結果

問題 No.1744 Selfish Spies 1 (à la Princess' Perfectionism)
ユーザー hitonanode
提出日時 2021-11-14 21:05:20
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 49 ms / 5,000 ms
コード長 15,858 bytes
コンパイル時間 3,182 ms
コンパイル使用メモリ 205,728 KB
実行使用メモリ 7,424 KB
最終ジャッジ日時 2024-11-30 05:37:52
合計ジャッジ時間 5,347 ms
ジャッジサーバーID
(参考情報)
judge2 / judge4
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
other AC * 39
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#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>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#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, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each
    (begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
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 <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l
    .second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l
    .second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end());
    return vec; }
template <typename 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 <typename 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 <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']';
    return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return
    is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << '
    ,'), ...);}, tpl); return os << ')'; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os;
    }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ',';
    os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os;
    }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}';
    return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')';
    return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v
    .second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp)
    os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const 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) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET <<
    endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ <<
    COLOR_RESET << endl : cerr)
#else
#define dbg(x) (x)
#define dbgif(cond, x) 0
#endif
// Bipartite matching of undirected bipartite graph (Hopcroft-Karp)
// https://ei1333.github.io/luzhiled/snippets/graph/hopcroft-karp.html
// Comprexity: O((V + E)sqrtV)
// int solve(): enumerate maximum number of matching / return -1 (if graph is not bipartite)
struct BipartiteMatching {
int V;
std::vector<std::vector<int>> to; // Adjacency list
std::vector<int> dist; // dist[i] = (Distance from i'th node)
std::vector<int> match; // match[i] = (Partner of i'th node) or -1 (No parter)
std::vector<int> used, vv;
std::vector<int> color; // color of each node(checking bipartition): 0/1/-1(not determined)
BipartiteMatching() = default;
BipartiteMatching(int V_) : V(V_), to(V_), match(V_, -1), used(V_), color(V_, -1) {}
void add_edge(int u, int v) {
assert(u >= 0 and u < V and v >= 0 and v < V and u != v);
to[u].push_back(v);
to[v].push_back(u);
}
void _bfs() {
dist.assign(V, -1);
std::vector<int> q;
int lq = 0;
for (int i = 0; i < V; i++) {
if (!color[i] and !used[i]) q.push_back(i), dist[i] = 0;
}
while (lq < int(q.size())) {
int now = q[lq++];
for (auto nxt : to[now]) {
int c = match[nxt];
if (c >= 0 and dist[c] == -1) q.push_back(c), dist[c] = dist[now] + 1;
}
}
}
bool _dfs(int now) {
vv[now] = true;
for (auto nxt : to[now]) {
int c = match[nxt];
if (c < 0 or (!vv[c] and dist[c] == dist[now] + 1 and _dfs(c))) {
match[nxt] = now, match[now] = nxt;
used[now] = true;
return true;
}
}
return false;
}
bool _color_bfs(int root) {
color[root] = 0;
std::vector<int> q{root};
int lq = 0;
while (lq < int(q.size())) {
int now = q[lq++], c = color[now];
for (auto nxt : to[now]) {
if (color[nxt] == -1) {
color[nxt] = !c, q.push_back(nxt);
} else if (color[nxt] == c) {
return false;
}
}
}
return true;
}
int solve() {
for (int i = 0; i < V; i++) {
if (color[i] == -1 and !_color_bfs(i)) return -1;
}
int ret = 0;
while (true) {
_bfs();
vv.assign(V, false);
int flow = 0;
for (int i = 0; i < V; i++) {
if (!color[i] and !used[i] and _dfs(i)) flow++;
}
if (!flow) break;
ret += flow;
}
return ret;
}
template <class OStream> friend OStream &operator<<(OStream &os, const BipartiteMatching &bm) {
os << "{N=" << bm.V << ':';
for (int i = 0; i < bm.V; i++) {
if (bm.match[i] > i) os << '(' << i << '-' << bm.match[i] << "),";
}
return os << '}';
}
};
// Directed graph library to find strongly connected components
// 0-indexed directed graph
// Complexity: O(V + E)
struct DirectedGraphSCC {
int V; // # of Vertices
std::vector<std::vector<int>> to, from;
std::vector<int> used; // Only true/false
std::vector<int> vs;
std::vector<int> cmp;
int scc_num = -1;
DirectedGraphSCC(int V = 0) : V(V), to(V), from(V), cmp(V) {}
void _dfs(int v) {
used[v] = true;
for (auto t : to[v])
if (!used[t]) _dfs(t);
vs.push_back(v);
}
void _rdfs(int v, int k) {
used[v] = true;
cmp[v] = k;
for (auto t : from[v])
if (!used[t]) _rdfs(t, k);
}
void add_edge(int from_, int to_) {
assert(from_ >= 0 and from_ < V and to_ >= 0 and to_ < V);
to[from_].push_back(to_);
from[to_].push_back(from_);
}
// Detect strongly connected components and return # of them.
// Also, assign each vertex `v` the scc id `cmp[v]` (0-indexed)
int FindStronglyConnectedComponents() {
used.assign(V, false);
vs.clear();
for (int v = 0; v < V; v++)
if (!used[v]) _dfs(v);
used.assign(V, false);
scc_num = 0;
for (int i = (int)vs.size() - 1; i >= 0; i--)
if (!used[vs[i]]) _rdfs(vs[i], scc_num++);
return scc_num;
}
// Find and output the vertices that form a closed cycle.
// output: {v_1, ..., v_C}, where C is the length of cycle,
// {} if there's NO cycle (graph is DAG)
int _c, _init;
std::vector<int> _ret_cycle;
bool _dfs_detectcycle(int now, bool b0) {
if (now == _init and b0) return true;
for (auto nxt : to[now])
if (cmp[nxt] == _c and !used[nxt]) {
_ret_cycle.emplace_back(nxt), used[nxt] = 1;
if (_dfs_detectcycle(nxt, true)) return true;
_ret_cycle.pop_back();
}
return false;
}
std::vector<int> DetectCycle() {
int ns = FindStronglyConnectedComponents();
if (ns == V) return {};
std::vector<int> cnt(ns);
for (auto x : cmp) cnt[x]++;
_c = std::find_if(cnt.begin(), cnt.end(), [](int x) { return x > 1; }) - cnt.begin();
_init = std::find(cmp.begin(), cmp.end(), _c) - cmp.begin();
used.assign(V, false);
_ret_cycle.clear();
_dfs_detectcycle(_init, false);
return _ret_cycle;
}
// After calling `FindStronglyConnectedComponents()`, generate a new graph by uniting all vertices
// belonging to the same component(The resultant graph is DAG).
DirectedGraphSCC GenerateTopologicalGraph() {
DirectedGraphSCC newgraph(scc_num);
for (int s = 0; s < V; s++)
for (auto t : to[s]) {
if (cmp[s] != cmp[t]) newgraph.add_edge(cmp[s], cmp[t]);
}
return newgraph;
}
};
// 2-SAT solver: Find a solution for `(Ai v Aj) ^ (Ak v Al) ^ ... = true`
// - `nb_sat_vars`: Number of variables
// - Considering a graph with `2 * nb_sat_vars` vertices
// - Vertices [0, nb_sat_vars) means `Ai`
// - vertices [nb_sat_vars, 2 * nb_sat_vars) means `not Ai`
struct SATSolver : DirectedGraphSCC {
int nb_sat_vars;
std::vector<int> solution;
SATSolver(int nb_variables = 0) : DirectedGraphSCC(nb_variables * 2), nb_sat_vars(nb_variables), solution(nb_sat_vars) {}
void add_x_or_y_constraint(bool is_x_true, int x, bool is_y_true, int y) {
assert(x >= 0 and x < nb_sat_vars);
assert(y >= 0 and y < nb_sat_vars);
if (!is_x_true) x += nb_sat_vars;
if (!is_y_true) y += nb_sat_vars;
add_edge((x + nb_sat_vars) % (nb_sat_vars * 2), y);
add_edge((y + nb_sat_vars) % (nb_sat_vars * 2), x);
}
// Solve the 2-SAT problem. If no solution exists, return `false`.
// Otherwise, dump one solution to `solution` and return `true`.
bool run() {
FindStronglyConnectedComponents();
for (int i = 0; i < nb_sat_vars; i++) {
if (cmp[i] == cmp[i + nb_sat_vars]) return false;
solution[i] = cmp[i] > cmp[i + nb_sat_vars];
}
return true;
}
};
// Dulmage–Mendelsohn (DM) decomposition DM
// return: [(W+0, W-0), (W+1,W-1),...,(W+(k+1), W-(k+1))]
// : sequence of pair (left vetrices, right vertices)
// - |W+0| < |W-0| or both empty
// - |W+i| = |W-i| (i = 1, ..., k)
// - |W+(k+1)| > |W-(k+1)| or both empty
// - W is topologically sorted
// Example:
// (2, 2, [(0,0), (0,1), (1,0)]) => [([],[]),([0,],[1,]),([1,],[0,]),([],[]),]
// Complexity: O(N + (N + M) sqrt(N))
// Verified: https://yukicoder.me/problems/no/1615
std::vector<std::pair<std::vector<int>, std::vector<int>>>
dulmage_mendelsohn(int L, int R, const std::vector<std::pair<int, int>> &edges) {
for (auto p : edges) {
assert(0 <= p.first and p.first < L);
assert(0 <= p.second and p.second < R);
}
BipartiteMatching bm(L + R);
for (auto p : edges) bm.add_edge(p.first, L + p.second);
bm.solve();
DirectedGraphSCC scc(L + R);
for (auto p : edges) scc.add_edge(p.first, L + p.second);
for (int l = 0; l < L; ++l) {
if (bm.match[l] >= L) scc.add_edge(bm.match[l], l);
}
int nscc = scc.FindStronglyConnectedComponents();
std::vector<int> cmp_map(nscc, -2);
std::vector<int> vis(L + R);
std::vector<int> st;
for (int c = 0; c < 2; ++c) {
std::vector<std::vector<int>> to(L + R);
auto color = [&L](int x) { return x >= L; };
for (auto p : edges) {
int u = p.first, v = L + p.second;
if (color(u) != c) std::swap(u, v);
to[u].push_back(v);
if (bm.match[u] == v) to[v].push_back(u);
}
for (int i = 0; i < L + R; ++i) {
if (bm.match[i] >= 0 or color(i) != c or vis[i]) continue;
vis[i] = 1, st = {i};
while (!st.empty()) {
int now = st.back();
cmp_map[scc.cmp[now]] = c - 1;
st.pop_back();
for (int nxt : to[now]) {
if (!vis[nxt]) vis[nxt] = 1, st.push_back(nxt);
}
}
}
}
int nset = 1;
for (int n = 0; n < nscc; ++n) {
if (cmp_map[n] == -2) cmp_map[n] = nset++;
}
for (auto &x : cmp_map) {
if (x == -1) x = nset;
}
nset++;
std::vector<std::pair<std::vector<int>, std::vector<int>>> groups(nset);
for (int l = 0; l < L; ++l) {
if (bm.match[l] < 0) continue;
int c = cmp_map[scc.cmp[l]];
groups[c].first.push_back(l);
groups[c].second.push_back(bm.match[l] - L);
}
for (int l = 0; l < L; ++l) {
if (bm.match[l] >= 0) continue;
int c = cmp_map[scc.cmp[l]];
groups[c].first.push_back(l);
}
for (int r = 0; r < R; ++r) {
if (bm.match[L + r] >= 0) continue;
int c = cmp_map[scc.cmp[L + r]];
groups[c].second.push_back(r);
}
return groups;
}
int main() {
int N, M, L;
cin >> N >> M >> L;
vector<pint> edges(L);
for (auto &[s, t] : edges) {
cin >> s >> t;
s--, t--;
}
dbg(edges);
auto dm = dulmage_mendelsohn(N, M, edges);
dbg(dm);
set<pint> fixed;
for (auto [us, vs] : dm) {
if (us.size() == 1 and vs.size() == 1) {
fixed.emplace(us[0], vs[0]);
}
}
for (auto [s, t] : edges) {
if (fixed.count(pint(s, t))) puts("No");
else puts("Yes");
}
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0