제출 #1196089

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1196089		madamadam3	늑대인간 (IOI18_werewolf)	C++20	7 / 100	316 ms	589824 KiB

werewolf

#include "werewolf.h"
#include <bits/stdc++.h>

using namespace std;

#define FOR(i, a, b) for (int i = a; i < b; i++)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define srt(x) sort(all(x))

typedef long long ll;
using vi = vector<int>;
using vl = vector<ll>;

/*
    A persistent DSU implementation that's slow and bad (copies the DSU each time)
*/

struct DSU {
    int n;
    vector<int> par, size;
    vector<bitset<3000>> has;

    DSU(int N) {
        n = N;
        par.assign(n, 0); iota(par.begin(), par.end(), 0); 
        size.assign(n, 1);
        has.assign(n, bitset<3000>());
        FOR(i, 0, n) has[i].flip(i);
    }

    int find_set(int v) {
        if (par[v] == v) {
            return v;
        }

        return find_set(par[v]);
    }

    void unite(int a, int b) {
        a = find_set(a);
        b = find_set(b);

        if (a != b) {
            if (size[a] < size[b]) swap(a, b);
            par[b] = a;
            size[a] += size[b];
            has[a] |= has[b];
        }
    }
};

struct PersistentDSU {
  int n, timer;
  vector<DSU> states;

  PersistentDSU(int N) {
    n = N;
    timer = 0;
    states.push_back(DSU(n));
  }

  int find_set(int v, int time) {
    return states[time].find_set(v);
  }

  void unite(int a, int b) {
    DSU nDSU = states.back();
    nDSU.unite(a, b);
    states.push_back(nDSU);
    timer++;
  }

  bool does_contain(int head, int node, int time) {
    return states[time].has[head].test(node);
  }
};

/*
  N = num nodes
  X, Y = edges
  S, E = start and end nodes
  L, R = human and werewolf cities
*/

/*
  Solution:
  - for a given value of l, each node u has a connected set of nodes H_u they can reach as a human (<= R)
  - for a given value of r, each node u has a connected set of nodes V_u they can reach as a vampire (>= L)
  - a query (start, end, L, R) is possible iff |H_u ∩ V_u| ≥ 1

  Implementation (slow):
  (1) persistent dsu data structure which supports set intersection queries
  (2) we just need 2 persistent dsus, one where we add nodes from 0 to n (red, vampire), and the other from n to 0 (blue, human), then do queries off
  (3) to answer a query (start, end, left, right) we need to find the set intersection of 
      blue_dsu[time = left][head of start].members and the set red_dsu[time = right[head of end] and count the number of intersections
*/

int n, m, q;
vi x, y, s, e, l, r;
vi queries;

vi check_validity(int N, vi X, vi Y, vi S, vi E, vi L, vi R) {
  n = N; x = X; y = Y; s = S; e = E; l = L; r = R;
  m = x.size(), q = S.size();
  vi A(q);
  
  auto blueDSU = PersistentDSU(n);
  auto redDSU = PersistentDSU(n);

  vi wB(m), wR(m); iota(all(wB), 0); iota(all(wR), 0);

  sort(all(wR), [&](int a, int b) {return max(X[a], Y[a]) < max(X[b], Y[b]);}); 
  sort(all(wB), [&](int a, int b) {return min(X[a], Y[a]) > min(X[b], Y[b]);});

  vi maxR(m), minB(m);
  FOR(i, 0, m) {
      maxR[i] = max(X[wR[i]], Y[wR[i]]);
      minB[i] = min(X[wB[i]], Y[wB[i]]);
  }

  for (auto &edge : wR) {
    redDSU.unite(X[edge], Y[edge]);
  }

  for (auto &edge : wB) {
    blueDSU.unite(X[edge], Y[edge]);
  }

  FOR(query, 0, q) {
    if (S[query] < L[query] || E[query] > R[query]) {
      A[query] = 0;
      continue;
    }

    // int timeRed = 0; // do binary search
    // int timeBlue = 0; // do binary search
    // timeRed = # of red-edges with max ≤ R[i]
    int timeRed = int(upper_bound(maxR.begin(), maxR.end(), R[query]) - maxR.begin());

    // timeBlue = # of blue-edges with min ≥ L[i]
    int lo = 0, hi = m;
    while (lo < hi) {
        int mid = (lo + hi) / 2;
        if (minB[mid] >= L[query]) lo = mid + 1;
        else hi = mid;
    }
    int timeBlue = lo;

    int red_parent = redDSU.find_set(E[query], timeRed);
    int blue_parent = blueDSU.find_set(S[query], timeBlue);

    bool can = (redDSU.states[timeRed].has[red_parent] & blueDSU.states[timeBlue].has[blue_parent]).any();
    A[query] = can ? 1 : 0;
  }

  return A;
}

• Subtask 1: 7 / 7
• Subtask 2: 0 / 8
• Subtask 3: 0 / 34
• Subtask 4: 0 / 51