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#252646#7774. 基础寄术练习题hos_lyric100 ✓37ms8312kbC++146.8kb2023-11-15 23:47:272023-11-15 23:47:27

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你现在查看的是最新测评结果

  • [2023-11-15 23:47:27]
  • 评测
  • 测评结果:100
  • 用时:37ms
  • 内存:8312kb
  • [2023-11-15 23:47:27]
  • 提交

answer

#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 <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")


////////////////////////////////////////////////////////////////////////////////
// Barrett
struct ModInt {
  static unsigned M;
  static unsigned long long NEG_INV_M;
  static void setM(unsigned m) { M = m; NEG_INV_M = -1ULL / M; }
  unsigned x;
  ModInt() : x(0U) {}
  ModInt(unsigned x_) : x(x_ % M) {}
  ModInt(unsigned long long x_) : x(x_ % M) {}
  ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  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) {
    const unsigned long long y = static_cast<unsigned long long>(x) * a.x;
    const unsigned long long q = static_cast<unsigned long long>((static_cast<unsigned __int128>(NEG_INV_M) * y) >> 64);
    const unsigned long long r = y - M * q;
    x = r - M * (r >= 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; }
};
unsigned ModInt::M;
unsigned long long ModInt::NEG_INV_M;
// !!!Use ModInt::setM!!!
////////////////////////////////////////////////////////////////////////////////

using Mint = ModInt;

constexpr int LIM_INV = 10010;
Mint inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV];

void prepare() {
  inv[1] = 1;
  for (int i = 2; i < LIM_INV; ++i) {
    inv[i] = -((Mint::M / i) * inv[Mint::M % i]);
  }
  fac[0] = invFac[0] = 1;
  for (int i = 1; i < LIM_INV; ++i) {
    fac[i] = fac[i - 1] * i;
    invFac[i] = invFac[i - 1] * inv[i];
  }
}
Mint binom(Int n, Int k) {
  if (n < 0) {
    if (k >= 0) {
      return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k);
    } else if (n - k >= 0) {
      return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k);
    } else {
      return 0;
    }
  } else {
    if (0 <= k && k <= n) {
      assert(n < LIM_INV);
      return fac[n] * invFac[k] * invFac[n - k];
    } else {
      return 0;
    }
  }
}


/*
  insert b
  
    1/(s[1]+b)(s[2]+b)(s[3]+b)...(s[n-1]+b)(s[n]+b)
  + 1/(s[1]+b)(s[2]+b)(s[3]+b)...(s[n-1]+b)(s[n]+b)
  + 1/(s[2])(s[2]+b)(s[3]+b)...(s[n-1]+b)(s[n]+b)
  + 1/(s[2])(s[3])(s[3]+b)...(s[n-1]+b)(s[n]+b)
  ...
  + 1/(s[2])(s[3])(s[4])...(s[n])(s[n]+b)
  
  = 2/(s[1]+b)(s[2]+b)(s[3]+b)...(s[n-1]+b)(s[n]+b)
  + (1/b)(1/s[2] - 1/(s[2]+b)) 1/(s[3]+b)...(s[n-1]+b)(s[n]+b)
  + 1/(s[2]) (1/b)(1/s[3] - 1/(s[3]+b)) 1/(s[4]+b)...(s[n-1]+b)(s[n]+b)
  ...
  + 1/(s[2])(s[3])(s[4])...(s[n-1]) (1/b)(1/s[n] - 1/(s[n]+b))
  
  = 2/(s[1]+b)(s[2]+b)(s[3]+b)...(s[n-1]+b)(s[n]+b)
  + (1/b) (1/s[2]...s[n] - 1/(s[2]+b)...(s[n]+b))
  
  
  f(x;a[1],...,a[n]) := 1/(x+a[1])(x+a[1]+a[2])...(x+a[1]+...+a[n])
  g(x;a[1],...,a[n]) := 1/        (x+a[1]+a[2])...(x+a[1]+...+a[n])
  
  f(x;b,a[1],...,a[n]) + f(x;a[1],b,...,a[n]) + ... + f(x;a[1],...,a[n],b)
  = (1/(x+b)) f(x+b;a[1],...,a[n])
  + (1/b) (f(x;a[1],...,a[n]) - f(x+b;a[1],...,a[n]))
  
  g(x;b,a[1],...,a[n]) + g(x;a[1],b,...,a[n]) + ... + g(x;a[1],...,a[n],b)
  = 2f(x+b;a[1],...,a[n])
  + (1/b) (g(x;a[1],...,a[n]) - g(x+b;a[1],...,a[n]))
  
  f(x;) = 1
  g(x;b) = 1
*/

int N, M, K, MO;
Mint f[110][5110], g[110][5110];

int main() {
  for (; ~scanf("%d%d%d%d", &N, &M, &K, &MO); ) {
    Mint::setM(MO);
    prepare();
    
    memset(f, 0, sizeof(f));
    memset(g, 0, sizeof(g));
    fill(f[0], f[0] + (M * (M + 1) / 2 + 1), 1);
    for (int b = M; b >= 1; --b) {
      const int s = (b - 1) * b / 2;
      for (int n = M - b; n >= 1; --n) for (int x = 0; x <= s; ++x) {
        g[n + 1][x] += 2 * f[n][x + b];
        g[n + 1][x] += inv[b] * (g[n][x] - g[n][x + b]);
      }
      for (int x = 0; x <= s; ++x) {
        g[1][x] += 1;
      }
      for (int n = M - b; n >= 0; --n) for (int x = 0; x <= s; ++x) {
        f[n + 1][x] += inv[x + b] * f[n][x + b];
        f[n + 1][x] += inv[b] * (f[n][x] - f[n][x + b]);
      }
    }
    
    const Mint ans = (K == 1) ? f[N][0] : g[N][0];
    printf("%u\n", ans.x);
  }
  return 0;
}

详细

Subtask #1:

score: 10
Accepted

Test #1:

score: 10
Accepted
time: 2ms
memory: 8292kb

input:

9 16 1 327134593

output:

162102742

result:

ok single line: '162102742'

Test #2:

score: 0
Accepted
time: 2ms
memory: 8092kb

input:

11 18 1 834359503

output:

256188485

result:

ok single line: '256188485'

Test #3:

score: 0
Accepted
time: 0ms
memory: 8076kb

input:

18 18 1 614802701

output:

552168146

result:

ok single line: '552168146'

Test #4:

score: 0
Accepted
time: 2ms
memory: 8300kb

input:

7 16 2 861918403

output:

306693876

result:

ok single line: '306693876'

Test #5:

score: 0
Accepted
time: 0ms
memory: 8256kb

input:

11 17 2 617904383

output:

393900291

result:

ok single line: '393900291'

Subtask #2:

score: 25
Accepted

Test #6:

score: 25
Accepted
time: 31ms
memory: 8124kb

input:

60 98 1 715015339

output:

690737273

result:

ok single line: '690737273'

Test #7:

score: 0
Accepted
time: 36ms
memory: 8060kb

input:

96 97 1 507892589

output:

481151247

result:

ok single line: '481151247'

Test #8:

score: 0
Accepted
time: 27ms
memory: 8124kb

input:

90 95 1 621080027

output:

255353202

result:

ok single line: '255353202'

Test #9:

score: 0
Accepted
time: 30ms
memory: 8012kb

input:

85 94 1 297115421

output:

122254364

result:

ok single line: '122254364'

Test #10:

score: 0
Accepted
time: 23ms
memory: 8068kb

input:

81 91 1 460412027

output:

148037986

result:

ok single line: '148037986'

Subtask #3:

score: 15
Accepted

Test #11:

score: 15
Accepted
time: 3ms
memory: 8304kb

input:

29 29 2 545875273

output:

171843225

result:

ok single line: '171843225'

Test #12:

score: 0
Accepted
time: 0ms
memory: 8292kb

input:

29 29 2 342070607

output:

291380196

result:

ok single line: '291380196'

Test #13:

score: 0
Accepted
time: 2ms
memory: 8100kb

input:

30 30 2 293965439

output:

148471965

result:

ok single line: '148471965'

Test #14:

score: 0
Accepted
time: 0ms
memory: 8068kb

input:

30 30 2 528219961

output:

203632962

result:

ok single line: '203632962'

Test #15:

score: 0
Accepted
time: 3ms
memory: 8140kb

input:

30 30 1 202836509

output:

158493990

result:

ok single line: '158493990'

Subtask #4:

score: 10
Accepted

Test #16:

score: 10
Accepted
time: 0ms
memory: 8064kb

input:

27 30 2 360712453

output:

80987914

result:

ok single line: '80987914'

Test #17:

score: 0
Accepted
time: 0ms
memory: 8312kb

input:

26 29 2 377615957

output:

278812897

result:

ok single line: '278812897'

Test #18:

score: 0
Accepted
time: 0ms
memory: 8120kb

input:

22 30 2 163686233

output:

19517828

result:

ok single line: '19517828'

Test #19:

score: 0
Accepted
time: 0ms
memory: 8064kb

input:

20 29 2 785657729

output:

713061509

result:

ok single line: '713061509'

Test #20:

score: 0
Accepted
time: 3ms
memory: 8040kb

input:

24 29 1 374090597

output:

312615700

result:

ok single line: '312615700'

Subtask #5:

score: 15
Accepted

Test #21:

score: 15
Accepted
time: 0ms
memory: 8308kb

input:

29 38 2 909155077

output:

745973305

result:

ok single line: '745973305'

Test #22:

score: 0
Accepted
time: 0ms
memory: 8304kb

input:

40 40 2 1067474879

output:

995503334

result:

ok single line: '995503334'

Test #23:

score: 0
Accepted
time: 0ms
memory: 8076kb

input:

32 37 2 751116719

output:

699924081

result:

ok single line: '699924081'

Test #24:

score: 0
Accepted
time: 0ms
memory: 8060kb

input:

33 37 2 496100951

output:

21741458

result:

ok single line: '21741458'

Test #25:

score: 0
Accepted
time: 3ms
memory: 8292kb

input:

34 38 1 499914887

output:

386116226

result:

ok single line: '386116226'

Subtask #6:

score: 10
Accepted

Test #26:

score: 10
Accepted
time: 8ms
memory: 8064kb

input:

57 66 2 767174999

output:

315351738

result:

ok single line: '315351738'

Test #27:

score: 0
Accepted
time: 10ms
memory: 8140kb

input:

52 69 2 399947623

output:

237685494

result:

ok single line: '237685494'

Test #28:

score: 0
Accepted
time: 8ms
memory: 8064kb

input:

63 64 2 903693961

output:

520250635

result:

ok single line: '520250635'

Test #29:

score: 0
Accepted
time: 7ms
memory: 8132kb

input:

65 70 2 268454909

output:

255864893

result:

ok single line: '255864893'

Test #30:

score: 0
Accepted
time: 7ms
memory: 8124kb

input:

58 68 1 562105223

output:

175445185

result:

ok single line: '175445185'

Subtask #7:

score: 15
Accepted

Test #31:

score: 15
Accepted
time: 32ms
memory: 8064kb

input:

96 96 2 453296971

output:

222864385

result:

ok single line: '222864385'

Test #32:

score: 0
Accepted
time: 25ms
memory: 8064kb

input:

85 96 2 859572601

output:

457416092

result:

ok single line: '457416092'

Test #33:

score: 0
Accepted
time: 29ms
memory: 8088kb

input:

89 94 2 753918677

output:

366789523

result:

ok single line: '366789523'

Test #34:

score: 0
Accepted
time: 28ms
memory: 8064kb

input:

91 92 2 202806031

output:

64270709

result:

ok single line: '64270709'

Test #35:

score: 0
Accepted
time: 37ms
memory: 8140kb

input:

100 100 1 493945957

output:

109570004

result:

ok single line: '109570004'