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#378362#7759. Permutation Counting 2wsyear100 ✓2935ms9600kbC++142.4kb2024-04-06 12:00:552024-04-06 12:00:56

Judging History

你现在查看的是最新测评结果

  • [2024-04-06 12:00:56]
  • 评测
  • 测评结果:100
  • 用时:2935ms
  • 内存:9600kb
  • [2024-04-06 12:00:55]
  • 提交

answer

// Author: Klay Thompson
// Problem: P10004 [集训队互测 2023] Permutation Counting 2
// Memory Limit: 512 MB
// Time Limit: 5000 ms
// 
// Powered by CP Editor (https://cpeditor.org)

#include <bits/stdc++.h>

#define rep(i, j, k) for (int i = (j); i <= (k); ++i)
#define per(i, j, k) for (int i = (j); i >= (k); --i)
#define SZ(v) int((v).size())
#define ALL(v) (v).begin(),(v).end()
#define fi first
#define se second
using ll = long long;
using pii = std::pair<int, int>;
using pll = std::pair<ll, ll>;

template<class T>inline void chkmn(T &x, T y) { if (y < x) x = y; }
template<class T>inline void chkmx(T &x, T y) { if (y > x) x = y; }

using namespace std;

const int maxn = 510;
const int maxm = 500010;

int n, mod, f[maxn][maxn], g[maxn][maxn], h[maxn], fac[maxm], ivf[maxm];

__int128 mu;
namespace barrett {
  inline ll reduce(ll x) {
    ll r = x - (mu * x >> 64) * mod;
    return r >= mod ? r - mod : r;
  }
  inline void setmod(ll mod) {
    mu = -1ull / mod;
  }
}
using namespace barrett;

int binom(int x, int y) {
  if (x < 0 || y < 0 || x < y) return 0;
  return reduce(1ll * reduce(1ll * fac[x] * ivf[y]) * ivf[x - y]);
}

int coe(int x) {
  return (x & 1) ? mod - 1 : 1;
}

inline void add(int &x, int y) {
  x += y;
  if (x >= mod) x -= mod;
}

inline int fpw(int x, int p) {
  int res = 1;
  while (p) {
    if (p & 1) res = 1ll * res * x % mod;
    x = 1ll * x * x % mod, p >>= 1;
  }
  return res;
}

int main() {
  cin.tie(nullptr) -> ios::sync_with_stdio(false);
  cin >> n >> mod, setmod(mod);
  fac[0] = 1;
  rep (i, 1, maxm - 1) fac[i] = 1ll * fac[i - 1] * i % mod;
  ivf[maxm - 1] = fpw(fac[maxm - 1], mod - 2);
  per (i, maxm - 1, 1) ivf[i - 1] = 1ll * ivf[i] * i % mod;
  rep (p, 1, n) {
    rep (j, 1, n) h[j] = 0;
    rep (j, 1, n) rep (q, 1, j) add(h[j], reduce(1ll * reduce(1ll * coe(j - q) * binom(j, q)) * binom(n + p * q - 1, n)));
    rep (i, p, n) rep (j, 1, n) add(f[i][j], reduce(1ll * reduce(1ll * coe(i - p) * binom(i, p)) * h[j]));
  }
  rep (p, 1, n) {
    rep (j, 1, n) h[j] = 0;
    rep (j, 1, n) rep (q, 1, j) add(h[j], reduce(1ll * reduce(1ll * coe(j - q) * f[p][q]) * binom(n - q, j - q)));
    rep (i, p, n) rep (j, 1, n) add(g[i][j], reduce(1ll * reduce(1ll * coe(i - p) * binom(n - p, i - p)) * h[j]));
  }
  per (i, n, 1) per (j, n, 1) cout << g[i][j] << " \n"[j == 1];
}

详细

Subtask #1:

score: 10
Accepted

Test #1:

score: 10
Accepted
time: 8ms
memory: 7504kb

input:

7 1001458121

output:

1 0 0 0 0 0 0
0 56 56 8 0 0 0
0 56 659 440 36 0 0
0 8 440 1520 440 8 0
0 0 36 440 659 56 0
0 0 0 8 56 56 0
0 0 0 0 0 0 1

result:

ok 49 tokens

Test #2:

score: 0
Accepted
time: 8ms
memory: 7600kb

input:

8 1008735209

output:

1 0 0 0 0 0 0 0
0 84 126 36 1 0 0 0
0 126 1773 1980 405 9 0 0
0 36 1980 8436 4761 405 1 0
0 1 405 4761 8436 1980 36 0
0 0 9 405 1980 1773 126 0
0 0 0 1 36 126 84 0
0 0 0 0 0 0 0 1

result:

ok 64 tokens

Subtask #2:

score: 15
Accepted

Test #3:

score: 15
Accepted
time: 8ms
memory: 7676kb

input:

14 1000253273

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 455 3003 6435 5005 1365 105 1 0 0 0 0 0 0
0 3003 112905 730665 1629435 1456560 529956 71940 2835 15 0 0 0 0
0 6435 730665 10865585 46433475 75169560 50184540 13633740 1349931 36735 120 0 0 0
0 5005 1629435 46433475 336576825 860578230 885230850 375891370 62035485 332475...

result:

ok 196 tokens

Test #4:

score: 0
Accepted
time: 8ms
memory: 7588kb

input:

15 1009800301

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 560 4368 11440 11440 4368 560 16 0 0 0 0 0 0 0
0 4368 188682 1482416 4160120 4899264 2511376 536384 41328 800 1 0 0 0 0
0 11440 1482416 26232784 139089120 291102560 265085216 106311200 17712368 1048560 15232 16 0 0 0
0 11440 4160120 139089120 216926039 947184153 39833...

result:

ok 225 tokens

Test #5:

score: 0
Accepted
time: 8ms
memory: 7608kb

input:

16 1006729121

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 680 6188 19448 24310 12376 2380 136 1 0 0 0 0 0 0 0
0 6188 305150 2867696 9916066 14924539 10288876 3196000 410329 17748 153 0 0 0 0 0
0 19448 2867696 59852036 387206263 15304436 216863763 683915984 173666645 18275272 650641 4828 1 0 0 0
0 24310 9916066 387206263 82...

result:

ok 256 tokens

Subtask #3:

score: 25
Accepted

Test #6:

score: 25
Accepted
time: 9ms
memory: 7680kb

input:

36 1003299797

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 7770 435897 10295472 124403620 854992152 552567909 334501587 855871755 616535351 836177106 87288018 849183199 348330136 38608020 2324784 66045 666 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 435897 133844910 939232742 752696285 9488...

result:

ok 1296 tokens

Test #7:

score: 0
Accepted
time: 9ms
memory: 7692kb

input:

37 1009736899

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 8436 501942 12620256 163011640 193585389 366265801 325233075 508510208 4472335 508510208 325233075 366265801 193585389 163011640 12620256 501942 8436 38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 501942 164674938 380061172 795391...

result:

ok 1369 tokens

Test #8:

score: 0
Accepted
time: 7ms
memory: 7640kb

input:

38 1002064493

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 9139 575757 15380937 211915132 673991551 105909500 89228335 917893160 782878886 231145424 634874749 53537001 904603957 635745396 61523748 3262623 82251 741 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 575757 201514950 26611267 ...

result:

ok 1444 tokens

Test #9:

score: 0
Accepted
time: 10ms
memory: 7636kb

input:

39 1000696681

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 9880 658008 18643560 273438880 310408078 24862708 197477816 671070872 191143189 191143189 671070872 197477816 24862708 310408078 273438880 18643560 658008 9880 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 658008 245336455 ...

result:

ok 1521 tokens

Test #10:

score: 0
Accepted
time: 10ms
memory: 7636kb

input:

40 1002813283

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 10660 749398 22481940 350343565 151022119 572250549 255038067 159674717 979042431 374977376 547170717 790491840 141687815 878961939 118286125 95548245 4496388 101270 820 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 749398...

result:

ok 1600 tokens

Subtask #4:

score: 25
Accepted

Test #11:

score: 25
Accepted
time: 29ms
memory: 7876kb

input:

96 1005401729

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 147440 64446024 781420036 468430311 27733626 62151757 454795566 711626792 885805006 401110492 711423106 32...

result:

ok 9216 tokens

Test #12:

score: 0
Accepted
time: 26ms
memory: 7876kb

input:

97 1003022927

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 152096 67910864 795115101 924546504 230011659 577127906 564913191 11843263 171607987 697964156 4314087 7...

result:

ok 9409 tokens

Test #13:

score: 0
Accepted
time: 27ms
memory: 7900kb

input:

98 1000259233

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 156849 71523144 883402282 582472554 858367843 730708960 476781508 806308877 286962083 221796390 327681...

result:

ok 9604 tokens

Test #14:

score: 0
Accepted
time: 34ms
memory: 7988kb

input:

99 1000444889

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 161700 75287520 442576 386074411 823487426 504618380 971268883 734797176 388493421 848753352 8574809...

result:

ok 9801 tokens

Test #15:

score: 0
Accepted
time: 29ms
memory: 8028kb

input:

100 1008746839

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 166650 79208745 50916937 213745970 953400361 882774939 595265332 362179793 339853992 820776686 204...

result:

ok 10000 tokens

Subtask #5:

score: 25
Accepted

Test #16:

score: 25
Accepted
time: 2860ms
memory: 9600kb

input:

496 1005266363

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...

result:

ok 246016 tokens

Test #17:

score: 0
Accepted
time: 2882ms
memory: 9592kb

input:

497 1000331767

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...

result:

ok 247009 tokens

Test #18:

score: 0
Accepted
time: 2914ms
memory: 9448kb

input:

498 1000148759

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...

result:

ok 248004 tokens

Test #19:

score: 0
Accepted
time: 2912ms
memory: 9468kb

input:

499 1000176851

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...

result:

ok 249001 tokens

Test #20:

score: 0
Accepted
time: 2935ms
memory: 9544kb

input:

500 1002873259

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...

result:

ok 250000 tokens