結果
| 問題 | No.3748 Three Pruning Order |
| コンテスト | |
| ユーザー |
 hos.lyric
|
| 提出日時 | 2026-09-25 23:56:50 |
| 言語 | C++14 (gcc 15.3.0 + boost 1.92.0 + ACL) |
| 結果 |
AC
不安定
|
| 実行時間 | 1,559 ms / 2,000 ms |
| + 157µs | |
| コード長 | 17,462 bytes |
| 記録 | |
| コンパイル時間 | 1,551 ms |
| コンパイル使用メモリ | 179,028 KB |
| 実行使用メモリ | 67,676 KB |
| 最終ジャッジ日時 | 2026-09-25 23:57:14 |
| 合計ジャッジ時間 | 22,871 ms |
|
ジャッジサーバーID （参考情報） |
judge2_0 / judge1_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 42 |
ソースコード
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <chrono>
#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 T> ostream &operator<<(ostream &os, const vector<T> &as);
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;
// point add, rectangle sum
template <class X, class Y, class T> struct Bit2d {
vector<X> xs;
vector<pair<Y, X>> yxs;
vector<vector<Y>> yss;
int m;
vector<int> ns;
vector<vector<T>> bit;
Bit2d() {}
void book(X x, Y y) {
xs.push_back(x);
yxs.emplace_back(y, x);
}
void build() {
sort(xs.begin(), xs.end());
xs.erase(unique(xs.begin(), xs.end()), xs.end());
m = xs.size();
yss.assign(m, {});
sort(yxs.begin(), yxs.end());
for (const auto &yx : yxs) {
const X x = yx.second;
const Y y = yx.first;
const int a = lower_bound(xs.begin(), xs.end(), x) - xs.begin();
assert(a < m); assert(xs[a] == x);
for (int u = a; u < m; u |= u + 1) yss[u].push_back(y);
}
ns.assign(m, 0);
bit.assign(m, {});
for (int u = 0; u < m; ++u) {
yss[u].erase(unique(yss[u].begin(), yss[u].end()), yss[u].end());
ns[u] = yss[u].size();
bit[u].assign(ns[u], 0);
}
}
void add(X x, Y y, T val) {
const int a = lower_bound(xs.begin(), xs.end(), x) - xs.begin();
assert(a < m); assert(xs[a] == x);
for (int u = a; u < m; u |= u + 1) {
const int b = lower_bound(yss[u].begin(), yss[u].end(), y) - yss[u].begin();
assert(b < ns[u]); assert(yss[u][b] == y);
for (int v = b; v < ns[u]; v |= v + 1) bit[u][v] += val;
}
}
T get(X x0, X x1, Y y0, Y y1) const {
const int a0 = lower_bound(xs.begin(), xs.end(), x0) - xs.begin();
const int a1 = lower_bound(xs.begin(), xs.end(), x1) - xs.begin();
T ret = 0;
for (int u = a0; u; u &= u - 1) ret -= get(u - 1, y0, y1);
for (int u = a1; u; u &= u - 1) ret += get(u - 1, y0, y1);
return ret;
}
private:
T get(int u, Y y0, Y y1) const {
T ret = 0;
const int b0 = lower_bound(yss[u].begin(), yss[u].end(), y0) - yss[u].begin();
const int b1 = lower_bound(yss[u].begin(), yss[u].end(), y1) - yss[u].begin();
for (int v = b0; v; v &= v - 1) ret -= bit[u][v - 1];
for (int v = b1; v; v &= v - 1) ret += bit[u][v - 1];
return ret;
}
};
// T: monoid representing information of an interval.
// T() should return the identity.
// T(S s) should represent a single element of the array.
// T::push(T &l, T &r) should push the lazy update.
// T::pull(const T &l, const T &r) should pull two intervals.
template <class T> struct SegmentTreeRange {
int logN, n;
vector<T> ts;
SegmentTreeRange() : logN(0), n(0) {}
explicit SegmentTreeRange(int n_) {
for (logN = 0, n = 1; n < n_; ++logN, n <<= 1) {}
ts.resize(n << 1);
}
template <class S> explicit SegmentTreeRange(const vector<S> &ss) {
const int n_ = ss.size();
for (logN = 0, n = 1; n < n_; ++logN, n <<= 1) {}
ts.resize(n << 1);
for (int i = 0; i < n_; ++i) at(i) = T(ss[i]);
build();
}
T &at(int i) {
return ts[n + i];
}
void build() {
for (int u = n; --u; ) pull(u);
}
inline void push(int u) {
ts[u].push(ts[u << 1], ts[u << 1 | 1]);
}
inline void pull(int u) {
ts[u].pull(ts[u << 1], ts[u << 1 | 1]);
}
// Applies T::f(args...) to [a, b).
template <class F, class... Args>
void ch(int a, int b, F f, Args &&... args) {
assert(0 <= a); assert(a <= b); assert(b <= n);
if (a == b) return;
a += n; b += n;
for (int h = logN; h; --h) {
const int aa = a >> h, bb = b >> h;
if (aa == bb) {
if ((aa << h) != a || (bb << h) != b) push(aa);
} else {
if ((aa << h) != a) push(aa);
if ((bb << h) != b) push(bb);
}
}
for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) {
if (aa & 1) (ts[aa++].*f)(args...);
if (bb & 1) (ts[--bb].*f)(args...);
}
for (int h = 1; h <= logN; ++h) {
const int aa = a >> h, bb = b >> h;
if (aa == bb) {
if ((aa << h) != a || (bb << h) != b) pull(aa);
} else {
if ((aa << h) != a) pull(aa);
if ((bb << h) != b) pull(bb);
}
}
}
// Calculates the product for [a, b).
T get(int a, int b) {
assert(0 <= a); assert(a <= b); assert(b <= n);
if (a == b) return T();
a += n; b += n;
for (int h = logN; h; --h) {
const int aa = a >> h, bb = b >> h;
if (aa == bb) {
if ((aa << h) != a || (bb << h) != b) push(aa);
} else {
if ((aa << h) != a) push(aa);
if ((bb << h) != b) push(bb);
}
}
T prodL, prodR, t;
for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) {
if (aa & 1) { t.pull(prodL, ts[aa++]); prodL = t; }
if (bb & 1) { t.pull(ts[--bb], prodR); prodR = t; }
}
t.pull(prodL, prodR);
return t;
}
// Calculates T::f(args...) of a monoid type for [a, b).
// op(-, -) should calculate the product.
// e() should return the identity.
template <class Op, class E, class F, class... Args>
#if __cplusplus >= 201402L
auto
#else
decltype((std::declval<T>().*F())())
#endif
get(int a, int b, Op op, E e, F f, Args &&... args) {
assert(0 <= a); assert(a <= b); assert(b <= n);
if (a == b) return e();
a += n; b += n;
for (int h = logN; h; --h) {
const int aa = a >> h, bb = b >> h;
if (aa == bb) {
if ((aa << h) != a || (bb << h) != b) push(aa);
} else {
if ((aa << h) != a) push(aa);
if ((bb << h) != b) push(bb);
}
}
auto prodL = e(), prodR = e();
for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) {
if (aa & 1) prodL = op(prodL, (ts[aa++].*f)(args...));
if (bb & 1) prodR = op((ts[--bb].*f)(args...), prodR);
}
return op(prodL, prodR);
}
// Find min b s.t. T::f(args...) returns true,
// when called for the partition of [a, b) from left to right.
// Returns n + 1 if there is no such b.
template <class F, class... Args>
int findRight(int a, F f, Args &&... args) {
assert(0 <= a); assert(a <= n);
if ((T().*f)(args...)) return a;
if (a == n) return n + 1;
a += n;
for (int h = logN; h; --h) push(a >> h);
for (; ; a >>= 1) if (a & 1) {
if ((ts[a].*f)(args...)) {
for (; a < n; ) {
push(a);
if (!(ts[a <<= 1].*f)(args...)) ++a;
}
return a - n + 1;
}
++a;
if (!(a & (a - 1))) return n + 1;
}
}
// Find max a s.t. T::f(args...) returns true,
// when called for the partition of [a, b) from right to left.
// Returns -1 if there is no such a.
template <class F, class... Args>
int findLeft(int b, F f, Args &&... args) {
assert(0 <= b); assert(b <= n);
if ((T().*f)(args...)) return b;
if (b == 0) return -1;
b += n;
for (int h = logN; h; --h) push((b - 1) >> h);
for (; ; b >>= 1) if ((b & 1) || b == 2) {
if ((ts[b - 1].*f)(args...)) {
for (; b <= n; ) {
push(b - 1);
if (!(ts[(b <<= 1) - 1].*f)(args...)) --b;
}
return b - n - 1;
}
--b;
if (!(b & (b - 1))) return -1;
}
}
};
////////////////////////////////////////////////////////////////////////////////
struct Node {
Mint sum, lz;
Node() : sum(0), lz(1) {}
Node(Mint val) : sum(val), lz(1) {}
void push(Node &l, Node &r) {
if (lz != 1) {
l.mul(lz);
r.mul(lz);
lz = 1;
}
}
void pull(const Node &l, const Node &r) {
sum = l.sum + r.sum;
}
void mul(Mint val) {
sum *= val;
lz *= val;
}
// leaf
void add(Mint val) {
sum += val;
}
};
int N, MO;
vector<int> P[3], invP[3];
Mint slow() {
vector<int> early(N, 0);
for (int u = 0; u < N; ++u) {
for (int p = 0; p < N; ++p) {
bool ok = true;
for (int h = 0; h < 3; ++h) ok = ok && (invP[h][p] < invP[h][u]);
if (ok) ++early[u];
}
}
cerr<<"[slow] early = "<<early<<endl;
Mint ans = 0;
for (int r = 0; r < N; ++r) {
Mint way = 1;
vector<int> vis(N, 0);
vis[r] = 1;
for (int h = 0; h < 3; ++h) {
vector<int> us;
for (int i = 0; i < invP[h][r]; ++i) {
const int u = P[h][i];
bool ok = true;
for (int hh = 0; hh < 3; ++hh) if (h != hh) ok = ok && (invP[hh][r] < invP[hh][u]);
if (ok) {
assert(!vis[u]);
vis[u] = 1;
us.push_back(u);
}
}
const int usLen = us.size();
us.push_back(r);
vector<Mint> dp(usLen + 1, 0);
dp[0] += 1;
for (int i = 0; i < usLen; ++i) for (int j = i + 1; j <= usLen; ++j) {
bool ok = true;
for (int hh = 0; hh < 3; ++hh) if (h != hh) ok = ok && (invP[hh][us[j]] < invP[hh][us[i]]);
if (ok) {
Mint coef = 1;
for (int k = i + 1; k < j; ++k) coef *= early[us[k]];
dp[j] += dp[i] * coef;
}
}
way *= dp[usLen];
}
for (int u = 0; u < N; ++u) if (!vis[u]) way *= early[u];
if(way)cerr<<"[slow] r = "<<r<<": way = "<<way<<endl;
ans += way;
}
return ans;
}
int segN;
vector<vector<int>> zss;
vector<SegmentTreeRange<Node>> segs;
vector<Mint> lz;
void segMul(int a, Mint val) {
segs[a].ch(0, (int)zss[a].size(), &Node::mul, val);
lz[a] *= val;
}
Mint segGet(int a, int l, int r, int y, int z) {
if (y <= l) {
return 0;
}
if (r <= y) {
const int pos = lower_bound(zss[a].begin(), zss[a].end(), z) - zss[a].begin();
return segs[a].get(0, pos).sum;
}
assert(a < segN);
if (lz[a] != 1) {
segMul(a << 1, lz[a]);
segMul(a << 1 | 1, lz[a]);
lz[a] = 1;
}
const int m = (l + r) / 2;
Mint ret = 0;
ret += segGet(a << 1, l, m, y, z);
ret += segGet(a << 1 | 1, m, r, y, z);
return ret;
}
void segAdd(int a, int l, int r, int y, int z, Mint val) {
assert(l <= y); assert(y < r);
const int pos = lower_bound(zss[a].begin(), zss[a].end(), z) - zss[a].begin();
segs[a].ch(pos, pos + 1, &Node::add, val);
if (a >= segN) return;
if (lz[a] != 1) {
segMul(a << 1, lz[a]);
segMul(a << 1 | 1, lz[a]);
lz[a] = 1;
}
const int m = (l + r) / 2;
if (y < m) {
segAdd(a << 1, l, m, y, z, val);
} else {
segAdd(a << 1 | 1, m, r, y, z, val);
}
}
Mint fast() {
vector<int> early(N, 0);
{
Bit2d<int, int, int> bit;
for (int u = 0; u < N; ++u) bit.book(invP[1][u], invP[2][u]);
bit.build();
for (int u = 0; u < N; ++u) {
early[u] = bit.get(0, invP[1][u], 0, invP[2][u]);
bit.add(invP[1][u], invP[2][u], +1);
}
}
// cerr<<"[fast] early = "<<early<<endl;
int r = 0;
for (int u = 1; u < N; ++u) {
int cnt = 0;
for (int h = 0; h < 3; ++h) if (invP[h][r] < invP[h][u]) ++cnt;
if (cnt <= 1) r = u;
}
// cerr<<"[fast] r = "<<r<<endl;
Mint ans = 1;
vector<int> vis(N, 0);
vis[r] = 1;
for (int h = 0; h < 3; ++h) {
const int h1 = (h + 1) % 3;
const int h2 = (h + 2) % 3;
vector<int> us;
for (int i = 0; i < invP[h][r]; ++i) {
const int u = P[h][i];
bool ok = true;
for (int hh = 0; hh < 3; ++hh) if (h != hh) ok = ok && (invP[hh][r] < invP[hh][u]);
if (ok) {
assert(!vis[u]);
vis[u] = 1;
us.push_back(u);
}
}
const int usLen = us.size();
us.push_back(r);
// cerr<<"[fast] us = "<<us<<endl;
vector<Mint> dp(usLen + 1, 0);
dp[usLen] = 1;
/*
for (int i = usLen; --i >= 0; ) {
Mint t = 0;
for (int j = usLen; j > i; --j) {
t *= early[us[j]];
if (invP[h1][us[i]] > invP[h1][us[j]] && invP[h2][us[i]] > invP[h2][us[j]]) {
t += dp[j];
}
}
dp[i] = t;
}
//*/
//*
for (segN = 1; segN < N; segN <<= 1) {}
zss.assign(segN << 1, {});
for (const int u : us) {
const int y = invP[h1][u];
const int z = invP[h2][u];
for (int a = segN + y; a; a >>= 1) zss[a].push_back(z);
}
segs.resize(segN << 1);
for (int a = 1; a < segN << 1; ++a) {
sort(zss[a].begin(), zss[a].end());
segs[a] = SegmentTreeRange<Node>((int)zss[a].size());
}
lz.assign(segN << 1, 1);
for (int i = usLen; i >= 0; --i) {
const int y = invP[h1][us[i]];
const int z = invP[h2][us[i]];
if (i < usLen) {
dp[i] = segGet(1, 0, segN, y, z);
segMul(1, early[us[i]]);
}
segAdd(1, 0, segN, y, z, dp[i]);
}
//*/
// cerr<<"[fast] us = "<<us<<", dp = "<<dp<<endl;
ans *= dp[0];
}
for (int u = 0; u < N; ++u) if (!vis[u]) ans *= early[u];
return ans;
}
int main() {
for (int numCases; ~scanf("%d", &numCases); ) { for (int caseId = 1; caseId <= numCases; ++caseId) {
scanf("%d%d", &N, &MO);
Mint::setM(MO);
for (int h = 0; h < 3; ++h) {
P[h].resize(N);
for (int i = N; --i >= 0; ) {
scanf("%d", &P[h][i]);
--P[h][i];
}
}
for (int h = 0; h < 3; ++h) {
invP[h].assign(N, -1);
for (int i = 0; i < N; ++i) invP[h][P[h][i]] = i;
}
for (int h = 0; h < 3; ++h) {
for (int i = 0; i < N; ++i) P[h][i] = invP[0][P[h][i]];
}
for (int h = 0; h < 3; ++h) {
invP[h].assign(N, -1);
for (int i = 0; i < N; ++i) invP[h][P[h][i]] = i;
// cerr<<"P["<<h<<"] = "<<P[h]<<", invP["<<h<<"] = "<<invP[h]<<endl;
}
const Mint ans = fast();
printf("%u\n", ans.x);
#ifdef LOCAL
slow();
#endif
}
#ifndef LOCAL
break;
#endif
}
return 0;
}
/*
[slow] early = [0, 0, 2, 0, 0, 5, 6, 1, 2, 2, 0, 2, 0, 6, 2, 1, 10, 6, 8, 16]
[slow] r = 1: way = 44236800
*/