結果

問題 No.8122 How Many Liars Are There?
コンテスト
ユーザー hos.lyric
提出日時 2025-04-01 23:03:14
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 285 ms / 2,000 ms
コード長 5,228 bytes
コンパイル時間 1,903 ms
コンパイル使用メモリ 127,488 KB
実行使用メモリ 7,848 KB
最終ジャッジ日時 2025-04-01 23:03:21
合計ジャッジ時間 7,401 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge6
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 65
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In function ‘int main()’:
main.cpp:168:12: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
  168 |       scanf("%d", &P[u]);
      |       ~~~~~^~~~~~~~~~~~~
main.cpp:173:12: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
  173 |       scanf("%d", &A[u]);
      |       ~~~~~^~~~~~~~~~~~~

ソースコード

diff # 

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <chrono>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")


struct Functional {
  int n;
  vector<int> par;
  int cyclesLen;
  vector<int> lens;
  vector<vector<int>> cycles;
  // cycle id or -1
  vector<int> on;
  // forest
  vector<vector<int>> graph;
  int zeit;
  vector<int> dis, fin, dep;
  // root is cycle[k][l]
  vector<int> ks, ls;
  
  Functional() {}
  Functional(const vector<int> &par_) : par(par_) {
    n = par.size();
    for (int u = 0; u < n; ++u) {
      assert(0 <= par[u]); assert(par[u] < n);
    }
    cycles.clear();
    vector<int> vis(n, -1);
    for (int s = 0; s < n; ++s) {
      int u = s;
      for (; !~vis[u]; u = par[u]) {
        vis[u] = s;
      }
      if (vis[u] == s) {
        vector<int> cycle;
        for (int v = u; ; ) {
          cycle.push_back(v);
          if ((v = par[v]) == u) break;
        }
        cycles.push_back(cycle);
      }
    }
    cyclesLen = cycles.size();
    lens.resize(cyclesLen);
    on.assign(n, -1);
    for (int k = 0; k < cyclesLen; ++k) {
      lens[k] = cycles[k].size();
      for (const int u : cycles[k]) {
        on[u] = k;
      }
    }
    graph.assign(n, {});
    for (int u = 0; u < n; ++u) if (!~on[u]) {
      graph[par[u]].push_back(u);
    }
    zeit = 0;
    dis.assign(n, -1);
    fin.assign(n, -1);
    dep.assign(n, 0);
    ks.assign(n, -1);
    ls.assign(n, -1);
    for (int k = 0; k < cyclesLen; ++k) {
      for (int l = 0; l < lens[k]; ++l) {
        dfs(k, l, cycles[k][l]);
      }
    }
  }
  void dfs(int k, int l, int u) {
    dis[u] = zeit++;
    ks[u] = k;
    ls[u] = l;
    for (const int v : graph[u]) {
      dep[v] = dep[u] + 1;
      dfs(k, l, v);
    }
    fin[u] = zeit;
  }
  
  // min d s.t. f^d(u) = v, or -1
  int dist(int u, int v) const {
    if (ks[u] != ks[v]) return -1;
    if (~on[v]) {
      int dl = ls[v] - ls[u];
      if (dl < 0) dl += lens[ks[u]];
      return dep[u] + dl;
    }
    return (dis[v] <= dis[u] && dis[u] < fin[v]) ? (dep[u] - dep[v]) : -1;
  };
};

////////////////////////////////////////////////////////////////////////////////


// \sum[u] f[u] + \sum[u] (f[u] xor f[P[u]] xor A[u]) = K

int N, K;
vector<int> P;
vector<int> A;

Functional F;

using BS = bitset<2010>;
BS dp[1010][2];
BS mul(BS fs, BS gs) {
  BS hs;
  for (int k = fs._Find_first(); k < (int)fs.size(); k = fs._Find_next(k)) {
    hs |= gs << k;
  }
  return hs;
}


void dfs(int u) {
  for (int x = 0; x < 2; ++x) {
    dp[u][x].reset();
    dp[u][x].set(x);
  }
  for (const int v : F.graph[u]) {
    dfs(v);
    for (int x = 0; x < 2; ++x) {
      BS tmp;
      for (int y = 0; y < 2; ++y) {
        tmp |= mul(dp[u][x], dp[v][y] << (x ^ y ^ A[v]));
      }
      dp[u][x] = tmp;
    }
  }
// for(int x=0;x<2;++x){cerr<<"dp["<<u<<"]["<<x<<"] = ";for(int k=0;k<=2*N;++k)cerr<<dp[u][x][k];cerr<<endl;}
}

int main() {
  for (; ~scanf("%d%d", &N, &K); ) {
    P.resize(N);
    for (int u = 0; u < N; ++u) {
      scanf("%d", &P[u]);
      --P[u];
    }
    A.resize(N);
    for (int u = 0; u < N; ++u) {
      scanf("%d", &A[u]);
    }
    K = 2*N - K;
    
    F = Functional(P);
// cerr<<"cycles = "<<F.cycles<<endl;
    
    memset(dp, 0, sizeof(dp));
    BS ans;
    ans.set(0);
    for (int k = 0; k < F.cyclesLen; ++k) {
      const int len = F.lens[k];
      const auto &us = F.cycles[k];
      for (int l = 0; l < len; ++l) {
        dfs(us[l]);
      }
      BS here;
      for (int s = 0; s < 2; ++s) {
        BS crt[2] = {};
        crt[s] = dp[us[0]][s];
        for (int l = 1; l < len; ++l) {
          BS nxt[2] = {};
          for (int x = 0; x < 2; ++x) for (int y = 0; y < 2; ++y) {
            nxt[y] |= mul(crt[x], dp[us[l]][y] << (x ^ y ^ A[us[l - 1]]));
          }
          for (int x = 0; x < 2; ++x) crt[x] = nxt[x];
        }
        for (int x = 0; x < 2; ++x) {
          here |= crt[x] << (x ^ s ^ A[us[len - 1]]);
        }
      }
      ans = mul(ans, here);
    }
// cerr<<"ans = ";for(int k=0;k<=2*N;++k)cerr<<ans[k];cerr<<endl;
    
    puts(ans[K] ? "Yes" : "No");
  }
  return 0;
}
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