QOJ.ac
QOJ
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 |
---|---|---|---|---|---|---|---|---|---|
#448084 | #7647. 树哈希 | JWRuixi | 70 | 837ms | 8856kb | C++20 | 4.3kb | 2024-06-19 10:56:23 | 2024-06-19 10:56:24 |
Judging History
answer
#ifdef LOCAL
#include "stdafx.h"
#else
#include <bits/stdc++.h>
#define IL inline
#define LL long long
#define eb emplace_back
#define L(i, j, k) for (int i = (j); i <= (k); ++i)
#define R(i, j, k) for (int i = (j); i >= (k); --i)
using namespace std;
using vi = vector<int>;
#endif
constexpr int N = 1e2 + 9;
int n, q, P;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
struct barrett {
unsigned m;
u64 B;
explicit barrett () : m(0), B(0) {}
explicit barrett (u32 _m) : m(_m), B((u64)(-1) / _m + 1) {}
u32 mod () const { return m; }
u32 rem (u64 z) const {
static u64 x, y;
x = (u64)(((u128)(z) * B) >> 64);
y = x * m;
return z - y + (z < y ? m : 0);
}
} bt;
template<class T>
IL void qm (T &x) {
x += (x >> 31) & P;
}
template<class T>
IL T qpow (T b, unsigned k = P - 2) {
T r = 1;
for (; k; k >>= 1, b = bt.rem(u64(b) * b)) if (k & 1) r = bt.rem(u64(r) * b);
return r;
}
struct mint {
int v;
mint (int _v = 0) : v(_v) {}
mint inv () const { return qpow(v, P - 2); }
#define DEF(o, e) \
mint& operator o##= (const mint &rhs) { e; return *this; } \
mint operator o (const mint &rhs) const { return mint(*this) o##= rhs; }
DEF(+, qm(v += rhs.v - P))
DEF(-, qm(v -= rhs.v))
DEF(*, v = bt.rem((u64)v * rhs.v))
DEF(/, *this *= rhs.inv())
#undef DEF
mint pow (unsigned k) const {
int r = 1;
u64 b = v;
for (; k; k >>= 1, b = b * b % P) if (k & 1) r = r * b % P;
return r;
}
};
mint fc[N], ifc[N], iv[N], C[N][N], pq[N], pw[N][N];
mint A[N][N][N];
void init () {
fc[0] = 1;
L (i, 1, n) {
fc[i] = fc[i - 1] * i;
}
ifc[n] = fc[n].inv();
R (i, n - 1, 0) {
ifc[i] = ifc[i + 1] * (i + 1);
}
iv[0] = iv[1] = 1;
L (i, 2, n) {
iv[i] = ifc[i] * fc[i - 1];
}
L (i, 0, n) {
C[i][0] = 1;
L (j, 1, i) {
C[i][j] = C[i - 1][j] + C[i - 1][j - 1];
}
}
pw[0][0] = 1;
L (i, 1, n) {
pw[i][0] = 1;
L (j, 1, n) {
pw[i][j] = pw[i][j - 1] * i;
}
}
pq[0] = 1;
L (i, 1, n) {
pq[i] = pq[i - 1] * q;
}
L (p, 1, n) {
auto f = A[p];
L (i, 0, n / p) {
f[1][i] = ifc[i].pow(p);
}
L (c, 2, n / p) {
L (i, 0, n / p) {
L (j, 0, i) {
f[c][i] += f[c - 1][j] * f[1][i - j];
}
}
}
}
}
namespace Poly {
mint f[N];
void Ln (mint *g, int n) {
L (i, 0, n) {
f[i] = 0;
}
L (i, 1, n) {
f[i] = g[i] * i;
L (j, 1, i - 1) {
f[i] -= f[j] * g[i - j];
}
}
L (i, 0, n) {
g[i] = f[i] * iv[i];
}
}
void Exp (mint *g, int n) {
L (i, 1, n) {
f[i] = 0;
g[i] *= i;
}
f[0] = 1;
L (i, 1, n) {
L (j, 1, i) {
f[i] += f[i - j] * g[j];
}
f[i] *= iv[i];
}
L (i, 0, n) {
g[i] = f[i];
}
}
}
using Poly::Ln;
using Poly::Exp;
int f[N];
mint g[N], h[N];
IL mint calc (int m) {
if (m == 1) {
return pq[f[1]] * pw[f[1]][f[1] - 1] * ifc[f[1]];
}
L (i, 1, m) {
g[i] = 0;
}
g[0] = 1;
L (p, 1, m - 1) {
if (!f[p]) {
continue;
}
L (i, 0, m) {
h[i] = 0;
}
L (i, 0, m) {
if (g[i].v) {
L (j, 0, (m - i) / p) {
h[i + j * p] += g[i] * A[p][f[p]][j];
}
}
}
L (i, 0, m) {
g[i] = h[i];
}
}
g[0] -= 1;
L (i, 1, m) {
g[i] *= q;
}
g[0] += 1;
Ln(g, m);
mint x = g[m], s = 1, ret = 0;
L (k, 1, f[m] - 1) {
s *= x;
ret += s * pw[f[m]][f[m] - k - 1] * k * C[f[m]][k] * pq[f[m] - k];
}
ret += s * x;
return ret * ifc[f[m]];
}
mint ns[N];
int a[N], tot, all;
void dfs (int i, mint cur) {
if (tot > 1 && a[tot] ^ a[tot - 1]) {
cur *= calc(a[tot - 1]);
}
ns[all] += cur * calc(a[tot]);
L (j, i, n - all) {
++f[a[++tot] = j];
all += j;
dfs(j, cur);
all -= j;
--f[a[tot--]];
}
}
int main () {
ios::sync_with_stdio(0), cin.tie(0);
cin >> n >> q >> P;
int nn = n;
n = min(n, 50);
bt = barrett(P);
init();
f[1] = a[tot = 1] = all = 1;
dfs(1, 1);
L (i, 1, n) {
ns[i] *= fc[i - 1];
cout << ns[i].v << '\n';
}
L (i, n + 1, nn) {
cout << "0\n";
}
}
// I love WHQ!
详细
Subtask #1:
score: 70
Acceptable Answer
Test #1:
score: 70
Acceptable Answer
time: 834ms
memory: 8856kb
input:
100 910342260 935929297
output:
910342260 816177711 569226551 514707635 267406725 391906453 250727611 208481307 81485772 23235693 216730633 285646992 175230876 274553119 174038157 203318484 775234565 322891510 933522659 900692754 745314049 700055439 779013783 855717291 855228480 586396378 894281940 384312444 837857031 272136268 26...
result:
points 0.70 You got 70 pts!
Test #2:
score: 70
Acceptable Answer
time: 836ms
memory: 8740kb
input:
100 222959056 947643239
output:
222959056 358599927 365062242 287299555 872152310 785181552 689517811 751458049 373969559 887125628 238000283 265869067 862846962 717459206 118380127 903859172 38731072 220551290 311944377 678478487 757437607 696077670 937732236 530238679 704937150 7448691 641846446 371506084 393996598 847615147 228...
result:
points 0.70 You got 70 pts!
Test #3:
score: 70
Acceptable Answer
time: 837ms
memory: 8732kb
input:
100 135352674 235854343
output:
135352674 116843515 129198122 128256418 202034449 101078108 134511179 26177395 38146936 177689345 171471260 220203615 2725266 54489245 202150371 51581049 9159057 174134120 214954721 6858381 164936156 136507834 11983036 56210425 230637079 37588391 129846550 182944624 160550968 143284554 172157415 229...
result:
points 0.70 You got 70 pts!
Test #4:
score: 70
Acceptable Answer
time: 829ms
memory: 8760kb
input:
100 538608644 566215339
output:
538608644 365236991 134179965 39370099 416828003 17910602 226317362 529379896 407121368 81806097 249408176 336758120 296361261 35236747 429449088 328368699 409154256 418665686 24463075 203118458 352974481 3351773 506522141 61405204 248921056 351694297 485859431 419342548 150905111 157365902 53232656...
result:
points 0.70 You got 70 pts!
Test #5:
score: 70
Acceptable Answer
time: 826ms
memory: 8796kb
input:
100 56831820 281897771
output:
56831820 213573518 5338712 114481529 104176011 222091299 258318286 168492731 248042852 279768543 163273831 250332871 125456436 55441194 94771937 85241933 265069860 227132810 189427807 26222782 184487649 201740742 267160664 98981147 101908728 84191074 210184730 48919201 18122051 176229976 226118070 1...
result:
points 0.70 You got 70 pts!