Submission #1142696

#	Time	Username	Problem	Language	Result	Execution time	Memory
1142696		OI_Account	Arranging Tickets (JOI17_arranging_tickets)	C++20	10 / 100	102 ms	26304 KiB

arranging_tickets

#include <bits/stdc++.h>
using namespace std;

const int N = 200'000;
const int S = 2 + 1'100'000;
const int M = 2 * (6'000'000 + 900'000);
const int INF = 1'000'000'000;

int n, m, l[N + 10], r[N + 10], c[N + 10];
int up[N + 10], x[N + 10], y[N + 10];
int idF[4 * N + 10], src, snk, counter;
int e, w[M + 10], pnt[S + 10], h[S + 10];
vector<pair<int, int>> adj[S + 10];
vector<int> vec;
int leaf[N + 10], pre[N + 10], suf[N + 10];
int s[N + 10];

void readInput() {
    cin >> n >> m;
    for (int i = 0; i < m; i++) {
        cin >> l[i] >> r[i] >> c[i];
        if (l[i] > r[i])
            swap(l[i], r[i]);
    }
}

void calcIdF(int id = 1, int l = 1, int r = n + 1) {
    idF[id] = ++counter;
    if (l + 1 == r) {
        leaf[l] = idF[id];
        return;
    }
    int mid = (l + r) >> 1;
    calcIdF(id << 1, l, mid);
    calcIdF(id << 1 | 1, mid, r);
}

void calcVer() {
    for (int i = 1; i <= m; i++) {
        up[i] = ++counter;
        x[i] = ++counter;
        y[i] = ++counter;
    }
    for (int i = 1; i <= n; i++) {
        pre[i] = ++counter;
        suf[i] = ++counter;
    }
    calcIdF();
    src = ++counter;    
    snk = ++counter;
}

void addEdge(int e1, int u, int v, int cap) {
    w[e1] = cap;
    adj[u].push_back({v, e1});
}

void addEdge(int u, int v, int cap) {
    int e1 = e, e2 = e + 1;
    addEdge(e1, u, v, cap);
    addEdge(e2, v, u, 0);
    e += 2;
}

void build(int id = 1, int l = 1, int r = n + 1) {
    if (l + 1 == r) {
        vec.push_back(e);
        addEdge(idF[id], snk, 0);
        return;
    }
    int mid = (l + r) >> 1;
    addEdge(idF[id], idF[id << 1], INF);
    addEdge(idF[id], idF[id << 1 | 1], INF);
    build(id << 1, l, mid);
    build(id << 1 | 1, mid, r);
}

void add(int st, int en, int val, int id = 1, int l = 1, int r = n + 1) {
    if (en <= l || r <= st)
        return;
    if (st <= l && r <= en) {
        addEdge(val, idF[id], INF);
        return;
    }
    int mid = (l + r) >> 1;
    add(st, en, val, id << 1, l, mid);
    add(st, en, val, id << 1 | 1, mid, r);
}

void addSegEdge(int u, int l, int r) {
    if (l <= r)
        add(l, r, u);
    else {
        addEdge(u, suf[l], INF);
        if (r != 1)
            addEdge(u, pre[r - 1], INF);
    }
}

void calcEdge() {
    build();
    for (int i = 1; i <= m; i++) {
        addEdge(src, up[i], 1);
        addEdge(up[i], x[i], 1);
        addEdge(up[i], y[i], 1);
        addSegEdge(x[i], l[i], r[i]);
        addSegEdge(y[i], r[i], l[i]);
    }
    for (int i = 1; i <= n; i++) {
        addEdge(pre[i], leaf[i], INF);
        addEdge(suf[i], leaf[i], INF);
        if (1 < i)
            addEdge(pre[i], pre[i - 1], INF);
        if (i < n)
            addEdge(suf[i], suf[i + 1], INF);
    }
}

void initW(int x) {
    for (int i = 0; i < e; i += 2) {
        w[i] = w[i] + w[i ^ 1];
        w[i ^ 1] = 0;
    }
    for (auto id: vec)
        w[id] = x;
}

void initBFS() {
    for (int i = 1; i <= snk; i++) 
        pnt[i] = h[i] = 0;
}

void BFS() {
    initBFS();
    queue<int> qu;
    h[src] = 1;
    qu.push(src);
    while (!qu.empty()) {
        int u = qu.front();
        qu.pop();
        for (auto [v, e]: adj[u])
            if (w[e] && !h[v]) {
                h[v] = h[u] + 1;
                qu.push(v);
            }
    }
}

int dfs(int u = src, int x = INF) {
    if (u == snk)
        return x;
    int sum = 0;
    while (pnt[u] < adj[u].size()) {
        int v = adj[u][pnt[u]].first, e = adj[u][pnt[u]].second;
        if (w[e] && h[v] == h[u] + 1) {
            int y = min(w[e], x);
            int pass = dfs(v, y);
            x -= pass;
            sum += pass;
            w[e] -= pass;
            w[e ^ 1] += pass;
            if (!x)
                break;
        }
        pnt[u]++;
    }
    return sum;
}

int dinic(int x) {
    int flow = 0;
    initW(x);
    while (true) {
        BFS();
        if (!h[snk])
            break;
        flow += dfs();
        cout << x << ' ' << flow << endl;
    }
    return flow;
}

/*void solve() {
    int l = 0, r = m + 1;
    while (r - l > 1) {
        int mid = (l + r) >> 1;
        if (dinic(mid) >= m)
            r = mid;
        else
            l = mid;
    }
    cout << r << flush;
}*/

void add(int l, int r) {
    s[l]++;
    if (r < n)
        s[r + 1]--;
}

void solve() {
    int ans = m;
    for (int mask = 0; mask < (1 << m); mask++) {
        for (int i = 0; i < m; i++)
            if ((mask & (1 << i)))
                add(l[i], r[i] - 1);
            else {
                if (l[i] != 1)
                    add(1, l[i] - 1);
                add(r[i], n);
            }
        int sum = 0, mx = 0;
        for (int i = 1; i <= n; i++) {
            sum += s[i];
            mx = max(mx, sum);
            s[i] = 0;
        }
        ans = min(ans, mx);
    }
    cout << ans << flush;
}

int main() {
    ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    readInput();
    /*calcVer();
    calcEdge();*/
    solve();
    return 0;
}

• Subtask 1: 10 / 10
• Subtask 2: 0 / 35
• Subtask 3: 0 / 20
• Subtask 4: 0 / 20
• Subtask 5: 0 / 15