Submission #70484361

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Source Code Expand

#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 <memory>
#include <numeric>
#include <optional>
#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> 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

vector<int> SubSolve(vector<vector<int>> to, vector<int> Pinv) {
    const int n = to.size();
    vector<int> in(n);
    REP(i, n) {
        for (int j : to.at(i)) in.at(j)++;
    }
    vector<int> ret(n);
    REP(t, n) {
        const int i = Pinv.at(t);
        for (int j : to.at(i)) {
            --in.at(j);
            if (in.at(j) == 0) ret.at(j) = t + 1;
        }
    }

    return ret;
}

#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;

    // Dijkstra algorithm
    // - Requirement: wmin >= 0
    // - Complexity: O(E log E)
    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);
                }
            }
        }
    }

    // Dijkstra algorithm
    // - Requirement: wmin >= 0
    // - Complexity: O(V^2 + E)
    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;
            }
        }
    }

    // Bellman-Ford algorithm
    // - Requirement: no negative loop
    // - Complexity: O(VE)
    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;
    }

    // Bellman-ford algorithm using deque
    // - Requirement: no negative loop
    // - Complexity: O(VE)
    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;
                    }
                }
            }
        }
    }

    // 01-BFS
    // - Requirement: all weights must be 0 or w (positive constant).
    // - Complexity: O(V + E)
    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;
                    }
                }
            }
        }
    }

    // Dial's algorithm
    // - Requirement: wmin >= 0
    // - Complexity: O(wmax * V + E)
    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;
                    }
                }
            }
        }
    }

    // Solver for DAG
    // - Requirement: graph is DAG
    // - Complexity: O(V + E)
    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;
    }

    // Retrieve a sequence of vertex ids that represents shortest path [s, ..., goal]
    // If not reachable to goal, return {}
    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);
        }
    }

    // Warshall-Floyd algorithm
    // - Requirement: no negative loop
    // - Complexity: O(E + V^3)
    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 <atcoder/segtree>

int op(int l, int r) { return max(l, r); }
int e() { return -1e9; }

int main() {
    int T;
    cin >> T;
    while (T--) {
        int N, M;
        cin >> N >> M;
        vector<pint> edges(M);
        for (auto &[x, y] : edges) cin >> x >> y, --x, --y;
        vector<int> P(N);
        cin >> P;
        REP(i, N) P.at(i)--;
        vector<int> Pinv(N);
        REP(i, N) Pinv.at(P.at(i)) = i;
        dbg(N);
        dbg(edges);
        dbg(Pinv);

        vector<int> rem_in(N);
        vector<vector<int>> to(N);
        vector<vector<int>> rev(N);
        for (auto [x, y] : edges) {
            rem_in.at(y)++;
            to.at(x).push_back(y);
            rev.at(y).push_back(x);
        }

        auto revPinv = Pinv;
        reverse(ALL(revPinv));

        auto frst = SubSolve(to, Pinv);
        auto last = SubSolve(rev, revPinv);
        // dbg(last);
        for (auto &e : last) { e = N - 1 - e; }
        dbg(P);
        dbg(frst);
        dbg(last);
        vector<tuple<int, int, int>> ranges;
        REP(i, N) ranges.emplace_back(P.at(i), frst.at(i), last.at(i));
        sort(ALL(ranges));
        dbg(ranges);

        // shortest_path<int> sp(N + 1);
        // REP(i, N) sp.add_edge(i, i + 1, 0);
        // REP(i, N) {
        //     const int s = frst.at(i), t = last.at(i);
        //     sp.add_edge(s, t + 1, -1);
        // }
        // sp.dag_solver(0);
        // cout << N + sp.dist.back() << '\n';

        atcoder::segtree<int, op, e> seg0(N + 1), seg1(N + 1);
        seg0.set(0, 0);
        seg1.set(0, 0);

        int all_best = 0;
        REP(i, N) {
            auto [_, s, t] = ranges.at(i);
            // const int s = frst.at(i), t = last.at(i);

            int best = 1;
            chmax(best, seg0.prod(0, s + 1) + 1);
            chmax(best, seg1.prod(0, i + 1) + 1);
            dbg(make_tuple(i, best));
            chmax(all_best, best);

            seg0.set(i + 1, best);
            seg1.set(t + 1, best);
        }


        cout << N - all_best << '\n';
        

        // vector<int> is_ok(N);

        // int ret = 0;
        // FOR(i, 1, N) {
        //     const int prv = Pinv.at(i - 1), now = Pinv.at(i);
        //     if (!rev.at(now).count(prv)) {
        //         dbg(make_tuple(prv, now));
        //         ++ret;
        //     }
        // }
        // for (int p : P) {

        //     // if (!is_ok.at(p)) ++ret;
        //     for (int nxt : to.at(p)) {
        //         rem_in.at(nxt)--;
        //     }
        // }

        // cout << ret << '\n';
    }
}

Submission Info

Judge Result