Submission #565707

#	Time	Username	Problem	Language	Result	Execution time	Memory
565707		kartel	Fountain Parks (IOI21_parks)	C++17	100 / 100	2968 ms	177756 KiB

parks

#include <bits/stdc++.h>
//#include "grader.cpp"
#include "parks.h"
#define F first
#define S second
#define pb push_back
#define sz(x) (int)x.size()
#define el "\n"
#define all(x) (x).begin(), (x).end()

//#pragma GCC optimize("unroll-loops")
//#pragma GCC optimize("-O3")
//#pragma GCC optimize("Ofast")

using namespace std;
typedef long long ll;

const int N = 5e5 + 500;

mt19937 rnd(time(0));

const int steps[4][2] = {{0, 2}, {2, 0}, {0, -2}, {-2, 0}};
const int dsteps[4][2] = {{1, 1}, {1, -1}, {-1, 1}, {-1, -1}};

map <pair <int, int>, pair <int, int> > road;

pair <int, int> block[N * 2];
int pr[N];
int cmp[2 * N], to[2 * N];
vector <int> g[2 * N], gr[2 * N], ord;
bool mk[2 * N];

int f(int v) {return (pr[v] == v ? v : pr[v] = f(pr[v]));}
void link(int v, int u) {
    v = f(v); u = f(u);
    if (v == u) {
        return;
    }
    pr[u] = v;
}

int nt(int x) {return (x < N ? x + N : x - N);}

void add_impl(int a, int b) {
    int na = nt(a), nb = nt(b);

    g[na].pb(b); gr[b].pb(na);
    g[nb].pb(a); gr[a].pb(nb);
}

void dfs(int v) {
    mk[v] = 1;
    for (auto u : g[v]) {
        if (mk[u]) {
            continue;
        }
        dfs(u);
    }
    ord.pb(v);
}
vector <pair <int, int> > pts;

void dfsd(int v) {
    mk[v] = 1;
    for (auto u : g[v]) {
        if (mk[u]) {
            continue;
        }
        int dx = pts[v].F - pts[u].F;
        int dy = pts[v].S - pts[u].S;
        block[u] = road[{dx, dy}];
        dfsd(u);
    }
}

void get_erased_2x2(vector <int> &x, vector <int> &y, map<pair <int, int>, int> &del) {
    map <pair <int, int>, int> cnt, who;

    for (int i = 0; i < sz(x); i++) {
        who[{x[i], y[i]}] = i;
        for (int j = 0; j < 4; j++) {
            int cx = x[i] + dsteps[j][0];
            int cy = y[i] + dsteps[j][1];

            cnt[{cx, cy}]++;
            if (cnt[{cx, cy}] == 4) {
                pts.pb({cx, cy});
            }
        }
    }
    sort(all(pts));
    cnt.clear();
    int ptr = 0;
    for (auto &[x, y] : pts) {
        cnt[{x, y}] = ptr++;
    }

    ptr = 0;
    for (auto &[x, y] : pts) {
        int par = (x / 2 + y / 2) % 2;
        for (int i = 0; i < 2; i++) {
            int cx = x + steps[i * 2 + par][0];
            int cy = y + steps[i * 2 + par][1];

            if (!cnt.count({cx, cy})) {
                continue;
            }
            g[cnt[{cx, cy}]].pb(ptr);
        }
        ptr++;
    }

    for (int i = 0; i < sz(pts); i++) {
        if (mk[i]) {
            continue;
        }

        int par = (pts[i].F / 2 + pts[i].S / 2) & 1;
        if (par & 1) {
            block[i] = road[{-2, 0}];
        } else {
            block[i] = road[{0, -2}];
        }
        queue <int> q;
        q.push(i); mk[i] = 1;
        while (sz(q)) {
            int v = q.front(); q.pop();

            for (auto u : g[v]) {
                if (mk[u]) {
                    continue;
                }
                int dx = pts[v].F - pts[u].F;
                int dy = pts[v].S - pts[u].S;
                block[u] = road[{dx, dy}];
                q.push(u);
                mk[u] = 1;
            }
        }
    }

    for (int i = 0; i < sz(pts); i++) {
        auto [x, y] = pts[i];

        auto [a, b] = block[i];
        int v = who[{x + dsteps[a][0], y + dsteps[a][1]}];
        int u = who[{x + dsteps[b][0], y + dsteps[b][1]}];

        del[{v, u}] = del[{u, v}] = 1;
    }
}

int construct_roads(vector <int> x, vector <int> y) {
    int n = sz(x);

    road[{0, 2}]  = {2, 0}; road[{2, 0}]  = {0, 1};
    road[{0, -2}] = {1, 3}; road[{-2, 0}] = {3, 2};

    map <pair <int, int>, int> mp;
    vector <pair <int, int> > r;
    map <pair <int, int>, int> del;
    vector <int> pm(n);
    iota(all(pm), 0);
    shuffle(all(pm), rnd);

    bool sd = 1;
    for (int i = 0; i < n; i++) {
        mp[{x[i], y[i]}] = i;
        pr[i] = i;
        sd &= (x[i] >= 2 && x[i] <= 4);
    }

    get_erased_2x2(x, y, del);
    for (auto i : pm) {
        for (int j = 0; j < 4; j++) {
            int cx = x[i] + steps[j][0];
            int cy = y[i] + steps[j][1];

            if (mp.count({cx, cy}) && f(i) != f(mp[{cx, cy}])) {
                int to = mp[{cx, cy}];
                if (del[{i, to}]) {
                    continue;
                }
                link(i, to);
                r.pb({i, to});
            }
        }
    }
    sort(all(r));
    r.resize(unique(all(r)) - r.begin());

    for (int i = 0; i < n; i++) {
        if (f(i) != f(0)) {
            return 0;
        }
    }
    vector <int> u, v, A, B;
    map <pair <int, int>, vector <int> > e;

    for (int i = 0; i < sz(r); i++) {
        int a = r[i].F, b = r[i].S;
        u.pb(a); v.pb(b);
        if (abs(x[a] - x[b]) == 0) {
            int lx = x[a];
            int ly = min(y[a], y[b]);

            e[{lx - 1, ly + 1}].pb(i);
            e[{lx + 1, ly + 1}].pb(nt(i));
        } else {
            int lx = min(x[a], x[b]);
            int ly = y[a];

            e[{lx + 1, ly + 1}].pb(i);
            e[{lx + 1, ly - 1}].pb(nt(i));
        }
    }
    for (int i = 0; i < 2 * N; i++) {
        mk[i] = 0;
        g[i].clear();
    }
    for (auto [p, v] : e) {
        int x = p.F, y = p.S;
        if (sz(v) == 1) {
            continue;
        }
        for (auto a : v) {
            for (auto b : v) {
                if (a == b) {
                    continue;
                }
                add_impl(a, b);
            }
        }
    }

    for (int i = 0; i < 2 * N; i++) {
        cmp[i] = -1;
        if (mk[i]) {
            continue;
        }
        dfs(i);
    }
    reverse(all(ord));

    int C = 0;
    for (auto v : ord) {
        function <void(int)> dfsr = [&](int v) {
            if (cmp[v] != -1) {
                return;
            }
            cmp[v] = C;
            for (auto u : gr[v]) {
                dfsr(u);
            }
        };

        dfsr(v);
        C++;
    }

    for (int i = 0; i < N; i++) {
        if (cmp[i] == cmp[nt(i)]) {
            return 0;
        }
        to[i] = (cmp[i] > cmp[nt(i)]);
    }

    for (int i = 0; i < sz(r); i++) {
        int a = r[i].F, b = r[i].S;
        if (abs(x[a] - x[b]) == 0) {
            int lx = x[a];
            int ly = min(y[a], y[b]);

            if (to[i]) {
                A.pb(lx + 1);
            } else {
                A.pb(lx - 1);
            }
            B.pb(ly + 1);
        } else {
            int lx = min(x[a], x[b]);
            int ly = y[a];

            if (to[i]) {
                B.pb(ly - 1);
            } else {
                B.pb(ly + 1);
            }
            A.pb(lx + 1);
        }
    }

    build(u, v, A, B);
    return 1;
}

Compilation message (stderr)

parks.cpp: In function 'int construct_roads(std::vector<int>, std::vector<int>)':
parks.cpp:222:13: warning: unused variable 'x' [-Wunused-variable]
  222 |         int x = p.F, y = p.S;
      |             ^
parks.cpp:222:22: warning: unused variable 'y' [-Wunused-variable]
  222 |         int x = p.F, y = p.S;
      |                      ^

• Subtask 1: 5 / 5
• Subtask 2: 10 / 10
• Subtask 3: 15 / 15
• Subtask 4: 20 / 20
• Subtask 5: 20 / 20
• Subtask 6: 30 / 30