#829804 (C++23) No.2160 みたりのDominator

• 問題: No.2160 みたりのDominator
• ユーザー: hitonanode
• 提出日時: 2023-01-02 11:50:55
• 言語: C++23 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 305 ms / 2,000 ms
• コード長: 19,106 bytes
• コンパイル時間: 2,703 ms
• コンパイル使用メモリ: 217,964 KB
• 実行使用メモリ: 57,740 KB
• 最終ジャッジ日時: 2024-11-27 00:41:22
• 合計ジャッジ時間: 13,534 ms
• ジャッジサーバーID （参考情報）: judge4 / judge3

ファイルパターン	結果
sample	AC * 3
other	AC * 93

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>
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; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
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 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 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) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif


struct Problem {
    int N1, N2, N3;
    vector<pint> edges;

    int s() const { return N1 + N2 + N3; }
    int t() const { return s() + 1; }

    pint get_v(int vid) const {
        if (vid < N1) return {0, vid};
        if (vid < N1 + N2) return {1, vid - N1};
        if (vid < N1 + N2 + N3) return {2, vid - N1 - N2};
        exit(1);
    }

    int convert_to(int did, int i) const {
        if (did == 0) return i;
        if (did == 1) return i + N1;
        if (did == 2) return i + N1 + N2;
        exit(1);
    }
};

Problem truncate(const Problem &p) {
    vector dels(3, vector<int>());
    dels.at(0).assign(p.N1, 0);
    dels.at(1).assign(p.N2, 0);
    dels.at(2).assign(p.N3, 0);

    for (auto [u, v] : p.edges) {
        if (u > v) swap(u, v);
        const auto [du, iu] = p.get_v(u);
        if (v == p.s() or v == p.t()) {
            if (v == p.s()) {
                // ++dels.at(du).front();
                // --dels.at(du).at(iu);
            } else {
                // ++dels.at(du).at(iu);
            }
        } else {
            const auto [dv, iv] = p.get_v(v);

            if (du == dv) {
                ++dels.at(du).at(min(iu, iv));
                --dels.at(du).at(max(iu, iv));
            }
        }
    }
    for (auto &v : dels) { FOR(i, 1, v.size()) v.at(i) += v.at(i - 1); }
    vector<vector<int>> alives(3);
    REP(d, 3) {
        REP(i, dels.at(d).size()) {
            if (!dels.at(d).at(i)) alives.at(d).push_back(i);
        }
    }
    Problem ret;
    ret.N1 = alives.at(0).size();
    ret.N2 = alives.at(1).size();
    ret.N3 = alives.at(2).size();
    for (auto [u, v] : p.edges) {
        if (u > v) swap(u, v);
        if (v == p.s() or v == p.t()) {
            const auto [du, iu] = p.get_v(u);
            int ju = arglb(alives.at(du), iu);
            if (v == p.s()) ret.edges.emplace_back(ret.convert_to(du, ju), ret.s());
            if (v == p.t()) ret.edges.emplace_back(ret.convert_to(du, ju), ret.t());
        } else {
            const auto [du, iu] = p.get_v(u);
            const auto [dv, iv] = p.get_v(v);
            int ju = arglb(alives.at(du), iu);
            int jv = arglb(alives.at(dv), iv);

            if (du == dv and ju == jv) continue;

            ret.edges.emplace_back(ret.convert_to(du, ju), ret.convert_to(dv, jv));
        }
    }
    ret.edges = sort_unique(ret.edges);
    return ret;
}

struct Rect {
    int xl, xr;
    int yl, yr;

    lint area() const {
        lint xw = max(0, xr - xl);
        lint yw = max(0, yr - yl);
        return xw * yw;
    }

    Rect bottom_left(int x, int y) { return Rect{xl, min(xr, x), yl, min(yr, y)}; }

    Rect top_right(int x, int y) { return Rect{max(xl, x), xr, max(yl, y), yr}; }

    template <class OStream> friend OStream &operator<<(OStream &os, const Rect &x) {
        return os << "(" << x.xl << "," << x.xr << "," << x.yl << "," << x.yr << ")";
    }
};

lint solve(const Problem &p) {
    vector<vector<int>> switch13(p.N3 + 1), switch23(p.N3 + 1);

    multiset<int> xubs, yubs;
    xubs.insert(p.N1 + 1);
    yubs.insert(p.N2 + 1);
    int xlb = 0, ylb = 0, zlb = 0, zub = 1 << 26;

    vector<pint> rectv12s;
    rectv12s.emplace_back(p.N1 + 1, p.N2 + 1);
    for (auto [u, v] : p.edges) {
        if (u > v) swap(u, v);
        const auto [du, iu] = p.get_v(u);
        if (v == p.s() or v == p.t()) {
            if (v == p.s()) {
                if (du == 0) chmax(xlb, iu + 1);
                if (du == 1) chmax(ylb, iu + 1);
                if (du == 2) chmax(zlb, iu + 1);
            } else {
                if (du == 0) xubs.insert(iu + 1);
                if (du == 1) yubs.insert(iu + 1);
                if (du == 2) chmin(zub, iu + 1);
            }
        } else {
            const auto [dv, iv] = p.get_v(v);
            assert(du != dv);
            if (du == 0 and dv == 1) {
                rectv12s.emplace_back(iu + 1, iv + 1);
            } else if (du == 0 and dv == 2) {
                switch13.at(iv).push_back(iu + 1);
                xubs.insert(iu + 1);
            } else if (du == 1 and dv == 2) {
                switch23.at(iv).push_back(iu + 1);
                yubs.insert(iu + 1);
            } else {
                // exit(1);
            }
        }
    }
    dbg(rectv12s);
    vector<Rect> rects;
    rects.push_back(Rect{0, p.N1 + 1, 0, p.N2 + 1});
    for (auto [x, y] : sort_unique(rectv12s)) {
        if (rects.empty()) continue;
        auto last = rects.back();
        rects.pop_back();
        while (rects.size() and rects.back().yl >= y) rects.pop_back();
        if (rects.size()) {
            rects.back() = rects.back().bottom_left(x, y);
            if (!rects.back().area()) rects.pop_back();
        }
        rects.push_back(last.bottom_left(x, y));
        if (!rects.back().area()) rects.pop_back();
        rects.push_back(last.top_right(x, y));
        if (!rects.back().area()) rects.pop_back();
    }
    vector<lint> area_sum{0};
    vector<int> xrs, yrs;
    for (auto r : rects) {
        auto tmp = area_sum.back() + r.area();
        area_sum.push_back(tmp);
        xrs.push_back(r.xr);
        yrs.push_back(r.yr);
    }
    dbg(make_tuple(rects));
    dbg(area_sum);

    auto calc_area_bottomleft = [&](int x, int y) -> lint {
        int i = min(arglb(xrs, x), arglb(yrs, y));
        lint ret = area_sum.at(i);
        if (i < int(rects.size())) ret += rects.at(i).bottom_left(x, y).area();
        return ret;
    };

    lint ret = 0;
    REP(z, p.N3 + 1) {
        int xub = *xubs.cbegin();
        int yub = *yubs.cbegin();
        if (z >= zlb and z <= zub and xlb < xub and ylb < yub) {
            ret += calc_area_bottomleft(xub, yub) + calc_area_bottomleft(xlb, ylb);
            ret -= calc_area_bottomleft(xub, ylb) + calc_area_bottomleft(xlb, yub);
        }

        for (int x : switch13.at(z)) {
            xubs.erase(xubs.lower_bound(x));
            chmax(xlb, x);
        }
        for (int y : switch23.at(z)) {
            yubs.erase(yubs.lower_bound(y));
            chmax(ylb, y);
        }
    }
    return ret;
}

// MaxFlow based and AtCoder Library, single class, no namespace, no private variables, compatible
// with C++11 Reference: <https://atcoder.github.io/ac-library/production/document_ja/maxflow.html>
template <class Cap> struct mf_graph {
    struct simple_queue_int {
        std::vector<int> payload;
        int pos = 0;
        void reserve(int n) { payload.reserve(n); }
        int size() const { return int(payload.size()) - pos; }
        bool empty() const { return pos == int(payload.size()); }
        void push(const int &t) { payload.push_back(t); }
        int &front() { return payload[pos]; }
        void clear() {
            payload.clear();
            pos = 0;
        }
        void pop() { pos++; }
    };

    mf_graph() : _n(0) {}
    mf_graph(int n) : _n(n), g(n) {}

    int add_edge(int from, int to, Cap cap) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        assert(0 <= cap);
        int m = int(pos.size());
        pos.push_back({from, int(g[from].size())});
        int from_id = int(g[from].size());
        int to_id = int(g[to].size());
        if (from == to) to_id++;
        g[from].push_back(_edge{to, to_id, cap});
        g[to].push_back(_edge{from, from_id, 0});
        return m;
    }

    struct edge {
        int from, to;
        Cap cap, flow;
    };

    edge get_edge(int i) {
        int m = int(pos.size());
        assert(0 <= i && i < m);
        auto _e = g[pos[i].first][pos[i].second];
        auto _re = g[_e.to][_e.rev];
        return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap};
    }
    std::vector<edge> edges() {
        int m = int(pos.size());
        std::vector<edge> result;
        for (int i = 0; i < m; i++) { result.push_back(get_edge(i)); }
        return result;
    }
    void change_edge(int i, Cap new_cap, Cap new_flow) {
        int m = int(pos.size());
        assert(0 <= i && i < m);
        assert(0 <= new_flow && new_flow <= new_cap);
        auto &_e = g[pos[i].first][pos[i].second];
        auto &_re = g[_e.to][_e.rev];
        _e.cap = new_cap - new_flow;
        _re.cap = new_flow;
    }

    std::vector<int> level, iter;
    simple_queue_int que;

    void _bfs(int s, int t) {
        std::fill(level.begin(), level.end(), -1);
        level[s] = 0;
        que.clear();
        que.push(s);
        while (!que.empty()) {
            int v = que.front();
            que.pop();
            for (auto e : g[v]) {
                if (e.cap == 0 || level[e.to] >= 0) continue;
                level[e.to] = level[v] + 1;
                if (e.to == t) return;
                que.push(e.to);
            }
        }
    }
    Cap _dfs(int v, int s, Cap up) {
        if (v == s) return up;
        Cap res = 0;
        int level_v = level[v];
        for (int &i = iter[v]; i < int(g[v].size()); i++) {
            _edge &e = g[v][i];
            if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue;
            Cap d = _dfs(e.to, s, std::min(up - res, g[e.to][e.rev].cap));
            if (d <= 0) continue;
            g[v][i].cap += d;
            g[e.to][e.rev].cap -= d;
            res += d;
            if (res == up) return res;
        }
        level[v] = _n;
        return res;
    }

    Cap flow(int s, int t) { return flow(s, t, std::numeric_limits<Cap>::max()); }
    Cap flow(int s, int t, Cap flow_limit) {
        assert(0 <= s && s < _n);
        assert(0 <= t && t < _n);
        assert(s != t);

        level.assign(_n, 0), iter.assign(_n, 0);
        que.clear();

        Cap flow = 0;
        while (flow < flow_limit) {
            _bfs(s, t);
            if (level[t] == -1) break;
            std::fill(iter.begin(), iter.end(), 0);
            Cap f = _dfs(t, s, flow_limit - flow);
            if (!f) break;
            flow += f;
        }
        return flow;
    }

    std::vector<bool> min_cut(int s) {
        std::vector<bool> visited(_n);
        simple_queue_int que;
        que.push(s);
        while (!que.empty()) {
            int p = que.front();
            que.pop();
            visited[p] = true;
            for (auto e : g[p]) {
                if (e.cap && !visited[e.to]) {
                    visited[e.to] = true;
                    que.push(e.to);
                }
            }
        }
        return visited;
    }

    void dump_graphviz(std::string filename = "maxflow") const {
        std::ofstream ss(filename + ".DOT");
        ss << "digraph{\n";
        for (int i = 0; i < _n; i++) {
            for (const auto &e : g[i]) {
                if (e.cap > 0) ss << i << "->" << e.to << "[label=" << e.cap << "];\n";
            }
        }
        ss << "}\n";
        ss.close();
        return;
    }

    int _n;
    struct _edge {
        int to, rev;
        Cap cap;
    };
    std::vector<std::pair<int, int>> pos;
    std::vector<std::vector<_edge>> g;
};


bool check_infeasible(const Problem &p) {
    const int gs = p.s(), gt = p.t();
    mf_graph<int> mf(gt + 1);

    REP(i, p.N1 - 1) mf.add_edge(i, i + 1, 1);
    REP(i, p.N2 - 1) mf.add_edge(p.N1 + i, p.N1 + i + 1, 1);
    REP(i, p.N3 - 1) mf.add_edge(p.N1 + p.N2 + i, p.N1 + p.N2 + i + 1, 1);

    if (p.N1) mf.add_edge(gs, 0, 1);
    if (p.N2) mf.add_edge(gs, p.N1, 1);
    if (p.N3) mf.add_edge(gs, p.N1 + p.N2, 1);

    if (p.N1) mf.add_edge(p.N1 - 1, gt, 1);
    if (p.N2) mf.add_edge(p.N1 + p.N2 - 1, gt, 1);
    if (p.N3) mf.add_edge(p.N1 + p.N2 + p.N3 - 1, gt, 1);

    for (auto [u, v] : p.edges) mf.add_edge(u, v, 1), mf.add_edge(v, u, 1);

    auto f = mf.flow(gs, gt, 4);
    return f == 4;
}

int main() {
    int M;
    Problem problem;
    cin >> problem.N1 >> problem.N2 >> problem.N3 >> M;
    while (M--) {
        int u, v;
        cin >> u >> v;
        --u, --v;
        if (u > v) swap(u, v);

        if (u == problem.s() and v == problem.t()) {
            puts("0");
            return 0;
        }

        problem.edges.emplace_back(u, v);
    }

    if (check_infeasible(problem)) {
        dbg("infeasible");
        puts("0");
        return 0;
    }

    problem = truncate(problem);
    cout << solve(problem) << endl;
}