Submission #1203020

#TimeUsernameProblemLanguageResultExecution timeMemory
1203020zeta7532Train (APIO24_train)C++20
In queue
0 ms0 KiB
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll INF = (1LL << 60);

// ---- Persistent Segment Tree for point-add & range-sum ----
struct PST {
    struct Node { int l, r, sum; };
    vector<Node> st;
    int N;
    PST(int _N): N(_N) {
        st.reserve(_N * 20);
        st.push_back({0, 0, 0});  // dummy node at index 0
    }
    // build an empty tree on [l..r], return root id
    int build(int l, int r) {
        int id = st.size();
        st.push_back({0, 0, 0});
        if (l < r) {
            int m = (l + r) >> 1;
            st[id].l = build(l, m);
            st[id].r = build(m + 1, r);
        }
        return id;
    }
    // point add: create a new version from prev, add v at position p
    int update(int prev, int l, int r, int p, int v) {
        int id = st.size();
        st.push_back(st[prev]);
        if (l == r) {
            st[id].sum += v;
        } else {
            int m = (l + r) >> 1;
            if (p <= m)
                st[id].l = update(st[prev].l, l, m, p, v);
            else
                st[id].r = update(st[prev].r, m + 1, r, p, v);
            st[id].sum = st[st[id].l].sum + st[st[id].r].sum;
        }
        return id;
    }
    // range sum on [ql..qr]
    int query(int id, int l, int r, int ql, int qr) const {
        if (!id || qr < l || r < ql) return 0;
        if (ql <= l && r <= qr) return st[id].sum;
        int m = (l + r) >> 1;
        return query(st[id].l, l, m, ql, qr)
             + query(st[id].r, m + 1, r, ql, qr);
    }
};

struct Train {
    int x, y;
    int a, b;
    ll c;
};

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, m, w;
    cin >> n >> m >> w;
    vector<ll> t(n);
    for (int i = 0; i < n; i++) {
        cin >> t[i];
    }

    vector<pair<int,int>> meals(w);
    for (int i = 0; i < w; i++) {
        cin >> meals[i].first >> meals[i].second;
    }

    vector<Train> trains(m);
    for (int i = 0; i < m; i++) {
        cin >> trains[i].x
            >> trains[i].y
            >> trains[i].a
            >> trains[i].b
            >> trains[i].c;
    }

    // 1) 時刻を座標圧縮
    vector<int> allT;
    allT.reserve(2*m + 2*w + 1);
    allT.push_back(0);
    for (auto &tr : trains) {
        allT.push_back(tr.a);
        allT.push_back(tr.b);
    }
    for (auto &me : meals) {
        allT.push_back(me.first);
        allT.push_back(me.second);
    }
    sort(allT.begin(), allT.end());
    allT.erase(unique(allT.begin(), allT.end()), allT.end());
    auto comp = [&](int x) {
        return int(lower_bound(allT.begin(), allT.end(), x) - allT.begin());
    };
    int Tsz = allT.size();

    // 2) meals を r_comp ごとにバケット化
    vector<vector<int>> meals_at_r(Tsz);
    for (auto &me : meals) {
        int lc = comp(me.first);
        int rc = comp(me.second);
        meals_at_r[rc].push_back(lc);
    }

    // 3) 永続セグ木の構築
    PST pst(Tsz);
    vector<int> version(Tsz);
    version[0] = pst.build(0, Tsz - 1);
    for (int lpos : meals_at_r[0]) {
        version[0] = pst.update(version[0], 0, Tsz - 1, lpos, 1);
    }
    for (int i = 1; i < Tsz; i++) {
        version[i] = version[i - 1];
        for (int lpos : meals_at_r[i]) {
            version[i] = pst.update(version[i], 0, Tsz - 1, lpos, 1);
        }
    }

    // g(b, a): 区間 (b, a) に完全包含される meal の数
    auto get_g = [&](int b, int a) {
        int bc = comp(b), ac = comp(a);
        if (ac == 0) return 0;
        int total = pst.query(version[ac - 1], 0, Tsz - 1, 0, Tsz - 1);
        int bad   = pst.query(version[ac - 1], 0, Tsz - 1, 0, bc);
        return total - bad;
    };

    // 4) 列車を出発時刻 a の昇順でソートするための idx
    vector<int> idx(m);
    iota(idx.begin(), idx.end(), 0);
    sort(idx.begin(), idx.end(),
         [&](int i, int j) { return trains[i].a < trains[j].a; });

    // DP, heap, deque の準備
    vector<ll> dp(m, INF);
    vector< priority_queue<pair<int,int>,
        vector<pair<int,int>>, greater<pair<int,int>>> > heap(n);
    vector< deque<int> > dq(n);

    // 初期状態:planet 0、時刻 0
    heap[0].push({0, -1});
    auto get_dp = [&](int j) {
        return (j < 0 ? 0LL : dp[j]);
    };
    auto get_b = [&](int j) {
        return (j < 0 ? 0 : trains[j].b);
    };

    ll ans = INF;

    // 5) メインループ
    for (int k = 0; k < m; k++) {
        int i = idx[k];
        int p = trains[i].x;
        int ai = trains[i].a;

        // step1: 時刻 ai までに到着した j を deque[p] に流し込む
        auto &hp = heap[p];
        auto &dq_p = dq[p];
        while (!hp.empty() && hp.top().first <= ai) {
            int j = hp.top().second;
            hp.pop();
            // 四辺形不等式にもとづく pop-back
            while (dq_p.size() >= 2) {
                int j2 = dq_p.back();
                int j1 = dq_p[dq_p.size() - 2];
                ll lhs = get_dp(j2)
                       + (ll)get_g(get_b(j2), ai) * t[p];
                ll rhs = get_dp(j1)
                       + (ll)get_g(get_b(j1), ai) * t[p];
                if (lhs >= rhs) dq_p.pop_back();
                else break;
            }
            dq_p.push_back(j);
        }

        // step2: 最適な遷移元
        if (!dq_p.empty()) {
            int j = dq_p.front();
            dp[i] = get_dp(j)
                  + (ll)get_g(get_b(j), ai) * t[p]
                  + trains[i].c;
            if (trains[i].y == n - 1)
                ans = min(ans, dp[i]);
        }

        // step3: i を到着 heap に追加
        heap[trains[i].y].push({trains[i].b, i});
    }

    if (ans >= INF / 2) ans = -1;
    cout << ans << "\n";
    return 0;
}