Submission #4074186
Source Code Expand
#pragma GCC optimize ("O3")
#include "bits/stdc++.h"
using namespace std;
using ll = long long int;
#define debugos cout
#define debug(v) {printf("L%d %s > ",__LINE__,#v);debugos<<(v)<<endl;}
#define debugv(v) {printf("L%d %s > ",__LINE__,#v);for(auto e:(v)){debugos<<e<<" ";}debugos<<endl;}
#define debuga(m,w) {printf("L%d %s > ",__LINE__,#m);for(int x=0;x<(w);x++){debugos<<(m)[x]<<" ";}debugos<<endl;}
#define debugaa(m,h,w) {printf("L%d %s >\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){debugos<<(m)[y][x]<<" ";}debugos<<endl;}}
#define ALL(v) (v).begin(),(v).end()
#define repeat(cnt,l) for(auto cnt=decltype(l)();(cnt)<(l);++(cnt))
#define rrepeat(cnt,l) for(auto cnt=(l)-1;0<=(cnt);--(cnt))
#define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt))
#define diterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);--(cnt))
const ll MD = 1000000007ll; const long double PI = 3.1415926535897932384626433832795L;
inline void assert_call(bool assertion, function<void()> f) { if (!assertion) { cerr << "assertion fault:" << endl; f(); abort(); } }
template<typename T1, typename T2> inline ostream& operator <<(ostream &o, const pair<T1, T2> p) { o << '(' << p.first << ':' << p.second << ')'; return o; }
template<typename Vec> inline ostream& _ostream_vecprint(ostream& os, const Vec& a) {
os << '['; for (const auto& e : a) os << ' ' << e << ' '; os << ']'; return os;
}
template<typename T> inline ostream& operator<<(ostream& o, const vector<T>& v) { return _ostream_vecprint(o, v); }
template<typename T, size_t S> inline ostream& operator<<(ostream& o, const array<T, S>& v) { return _ostream_vecprint(o, v); }
template<typename T> inline T& chmax(T& to, const T& val) { return to = max(to, val); }
template<typename T> inline T& chmin(T& to, const T& val) { return to = min(to, val); }
void bye(string s, int code = 0) { cout << s << endl; exit(code); }
mt19937_64 randdev(8901016);
template<typename T, typename Random = decltype(randdev), typename enable_if<is_integral<T>::value>::type* = nullptr>
inline T rand(T l, T h, Random& rand = randdev) { return uniform_int_distribution<T>(l, h)(rand); }
template<typename T, typename Random = decltype(randdev), typename enable_if<is_floating_point<T>::value>::type* = nullptr>
inline T rand(T l, T h, Random& rand = randdev) { return uniform_real_distribution<T>(l, h)(rand); }
#if defined(_WIN32) || defined(_WIN64)
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#elif defined(__GNUC__)
#else
#define getchar_unlocked getchar
#define putchar_unlocked putchar
#endif
namespace {
#define isvisiblechar(c) (0x21<=(c)&&(c)<=0x7E)
class MaiScanner {
public:
template<typename T> void input_integer(T& var) noexcept {
var = 0; T sign = 1;
int cc = getchar_unlocked();
for (; cc < '0' || '9' < cc; cc = getchar_unlocked())
if (cc == '-') sign = -1;
for (; '0' <= cc && cc <= '9'; cc = getchar_unlocked())
var = (var << 3) + (var << 1) + cc - '0';
var = var * sign;
}
inline int c() noexcept { return getchar_unlocked(); }
inline MaiScanner& operator>>(int& var) noexcept { input_integer<int>(var); return *this; }
inline MaiScanner& operator>>(long long& var) noexcept { input_integer<long long>(var); return *this; }
inline MaiScanner& operator>>(string& var) {
int cc = getchar_unlocked();
for (; !isvisiblechar(cc); cc = getchar_unlocked());
for (; isvisiblechar(cc); cc = getchar_unlocked())
var.push_back(cc);
return *this;
}
template<typename IT> inline void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; }
};
class MaiPrinter {
public:
template<typename T>
void output_integer(T var) noexcept {
if (var == 0) { putchar_unlocked('0'); return; }
if (var < 0)
putchar_unlocked('-'),
var = -var;
char stack[32]; int stack_p = 0;
while (var)
stack[stack_p++] = '0' + (var % 10),
var /= 10;
while (stack_p)
putchar_unlocked(stack[--stack_p]);
}
inline MaiPrinter& operator<<(char c) noexcept { putchar_unlocked(c); return *this; }
inline MaiPrinter& operator<<(int var) noexcept { output_integer<int>(var); return *this; }
inline MaiPrinter& operator<<(long long var) noexcept { output_integer<long long>(var); return *this; }
inline MaiPrinter& operator<<(char* str_p) noexcept { while (*str_p) putchar_unlocked(*(str_p++)); return *this; }
inline MaiPrinter& operator<<(const string& str) {
const char* p = str.c_str();
const char* l = p + str.size();
while (p < l) putchar_unlocked(*p++);
return *this;
}
template<typename IT> void join(IT begin, IT end, char sep = ' ') { for (bool b = 0; begin != end; ++begin, b = 1) b ? *this << sep << *begin : *this << *begin; }
};
}
MaiScanner scanner;
MaiPrinter printer;
//
class Graph {
public:
size_t n;
vector<vector<int>> vertex_to;
Graph(size_t n = 1) :n(n), vertex_to(n) {}
inline size_t size() const { return n; }
void resize(size_t _n) { vertex_to.resize(n = _n); }
void connect(int from, int to) {
vertex_to[(size_t)from].emplace_back(to);
vertex_to[(size_t)to].emplace_back(from);
}
};
inline int bitcount(int x) {
return bitset<31>(x).count();
}
// 半分全列挙
pair<int, vector<int>> vertex_cover(const Graph& graph) {
const int n = graph.n;
const int n_A = n / 2;
const int n_B = n - n_A;
const int inf = 1e9;
// group A : i < n_A
// group B : i >= n_A
// dp[S] : S \subseteq V_A,
vector<int> ans_partial_A(1 << n_A, 0);
// Sが独立集合なら0,独立集合でないならinfとなるように初期状態を構成する.
for (int i = 0; i < n_A; ++i) {
int bit = 1 << i;
for (int j : graph.vertex_to[i])
if (j < n_A)
ans_partial_A[bit | (1 << j)] = inf; // 頂点数2
}
for (int bit = 3; bit < 1 << n_A; ++bit) {
if (bitcount(bit) <= 1) continue;
for (int i = 0; i < n_A; ++i) {
ans_partial_A[bit | (1 << i)] |= ans_partial_A[bit];
}
}
// groupA の部分集合の解を全列挙
// ここでは groupA と groupB のカットエッジの被覆は考えない.
for (int bit = 1; bit < 1 << n_A; ++bit) {
for (int i = 0; i < n_A; ++i) {
if (bit & (1 << i)) continue;
ans_partial_A[bit | (1 << i)] = min(
ans_partial_A[bit | (1 << i)],
ans_partial_A[bit] + 1
);
}
}
// dp[S] Sは独立集合ではない
vector<int8_t> not_independent_B(1 << n_B, 0);
for (int _i = 0; _i < n_B; ++_i) {
int bit = 1 << _i;
for (int j : graph.vertex_to[n_A + _i])
if (n_A <= j)
not_independent_B[bit | (1 << (j - n_A))] = 1;
}
for (int bit = 3; bit < 1 << n_B; ++bit) {
if (bitcount(bit) <= 1) continue;
for (int _i = 0; _i < n_B; ++_i) {
not_independent_B[bit | (1 << _i)] |= not_independent_B[bit];
}
}
// dp[S] Sに隣接する頂点のbit配列
vector<int> adjacent2B(1 << n_B, 0);
for (int _i = 0; _i < n_B; ++_i) {
int bit = 0;
for (int j : graph.vertex_to[n_A + _i])
if (j < n_A)
bit |= 1 << j;
adjacent2B[1 << _i] = bit;
}
for (int bit = 1; bit < 1 << n_B; ++bit) {
for (int _i = 0; _i < n_B; ++_i) {
adjacent2B[bit | (1 << _i)] |= adjacent2B[bit];
}
}
// answer
int best = inf;
pair<int,int> vtx_selection;
// groupB の部分集合を全列挙
for (int bit = 0; bit < 1 << n_B; ++bit) {
// choice_Bが頂点被覆でないなら,reject
if (not_independent_B[((1 << n_B) - 1) ^ bit]) continue;
int mask_A = (1 << n_A) - 1;
int fix_A = 0;
int adj = adjacent2B[((1 << n_B) - 1) ^ bit];
for (int i = 0; i < n_A; ++i) {
// choice_B で選んでいない頂点が,groupAと隣接するならば
if (adj & (1 << i)) {
// そのgroupAの頂点は必ず選択する.
mask_A ^= 1 << i; // 頂点jは考慮しなくてよい
++fix_A; // 必ず選択することにしたので
}
}
int score = ans_partial_A[mask_A] + bitcount(bit) + fix_A;
if (score < best) {
best = score;
vtx_selection.first = mask_A;
vtx_selection.second = bit;
}
}
// 選んだ頂点の復元
vector<int> selection;
for (int i = 0; i < n_B; ++i) {
if (vtx_selection.second & (1 << i))
selection.push_back(n_A + i);
}
for (int i = 0; i < n_A; ++i) {
if ((vtx_selection.first & (1 << i)) == 0)
selection.push_back(i);
}
{
int m = vtx_selection.first;
int curr = ans_partial_A[m];
while (m > 0) {
int bi;
for (int i = 0; i < n_A; ++i) {
if ((m & (1 << i)) == 0) continue;
int a = ans_partial_A[m ^ (1 << i)];
if (curr == a) {
bi = -1;
m ^= (1 << i);
break;
}
else if (curr - 1 == a) {
bi = i;
}
}
if (bi >= 0) {
m ^= (1 << bi);
selection.push_back(bi);
--curr;
}
}
}
sort(selection.begin(), selection.end());
selection.shrink_to_fit();
return make_pair(best, selection);
}
pair<int, vector<int>> independentSet(const Graph& graph) {
int bestScore = 0;
vector<int8_t> bestSelection;
vector<int8_t> selection(graph.size());
int initScore = 0, initRem = graph.size();
for (int i = 0; i < graph.size(); ++i) {
if (graph.vertex_to[i].empty()) {
selection[i] = 1;
++initScore;
--initRem;
continue;
}
if (graph.vertex_to[i].size() == 1 &&
selection[i] == 0) {
selection[i] = 1;
if (selection[graph.vertex_to[i][0]] == 0) {
--initRem;
selection[graph.vertex_to[i][0]] = -1;
}
++initScore;
--initRem;
continue;
}
}
vector<int> sortedIdx(graph.size());
iota(sortedIdx.begin(), sortedIdx.end(), 0);
sort(sortedIdx.begin(), sortedIdx.end(),
[&graph](int l, int r) {return graph.vertex_to[l].size() > graph.vertex_to[r].size(); });
auto dfs = [&](auto dfs, int idxx, int rem, int score) -> void {
if (idxx == graph.size()) {
if (bestScore < score) {
bestScore = score;
bestSelection = selection;
}
return;
}
int idx = sortedIdx[idxx];
if (score + rem < bestScore) return;
if (selection[idx] != 0) {
dfs(dfs, idxx + 1, rem, score);
return;
}
int cnte = 0;
for (int e : graph.vertex_to[idx])
cnte += selection[e] >= 0;
if (cnte > 1)
dfs(dfs, idxx + 1, rem, score);
selection[idx] = idx + 2;
for (int e : graph.vertex_to[idx]) {
if (selection[e] == 0) {
selection[e] = -idx - 2;
--rem;
}
}
dfs(dfs, idxx + 1, rem - 1, score + 1);
selection[idx] = 0;
for (int e : graph.vertex_to[idx]) {
if (selection[e] == -idx - 2) {
selection[e] = 0;
++rem;
}
}
return;
};
bestScore = initScore;
bestSelection = selection;
dfs(dfs, 0, initRem, initScore);
vector<int> idxs;
for (int i = 0; i < graph.size(); ++i)
if (bestSelection[i] > 0) idxs.push_back(i);
idxs.shrink_to_fit();
return make_pair(bestScore, idxs);
}
int N, M;
Graph g;
int main2() {
scanner >> N >> M;
repeat(_, 99999){
g = Graph(N);
repeat(i, M) {
int a, b;
a = rand(0, N-1);
b = rand(0, N-1);
if (a == b) {--i;continue;}
//--a; --b;
g.connect(a, b);
}
for (auto& a : g.vertex_to) {
sort(ALL(a));
a.erase(unique(ALL(a)), a.end());
}
auto ans = independentSet(g);
auto ans2 = vertex_cover(g);
//debug(ans.first);
//debug(ans2.first);
if (ans.first != N - ans2.first){
debug(ans);
debug(ans2);
repeat(i, N) {
for (auto j :g.vertex_to[i])
if (i < j) cout << i+1 << " " << j+1 << endl;
}
abort();
}
assert(ans.first == ans.second.size());
}
//printer << ans.first << '\n';
return 0;
}
int main() {
scanner >> N >> M;
g.resize(N);
repeat(i, M) {
int a, b;
scanner >> a >> b;
--a; --b;
g.connect(a, b);
}
for (auto& a : g.vertex_to) {
sort(ALL(a));
a.erase(unique(ALL(a)), a.end());
}
auto ans = independentSet(g);
// auto ans2 = vertex_cover(g);
// assert(ans.first == N - ans2.first);
// assert(ans.first == ans.second.size());
printer << ans.first << '\n';
return 0;
}
Submission Info
Submission Time |
|
Task |
G - Mixture Drug |
User |
m_buyoh |
Language |
C++14 (GCC 5.4.1) |
Score |
0 |
Code Size |
14334 Byte |
Status |
TLE |
Exec Time |
2103 ms |
Memory |
256 KB |
Judge Result
Set Name |
Sample |
All |
Score / Max Score |
0 / 0 |
0 / 600 |
Status |
|
|
Set Name |
Test Cases |
Sample |
sample_01.txt, sample_02.txt, sample_03.txt |
All |
sample_01.txt, sample_02.txt, sample_03.txt, subtask_1_1.txt, subtask_1_10.txt, subtask_1_11.txt, subtask_1_12.txt, subtask_1_13.txt, subtask_1_14.txt, subtask_1_15.txt, subtask_1_16.txt, subtask_1_17.txt, subtask_1_18.txt, subtask_1_19.txt, subtask_1_2.txt, subtask_1_20.txt, subtask_1_21.txt, subtask_1_22.txt, subtask_1_23.txt, subtask_1_24.txt, subtask_1_25.txt, subtask_1_26.txt, subtask_1_27.txt, subtask_1_28.txt, subtask_1_29.txt, subtask_1_3.txt, subtask_1_30.txt, subtask_1_31.txt, subtask_1_32.txt, subtask_1_33.txt, subtask_1_34.txt, subtask_1_35.txt, subtask_1_36.txt, subtask_1_37.txt, subtask_1_38.txt, subtask_1_39.txt, subtask_1_4.txt, subtask_1_40.txt, subtask_1_41.txt, subtask_1_42.txt, subtask_1_43.txt, subtask_1_44.txt, subtask_1_45.txt, subtask_1_46.txt, subtask_1_47.txt, subtask_1_48.txt, subtask_1_5.txt, subtask_1_6.txt, subtask_1_7.txt, subtask_1_8.txt, subtask_1_9.txt |
Case Name |
Status |
Exec Time |
Memory |
sample_01.txt |
AC |
1 ms |
256 KB |
sample_02.txt |
AC |
1 ms |
256 KB |
sample_03.txt |
AC |
1 ms |
256 KB |
subtask_1_1.txt |
AC |
1 ms |
256 KB |
subtask_1_10.txt |
AC |
67 ms |
256 KB |
subtask_1_11.txt |
AC |
1 ms |
256 KB |
subtask_1_12.txt |
AC |
209 ms |
256 KB |
subtask_1_13.txt |
AC |
1 ms |
256 KB |
subtask_1_14.txt |
AC |
1 ms |
256 KB |
subtask_1_15.txt |
AC |
1 ms |
256 KB |
subtask_1_16.txt |
AC |
1 ms |
256 KB |
subtask_1_17.txt |
AC |
1 ms |
256 KB |
subtask_1_18.txt |
AC |
2 ms |
256 KB |
subtask_1_19.txt |
AC |
1 ms |
256 KB |
subtask_1_2.txt |
AC |
1 ms |
256 KB |
subtask_1_20.txt |
AC |
1 ms |
256 KB |
subtask_1_21.txt |
AC |
1 ms |
256 KB |
subtask_1_22.txt |
AC |
1 ms |
256 KB |
subtask_1_23.txt |
AC |
1 ms |
256 KB |
subtask_1_24.txt |
AC |
4 ms |
256 KB |
subtask_1_25.txt |
AC |
1 ms |
256 KB |
subtask_1_26.txt |
TLE |
2103 ms |
256 KB |
subtask_1_27.txt |
AC |
62 ms |
256 KB |
subtask_1_28.txt |
AC |
2 ms |
256 KB |
subtask_1_29.txt |
AC |
1 ms |
256 KB |
subtask_1_3.txt |
AC |
1 ms |
256 KB |
subtask_1_30.txt |
AC |
1 ms |
256 KB |
subtask_1_31.txt |
AC |
1 ms |
256 KB |
subtask_1_32.txt |
AC |
1 ms |
256 KB |
subtask_1_33.txt |
AC |
1 ms |
256 KB |
subtask_1_34.txt |
AC |
1 ms |
256 KB |
subtask_1_35.txt |
AC |
5 ms |
256 KB |
subtask_1_36.txt |
AC |
3 ms |
256 KB |
subtask_1_37.txt |
AC |
1 ms |
256 KB |
subtask_1_38.txt |
AC |
1 ms |
256 KB |
subtask_1_39.txt |
AC |
1 ms |
256 KB |
subtask_1_4.txt |
AC |
1 ms |
256 KB |
subtask_1_40.txt |
AC |
1 ms |
256 KB |
subtask_1_41.txt |
AC |
1 ms |
256 KB |
subtask_1_42.txt |
AC |
1 ms |
256 KB |
subtask_1_43.txt |
AC |
1 ms |
256 KB |
subtask_1_44.txt |
AC |
1 ms |
256 KB |
subtask_1_45.txt |
AC |
1 ms |
256 KB |
subtask_1_46.txt |
AC |
1 ms |
256 KB |
subtask_1_47.txt |
AC |
1 ms |
256 KB |
subtask_1_48.txt |
AC |
1 ms |
256 KB |
subtask_1_5.txt |
AC |
25 ms |
256 KB |
subtask_1_6.txt |
AC |
68 ms |
256 KB |
subtask_1_7.txt |
AC |
2 ms |
256 KB |
subtask_1_8.txt |
AC |
11 ms |
256 KB |
subtask_1_9.txt |
AC |
64 ms |
256 KB |