inc = 2;
double restart_first = 100;
while (status == l_Undef) {
double rest_base = luby(restart_inc, curr_restarts);
status = search(rest_base * restart_first);
curr_restarts++;
}
answer = status;
return status;
};
void addClause(std::vector<int> &clause) {
std::vector<Lit> lits;
lits.resize(clause.size());
for (int i = 0; i < clause.size(); i++) {
int var = abs(clause[i]) - 1;
while (var >= nVars()) newVar();
lits[i] =
std::move((clause[i] > 0 ? mkLit(var, false) : mkLit(var, true)));
}
addClause_(lits);
}
void printAnswer() {
if (answer == 0) {
std::cout << "SAT" << std::endl;
for (int i = 0; i < assigns.size(); i++) {
if (assigns[i] == 0) {
std::cout << (i + 1) << " ";
} else {
std::cout << -(i + 1) << " ";
}
}
std::cout << "0" << std::endl;
} else {
std::cout << "UNSAT" << std::endl;
}
}
};
} // namespace togasat
#endif // TOGASAT_HPP
int main() {
int n, m; cin >> n >> m;
vector<vector<int>> graph(n);
while (m--) {
int u, v; cin >> u >> v; --u; --v;
graph[v].emplace_back(u);
}
vector<vector<int>> room{vector<int>(n)};
iota(ALL(room.back()), 0);
map<pair<int, int>, vector<int>> adj;
FOR(i, 1, n) adj[{i - 1, i}].emplace_back(0);
adj[{0, n - 1}].emplace_back(0);
vector<int> node{0};
FOR(i, 1, n) {
sort(ALL(graph[i]), greater<int>());
for (int u : graph[i]) {
const int idx = room.size();
room.emplace_back(vector<int>{i});
for (int ver = i; node.back() > u;) {
adj[{node.back(), ver}].emplace_back(idx);
ver = node.back();
node.pop_back();
room.back().emplace_back(ver);
}
adj[{u, room.back().back()}].emplace_back(idx);
adj[{u, i}].emplace_back(idx);
room.back().emplace_back(u);
}
node.emplace_back(i);
}
const int idx = room.size();
FOR(j, 1, node.size()) adj[{node[j - 1], node[j]}].emplace_back(idx);
adj[{0, node.back()}].emplace_back(idx);
room.emplace_back(node);
// for (const vector<int>& room_i : room) {
// REP(j, room_i.size()) cerr << room_i[j] << " \n"[j + 1 == room_i.size()];
// }
// for (const auto [uv, rooms] : adj) {
// const auto [u, v] = uv;
// cerr << '{' << u << ',' << v << '}';
// for (int room : rooms) cerr << ' ' << room;
// cerr << '\n';
// }
const int room_size = room.size(), x = n + room_size;
int lb = 3, ub = min(x, 10);
while (ub - lb > 1) {
const int mid = (lb + ub) / 2;
togasat::Solver solver;
REP(i, x) {
vector<int> clause(mid);
iota(ALL(clause), i * mid + 1);
solver.addClause(clause);
}
REP(i, n) REP(k, mid) {
vector<int> clause{-(i * mid + k + 1), -((i + 1) % n * mid + k + 1)};
solver.addClause(clause);
}
REP(v, n) for (int u : graph[v]) {
REP(k, mid) {
vector<int> clause{-(u * mid + k + 1), -(v * mid + k + 1)};
solver.addClause(clause);
}
}
REP(i, room_size) for (int j : room[i]) {
REP(k, mid) {
vector<int> clause{-((n + i) * mid + k + 1), -(j * mid + k + 1)};
solver.addClause(clause);
}
}
for (const auto [_, rooms] : adj) {
const int u = rooms[0], v = rooms[1];
REP(k, mid) {
vector<int> clause{-((n + u) * mid + k + 1), -((n + v) * mid + k + 1)};
solver.addClause(clause);
}
}
(solver.solve() == 0 ? ub : lb) = mid;
}
cout << ub << '\n';
return 0;
}