結果

問題 No.907 Continuous Kadomatu
ユーザー 👑 emthrmemthrm
提出日時 2020-02-06 02:14:26
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 591 ms / 2,000 ms
コード長 6,202 bytes
コンパイル時間 2,439 ms
コンパイル使用メモリ 218,992 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-09-24 11:52:51
合計ジャッジ時間 6,739 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,812 KB
testcase_01 AC 2 ms
6,816 KB
testcase_02 AC 2 ms
6,944 KB
testcase_03 AC 2 ms
6,944 KB
testcase_04 AC 2 ms
6,940 KB
testcase_05 AC 20 ms
6,940 KB
testcase_06 AC 2 ms
6,944 KB
testcase_07 AC 7 ms
6,944 KB
testcase_08 AC 16 ms
6,944 KB
testcase_09 AC 9 ms
6,940 KB
testcase_10 AC 35 ms
6,944 KB
testcase_11 AC 51 ms
6,944 KB
testcase_12 AC 131 ms
6,944 KB
testcase_13 AC 148 ms
6,940 KB
testcase_14 AC 168 ms
6,940 KB
testcase_15 AC 161 ms
6,940 KB
testcase_16 AC 166 ms
6,940 KB
testcase_17 AC 178 ms
6,944 KB
testcase_18 AC 165 ms
6,944 KB
testcase_19 AC 178 ms
6,944 KB
testcase_20 AC 179 ms
6,940 KB
testcase_21 AC 177 ms
6,940 KB
testcase_22 AC 177 ms
6,940 KB
testcase_23 AC 591 ms
6,940 KB
testcase_24 AC 587 ms
6,940 KB
testcase_25 AC 2 ms
6,940 KB
testcase_26 AC 2 ms
6,940 KB
testcase_27 AC 2 ms
6,940 KB
testcase_28 AC 2 ms
6,940 KB
testcase_29 AC 2 ms
6,944 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
template <typename T> using posteriority_queue = priority_queue<T, vector<T>, greater<T> >;
const int INF = 0x3f3f3f3f;
const ll LINF = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-8;
const int MOD = 1000000007;
// const int MOD = 998244353;
const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
const int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
template <typename T> void unique(vector<T> &a) { a.erase(unique(ALL(a)), a.end()); }
struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  }
} iosetup;

int mod = MOD;
struct ModInt {
  unsigned val;
  ModInt(): val(0) {}
  ModInt(ll x) : val(x >= 0 ? x % mod : x % mod + mod) {}
  ModInt pow(ll exponent) {
    ModInt tmp = *this, res = 1;
    while (exponent > 0) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }
  ModInt &operator+=(const ModInt &x) { if((val += x.val) >= mod) val -= mod; return *this; }
  ModInt &operator-=(const ModInt &x) { if((val += mod - x.val) >= mod) val -= mod; return *this; }
  ModInt &operator*=(const ModInt &x) { val = static_cast<unsigned long long>(val) * x.val % mod; return *this; }
  ModInt &operator/=(const ModInt &x) { return *this *= x.inv(); }
  bool operator==(const ModInt &x) const { return val == x.val; }
  bool operator!=(const ModInt &x) const { return val != x.val; }
  bool operator<(const ModInt &x) const { return val < x.val; }
  bool operator<=(const ModInt &x) const { return val <= x.val; }
  bool operator>(const ModInt &x) const { return val > x.val; }
  bool operator>=(const ModInt &x) const { return val >= x.val; }
  ModInt &operator++() { if (++val == mod) val = 0; return *this; }
  ModInt operator++(int) { ModInt res = *this; ++*this; return res; }
  ModInt &operator--() { val = (val == 0 ? mod : val) - 1; return *this; }
  ModInt operator--(int) { ModInt res = *this; --*this; return res; }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { return ModInt(val ? mod - val : 0); }
  ModInt operator+(const ModInt &x) const { return ModInt(*this) += x; }
  ModInt operator-(const ModInt &x) const { return ModInt(*this) -= x; }
  ModInt operator*(const ModInt &x) const { return ModInt(*this) *= x; }
  ModInt operator/(const ModInt &x) const { return ModInt(*this) /= x; }
  friend ostream &operator<<(ostream &os, const ModInt &x) { return os << x.val; }
  friend istream &operator>>(istream &is, ModInt &x) { ll val; is >> val; x = ModInt(val); return is; }
private:
  ModInt inv() const {
    // assert(__gcd(val, mod) == 1);
    unsigned a = val, b = mod; int x = 1, y = 0;
    while (b) {
      unsigned tmp = a / b;
      swap(a -= tmp * b, b);
      swap(x -= tmp * y, y);
    }
    return ModInt(x);
  }
};
ModInt abs(const ModInt &x) { return x; }
struct Combinatorics {
  int val; // "val!" and "mod" must be disjoint.
  vector<ModInt> fact, fact_inv, inv;
  Combinatorics(int val = 10000000) : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) {
    fact[0] = 1;
    FOR(i, 1, val + 1) fact[i] = fact[i - 1] * i;
    fact_inv[val] = ModInt(1) / fact[val];
    for (int i = val; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i;
    FOR(i, 1, val + 1) inv[i] = fact[i - 1] * fact_inv[i];
  }
  ModInt nCk(int n, int k) {
    if (n < 0 || n < k || k < 0) return ModInt(0);
    // assert(n <= val && k <= val);
    return fact[n] * fact_inv[k] * fact_inv[n - k];
  }
  ModInt nPk(int n, int k) {
    if (n < 0 || n < k || k < 0) return ModInt(0);
    // assert(n <= val);
    return fact[n] * fact_inv[n - k];
  }
  ModInt nHk(int n, int k) {
    if (n < 0 || k < 0) return ModInt(0);
    return (k == 0 ? ModInt(1) : nCk(n + k - 1, k));
  }
};

int main() {
  int n; cin >> n;
  vector a(n, 0), b(n, 0), comp{INF};
  REP(i, n) {
    cin >> a[i] >> b[i];
    comp.emplace_back(a[i]);
    comp.emplace_back(b[i]);
  }
  sort(ALL(comp));
  unique(comp);
  int m = comp.size();
  REP(i, n) {
    a[i] = lower_bound(ALL(comp), a[i]) - comp.begin();
    b[i] = lower_bound(ALL(comp), b[i]) - comp.begin();
  }

  // f[i] := g[i] / i!
  // ここで g[i] は 1, 2,..., n の順列の内, 門松列列の総数の半数
  // 半数は i が奇数ならば a[i] > a[i + 1]
  //        i が偶数ならば a[i] < a[i + 1] となっている
  Combinatorics com(n + 1);
  vector f(n + 1, ModInt(0));
  f[1] = 1;
  f[2] = ModInt(1) / 2;
  FOR(i, 3, n + 1) {
    // https://yukicoder.me/problems/no/336
    ModInt g = 0;
    REP(j, i / 2 + 1) {
      int k = i + 1 - 2 * j;
      ModInt tmp = 0;
      REP(x, k + 1) tmp += com.nCk(k, x) * ModInt(k - 2 * x).pow(i + 1) / k * (x & 1 ? -1 : 1);
      g += tmp / ModInt(2).pow(k - 1) * (j & 1 ? -1 : 1);
    }
    f[i] = g * com.fact_inv[i] / 2;
  }

  // dp[i][j] := i 列目まで見たときに a[i] ∈ [j, j + 1] となる確率
  vector dp(n + 1, vector(m - 1, ModInt(0)));
  dp[0][m - 2] = 1;
  REP(i, n) {
    // REP(k, m - 1) cerr << dp[i][k] << " \n"[k + 1 == m - 1];
    if (i & 1) {
      // i が奇数
      // dp[i][j] := a[i] ∈ (-∞, j + 1] に変換
      FOR(j, 1, m - 1) dp[i][j] += dp[i][j - 1];
    } else {
      // i が偶数
      // dp[i][j] := a[i] ∈ [j, ∞) に変換
      for (int j = m - 3; j >= 0; --j) dp[i][j] += dp[i][j + 1];
    }
    REP(j, m - 2) {
      ModInt p = 1;
      for (int k = i; k >= 0; --k) {
        if (j < a[k] || b[k] < j + 1) break;
        (p *= comp[j + 1] - comp[j]) /= comp[b[k]] - comp[a[k]];
        int idx = (k & 1 ? j - 1 : j + 1);
        if (idx >= 0) dp[i + 1][j] += dp[k][idx] * p * f[i - k + 1];
      }
    }
  }
  // REP(i, n + 1) REP(k, m - 1) cerr << dp[i][k] << " \n"[k + 1 == m - 1];
  cout << accumulate(ALL(dp[n]), ModInt(0)) << '\n';
  return 0;
}
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