結果

問題 No.1938 Lagrange Sum
コンテスト
ユーザー hos.lyric
提出日時 2022-05-13 21:33:00
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,980 ms / 3,000 ms
コード長 4,342 bytes
コンパイル時間 1,044 ms
コンパイル使用メモリ 104,904 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-07-22 01:05:35
合計ジャッジ時間 27,788 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 25
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 #
raw source code 

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#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> 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; }

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;


int N;
Mint W;
vector<Mint> X, Y;

int main() {
  for (; ~scanf("%d%u", &N, &W.x); ) {
    X.resize(N);
    Y.resize(N);
    for (int i = 0; i < N; ++i) {
      scanf("%u%u", &X[i].x, &Y[i].x);
    }
    
    Mint ans = 0;
    for (int j = 0; j < N; ++j) {
      Mint denom = 1;
      for (int i = 0; i < N; ++i) if (i != j) {
        denom *= (X[j] - X[i]);
      }
      vector<Mint> ws(N);
      for (int i = 0; i < N; ++i) {
        ws[i] = (i == j) ? 1 : (W - X[i]);
      }
      vector<Mint> ls(N + 1), rs(N + 1);
      ls[0] = 1;
      for (int i = 0; i < N; ++i) ls[i + 1] = ls[i] * ws[i];
      rs[N] = 1;
      for (int i = N; --i >= 0; ) rs[i] = ws[i] * rs[i + 1];
      Mint sum = 0;
      for (int i = 0; i < N; ++i) if (i != j) {
        sum += ls[i] * rs[i + 1] * (X[j] - X[i]);
      }
      ans += Y[j] * denom.inv() * sum;
    }
    printf("%u\n", ans.x);
  }
  return 0;
}
0