제출 #1230340

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1230340		rxlfd314	분수 공원 (IOI21_parks)	C++20	70 / 100	2161 ms	126756 KiB

parks

#include "parks.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ari2 = array<int, 2>;
using ari3 = array<int, 3>;
using arl2 = array<ll, 2>;
using arl3 = array<ll, 3>;
template <class T> using vt = vector<T>;
#define all(x) begin(x), end(x)
#define size(x) (int((x).size()))
#define REP(a,b,c,d) for(int a=(b);(d)>0?a<=(c):a>=(c);a+=(d))
#define FOR(a,b,c) REP(a,b,c,1)
#define ROF(a,b,c) REP(a,b,c,-1)

struct DSU {
  vt<int> uf;
  DSU(const int n) : uf(n, -1) {}
  int find(const int i) {
    return uf[i] < 0 ? i : uf[i] = find(uf[i]);
  }
  bool unite(int a, int b) {
    if ((a = find(a)) == (b = find(b)))
      return false;
    if (uf[a] > uf[b])
      swap(a, b);
    uf[a] += uf[b];
    uf[b] = a;
    return true;
  }
};

constexpr int dir[5] = {2, 0, -2, 0, 2};

struct Edge {
  int to, cap, flow, ind;
};

struct Dinic {
  const int N;
  vt<vt<Edge>> adj;
  vt<int> dist, ptr;
  Dinic(const int n) : N(n), adj(n), dist(n), ptr(n) {}
  void add_edge(const int a, const int b, const int c) {
    adj[a].push_back({b, c, 0, size(adj[b])});
    adj[b].push_back({a, 0, 0, size(adj[a]) - 1});
  }
  bool bfs() {
    fill(all(dist), N);
    dist[0] = 0;
    queue<int> qu;
    qu.push(0);
    while (size(qu)) {
      const int i = qu.front();
      qu.pop();
      for (const auto &[j, cap, flow, ind] : adj[i])
        if (cap - flow > 0 && dist[i] + 1 < dist[j]) {
          dist[j] = dist[i] + 1;
          qu.push(j);
        }
    }
    return dist[N-1] < N;
  }
  int dfs(const int i, const int F) {
    if (!F)
      return 0;
    if (i == N-1)
      return F;
    for (; ptr[i] < size(adj[i]); ptr[i]++) {
      auto &[j, cap, flow, ind] = adj[i][ptr[i]];
      if (dist[i] + 1 != dist[j])
        continue;
      const int v = dfs(j, min(F, cap - flow));
      if (v) {
        flow += v;
        adj[j][ind].flow -= v;
        return v;
      }
    }
    return 0;
  }
  vt<ari2> solve() {
    while (bfs()) {
      fill(all(ptr), 0);
      while (dfs(0, INT_MAX));
    }
    vt<ari2> pairs;
    FOR(i, 1, N-2)
      for (const auto &[j, cap, flow, ind] : adj[i])
        if (flow == 1 && j != N-1)
          pairs.push_back({i, j});
    return pairs;
  }
};

int construct_roads(vt<int> X, vt<int> Y) {
  const int N = size(X);
  map<ari2, int> points;
  vt<ari2> edges;
  FOR(i, 0, N-1) {
    FOR(j, 0, 3) {
      const int x = X[i] + dir[j];
      const int y = Y[i] + dir[j+1];
      if (points.find({x, y}) != points.end()) {
        const int k = points[{x, y}];
        edges.push_back({i, k});
      }
    }
    points[{X[i], Y[i]}] = i;
  }
  if (*max_element(all(X)) <= 6) {
    DSU uf(N);
    vt<int> A, B, C, D;
    vt<ari3> fours;
    for (const auto &[i, j] : edges) {
      if (X[i] == X[j]) {
        uf.unite(i, j);
        if (X[i] == 2) {
          A.push_back(i);
          B.push_back(j);
          C.push_back(1);
          D.push_back(Y[i] + Y[j] >> 1);
        } else if (X[i] == 6) {
          A.push_back(i);
          B.push_back(j);
          C.push_back(7);
          D.push_back(Y[i] + Y[j] >> 1);
        } else {
          fours.push_back({Y[i] + Y[j] >> 1, i, j});
        }
      }
    }
    sort(all(fours));
    int add = 1;
    set<ari2> have;
    for (const auto &[_, i, j] : fours) {
      A.push_back(i);
      B.push_back(j);
      C.push_back(4 + add);
      D.push_back(Y[i] + Y[j] >> 1);
      have.insert({4 + add, Y[i] + Y[j] >> 1});
      add *= -1;
    }
    for (const auto &[i, j] : edges) {
      if (Y[i] == Y[j]) {
        if (!uf.unite(i, j))
          continue;
        A.push_back(i);
        B.push_back(j);
        const int x = X[i] + X[j] >> 1;
        C.push_back(x);
        if (have.count({x, Y[i] + 1})) {
          assert(!have.count({x, Y[i] - 1}));
          have.insert({x, Y[i] - 1});
          D.push_back(Y[i] - 1);
        } else {
          have.insert({x, Y[i] + 1});
          D.push_back(Y[i] + 1);
        }
      }
    }
    assert(size(A) == size(B) && size(B) == size(C) && size(C) == size(D));
    if (size(A) != N - 1)
      return 0;
    build(A, B, C, D);
    return 1;
  }
  DSU uf(N);
  vt<ari2> used;
  FOR(x, 0, size(edges) - 1) {
    auto &[i, j] = edges[x];
    if (!uf.unite(i, j))
      continue;
    if (i > j)
      swap(i, j);
    used.push_back({i, j});
  }
  if (size(used) != N - 1)
    return 0;
  map<ari2, int> benches;
  vt<ari2> benches2;
  int M = 0;
  for (const auto &[i, j] : used) {
    const auto check = [&](const ari2 b) {
      if (benches.find(b) != benches.end())
        return;
      benches[b] = M++;
      benches2.push_back(b);
    };
    if (X[i] == X[j]) {
      check({X[i] - 1, Y[i] + Y[j] >> 1});
      check({X[i] + 1, Y[i] + Y[j] >> 1});
    } else {
      check({X[i] + X[j] >> 1, Y[i] - 1});
      check({X[i] + X[j] >> 1, Y[i] + 1});
    }
  }
  Dinic flow(N+M+1);
  int cur = 0;
  FOR(x, 0, N-2) {
    flow.add_edge(0, x + 1, 1);
    const auto &[i, j] = used[x];
    const auto check = [&](const ari2 b) {
      flow.add_edge(x + 1, benches[b] + N, 1);
    };
    if (X[i] == X[j]) {
      check({X[i] - 1, Y[i] + Y[j] >> 1});
      check({X[i] + 1, Y[i] + Y[j] >> 1});
    } else {
      check({X[i] + X[j] >> 1, Y[i] - 1});
      check({X[i] + X[j] >> 1, Y[i] + 1});
    }
  }
  FOR(i, N, N+M-1)
    flow.add_edge(i, N+M, 1);
  vt<ari2> pairs = flow.solve();
  if (size(pairs) != N - 1)
    return 0;
  vt<int> A, B, C, D;
  for (auto &[i, j] : pairs) {
    i--, j -= N;
    A.push_back(used[i][0]);
    B.push_back(used[i][1]);
    C.push_back(benches2[j][0]);
    D.push_back(benches2[j][1]);
  }
  build(A, B, C, D);
  return 1;
}

• Subtask 1: 5 / 5
• Subtask 2: 10 / 10
• Subtask 3: 15 / 15
• Subtask 4: 20 / 20
• Subtask 5: 20 / 20
• Subtask 6: 0 / 30