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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#451475#8717. 骰子propane#TL 1ms6168kbC++208.8kb2024-06-23 14:37:402024-06-23 14:37:40

Judging History

你现在查看的是最新测评结果

  • [2024-06-23 14:37:40]
  • 评测
  • 测评结果:TL
  • 用时:1ms
  • 内存:6168kb
  • [2024-06-23 14:37:40]
  • 提交

answer

#include<bits/stdc++.h>
using namespace std;
using LL = long long;
template<const int T>
struct ModInt {
    const static int mod = T;
    int x;
    ModInt(int x = 0) : x(x % mod) {}
    ModInt(long long x) : x(int(x % mod)) {} 
    int val() { return x; }
    ModInt operator + (const ModInt &a) const { int x0 = x + a.x; return ModInt(x0 < mod ? x0 : x0 - mod); }
    ModInt operator - (const ModInt &a) const { int x0 = x - a.x; return ModInt(x0 < 0 ? x0 + mod : x0); }
    ModInt operator * (const ModInt &a) const { return ModInt(1LL * x * a.x % mod); }
    ModInt operator / (const ModInt &a) const { return *this * a.inv(); }
    bool operator == (const ModInt &a) const { return x == a.x; };
    bool operator != (const ModInt &a) const { return x != a.x; };
    void operator += (const ModInt &a) { x += a.x; if (x >= mod) x -= mod; }
    void operator -= (const ModInt &a) { x -= a.x; if (x < 0) x += mod; }
    void operator *= (const ModInt &a) { x = 1LL * x * a.x % mod; }
    void operator /= (const ModInt &a) { *this = *this / a; }
    friend ModInt operator + (int y, const ModInt &a){ int x0 = y + a.x; return ModInt(x0 < mod ? x0 : x0 - mod); }
    friend ModInt operator - (int y, const ModInt &a){ int x0 = y - a.x; return ModInt(x0 < 0 ? x0 + mod : x0); }
    friend ModInt operator * (int y, const ModInt &a){ return ModInt(1LL * y * a.x % mod);}
    friend ModInt operator / (int y, const ModInt &a){ return ModInt(y) / a;}
    friend ostream &operator<<(ostream &os, const ModInt &a) { return os << a.x;}
    friend istream &operator>>(istream &is, ModInt &t){return is >> t.x;}

    ModInt pow(long long n) const {
        ModInt res(1), mul(x);
        while(n){
            if (n & 1) res *= mul;
            mul *= mul;
            n >>= 1;
        }
        return res;
    }
    
    ModInt inv() const {
        int a = x, b = mod, u = 1, v = 0;
        while (b) {
            int t = a / b;
            a -= t * b; swap(a, b);
            u -= t * v; swap(u, v);
        }
        if (u < 0) u += mod;
        return u;
    }
    
};
using mint = ModInt<1000000007>;

namespace FastFourierTransform {
  using real = double;

  struct C {
    real x, y;

    C() : x(0), y(0) {}

    C(real x, real y) : x(x), y(y) {}

    inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }

    inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }

    inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); }

    inline C conj() const { return C(x, -y); }
  };

  const real PI = acosl(-1);
  int base = 1;
  vector< C > rts = { {0, 0},
                     {1, 0} };
  vector< int > rev = {0, 1};


  void ensure_base(int nbase) {
    if(nbase <= base) return;
    rev.resize(1 << nbase);
    rts.resize(1 << nbase);
    for(int i = 0; i < (1 << nbase); i++) {
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    while(base < nbase) {
      real angle = PI * 2.0 / (1 << (base + 1));
      for(int i = 1 << (base - 1); i < (1 << base); i++) {
        rts[i << 1] = rts[i];
        real angle_i = angle * (2 * i + 1 - (1 << base));
        rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
      }
      ++base;
    }
  }

  void fft(vector< C > &a, int n) {
    assert((n & (n - 1)) == 0);
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = base - zeros;
    for(int i = 0; i < n; i++) {
      if(i < (rev[i] >> shift)) {
        swap(a[i], a[rev[i] >> shift]);
      }
    }
    for(int k = 1; k < n; k <<= 1) {
      for(int i = 0; i < n; i += 2 * k) {
        for(int j = 0; j < k; j++) {
          C z = a[i + j + k] * rts[j + k];
          a[i + j + k] = a[i + j] - z;
          a[i + j] = a[i + j] + z;
        }
      }
    }
  }

  vector< long long > multiply(const vector< int > &a, const vector< int > &b) {
    int need = (int) a.size() + (int) b.size() - 1;
    int nbase = 1;
    while((1 << nbase) < need) nbase++;
    ensure_base(nbase);
    int sz = 1 << nbase;
    vector< C > fa(sz);
    for(int i = 0; i < sz; i++) {
      int x = (i < (int) a.size() ? a[i] : 0);
      int y = (i < (int) b.size() ? b[i] : 0);
      fa[i] = C(x, y);
    }
    fft(fa, sz);
    C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
    for(int i = 0; i <= (sz >> 1); i++) {
      int j = (sz - i) & (sz - 1);
      C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
      fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
      fa[i] = z;
    }
    for(int i = 0; i < (sz >> 1); i++) {
      C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
      C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];
      fa[i] = A0 + A1 * s;
    }
    fft(fa, sz >> 1);
    vector< long long > ret(need);
    for(int i = 0; i < need; i++) {
      ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
    }
    return ret;
  }
};

template< typename T >
struct ArbitraryModConvolution {
  using real = FastFourierTransform::real;
  using C = FastFourierTransform::C;

  ArbitraryModConvolution() = default;

  static vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) {
    if(need == -1) need = a.size() + b.size() - 1;
    int nbase = 0;
    while((1 << nbase) < need) nbase++;
    FastFourierTransform::ensure_base(nbase);
    int sz = 1 << nbase;
    vector< C > fa(sz);
    for(int i = 0; i < a.size(); i++) {
      fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15);
    }
    fft(fa, sz);
    vector< C > fb(sz);
    if(a == b) {
      fb = fa;
    } else {
      for(int i = 0; i < b.size(); i++) {
        fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15);
      }
      fft(fb, sz);
    }
    real ratio = 0.25 / sz;
    C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
    for(int i = 0; i <= (sz >> 1); i++) {
      int j = (sz - i) & (sz - 1);
      C a1 = (fa[i] + fa[j].conj());
      C a2 = (fa[i] - fa[j].conj()) * r2;
      C b1 = (fb[i] + fb[j].conj()) * r3;
      C b2 = (fb[i] - fb[j].conj()) * r4;
      if(i != j) {
        C c1 = (fa[j] + fa[i].conj());
        C c2 = (fa[j] - fa[i].conj()) * r2;
        C d1 = (fb[j] + fb[i].conj()) * r3;
        C d2 = (fb[j] - fb[i].conj()) * r4;
        fa[i] = c1 * d1 + c2 * d2 * r5;
        fb[i] = c1 * d2 + c2 * d1;
      }
      fa[j] = a1 * b1 + a2 * b2 * r5;
      fb[j] = a1 * b2 + a2 * b1;
    }
    fft(fa, sz);
    fft(fb, sz);
    vector< T > ret(need);
    for(int i = 0; i < need; i++) {
      long long aa = llround(fa[i].x);
      long long bb = llround(fb[i].x);
      long long cc = llround(fa[i].y);
      aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;
      ret[i] = aa + (bb << 15) + (cc << 30);
    }
    return ret;
  }
};

const int maxn = 6e5 + 5;
mint ans[maxn];
int b[205];
vector<mint> p[1505];
int n, m, q;

ArbitraryModConvolution<mint> fft;

vector<array<int, 3> > tr[1505 * 4];

void modify(int u, int l, int r, const array<int, 3> &q){
    if (l == r){
        tr[u].push_back(q);
        return;
    }
    int mid = (l + r) / 2;
    if (q[0] <= mid and q[1] > mid){
        tr[u].push_back(q);
        return;
    }
    if (q[1] <= mid) modify(2 * u, l, mid, q);
    else modify(2 * u + 1, mid + 1, r, q);
}

vector<mint> dp[1505];

void solve(int u, int l, int r){
    if (l == r){
        mint sum = 0;
        for(int j = 0; j <= m; j++) sum += b[j] * p[r][j];
        for(auto [l, r, id] : tr[u]){
            ans[id] = sum;
        }
        return;
    }
    int mid = (l + r) / 2;
    solve(2 * u, l, mid);
    solve(2 * u + 1, mid + 1, r);
    if (!tr[u].empty()){
        dp[mid] = p[mid];
        dp[mid + 1] = p[mid + 1];
        for(int i = mid - 1; i >= l; i--){
            dp[i] = fft.multiply(p[i], dp[i + 1]);
            dp[i].resize(m + 1);
        }
        for(int i = mid + 2; i <= r; i++){
            dp[i] = fft.multiply(p[i], dp[i - 1]);
            dp[i].resize(m + 1);
        }
        for(auto [l, r, id] : tr[u]){
            auto c = fft.multiply(dp[l], dp[r]);
            mint sum = 0;
            for(int j = 0; j <= m; j++) sum += b[j] * c[j];
            ans[id] = sum; 
        }
    }
}

int main(){

#ifdef LOCAL
    freopen("data.in", "r", stdin);
    freopen("data.out", "w", stdout);
#endif

    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(0);

    cin >> n >> m >> q;
    for(int i = 0; i <= m; i++) cin >> b[i];
    for(int i = 1; i <= n; i++){
        p[i].resize(m + 1);
        for(int j = 0; j <= m; j++){
            int x;
            cin >> x;
            p[i][j] = x;
        }
    }
    for(int i = 0; i < q; i++){
        int l, r;
        cin >> l >> r;
        modify(1, 1, n, {l, r, i});
    }
    solve(1, 1, n);
    for(int i = 0; i < q; i++){
        cout << ans[i] << '\n';
    }

}

詳細信息

Test #1:

score: 100
Accepted
time: 1ms
memory: 6104kb

input:

3 3 3
4 3 2 1
0 1 0 1000000007
0 500000004 0 500000004
0 0 500000004 500000004
1 1
1 2
1 3

output:

3
1
0

result:

ok 3 number(s): "3 1 0"

Test #2:

score: 0
Accepted
time: 0ms
memory: 6168kb

input:

3 3 6
4 3 2 1
1000000007 0 1 0
1000000007 1 0 0
1000000007 0 1 0
1 1
1 2
1 3
2 2
2 3
3 3

output:

2
1
0
3
1
2

result:

ok 6 numbers

Test #3:

score: 0
Accepted
time: 1ms
memory: 6004kb

input:

1 1 1
604063100 57375033
742299910 257700098
1 1

output:

148903503

result:

ok 1 number(s): "148903503"

Test #4:

score: -100
Time Limit Exceeded

input:

1500 200 600000
253665324 876103781 804024983 929290295 908790466 176299158 528078340 696679927 416465140 509641654 705083449 361711737 250659645 735832780 35321360 383752049 203979021 178832532 785212637 514502839 169840231 65809146 504755349 516829442 382478309 901925498 142312128 782336477 741339...

output:


result: