結果
| 問題 |
No.1712 Read and Pile
|
| コンテスト | |
| ユーザー |
 hos.lyric
|
| 提出日時 | 2021-10-22 21:08:21 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 15,724 bytes |
| コンパイル時間 | 3,074 ms |
| コンパイル使用メモリ | 148,040 KB |
| 実行使用メモリ | 59,020 KB |
| 最終ジャッジ日時 | 2024-09-23 04:04:08 |
| 合計ジャッジ時間 | 41,109 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 27 TLE * 13 |
ソースコード
#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#pragma GCC target ("avx")
#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 <map>
#include <numeric>
#include <queue>
#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> 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; }
////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
static constexpr unsigned M = M_;
unsigned x;
constexpr ModInt() : x(0U) {}
constexpr ModInt(unsigned x_) : x(x_ % M) {}
constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
constexpr 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) { x = (static_cast<unsigned long long>(x) * a.x) % 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; }
};
////////////////////////////////////////////////////////////////////////////////
constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;
// 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::merge(const T &l, const T &r) should merge two intervals.
template <class T> struct SegmentTreeRange {
int logN, n;
vector<T> ts;
SegmentTreeRange() {}
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; ) merge(u);
}
inline void push(int u) {
ts[u].push(ts[u << 1], ts[u << 1 | 1]);
}
inline void merge(int u) {
ts[u].merge(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) merge(aa);
} else {
if ((aa << h) != a) merge(aa);
if ((bb << h) != b) merge(bb);
}
}
}
// 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);
a <<= 1;
if (!(ts[a].*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);
b <<= 1;
if (!(ts[b - 1].*f)(args...)) --b;
}
return b - n - 1;
}
--b;
if (!(b & (b - 1))) return -1;
}
}
}
};
////////////////////////////////////////////////////////////////////////////////
struct Node0 {
int sz, sum;
int lz;
Node0() : sz(0), sum(0), lz(0) {}
void push(Node0 &l, Node0 &r) {
l.add(lz);
r.add(lz);
lz = 0;
}
void merge(const Node0 &l, const Node0 &r) {
sz = l.sz + r.sz;
sum = l.sum + r.sum;
}
void add(int val) {
sum += sz * val;
lz += val;
}
int getSum() const {
return sum;
}
};
int getSum(SegmentTreeRange<Node0> &seg, int a, int b) {
return seg.get(a, b,
[&](int l, int r) -> int { return l + r; },
[&]() -> int { return 0; },
&Node0::getSum);
}
struct Node {
Mint x[2], y[3];
int lz;
Node() : x{}, y{}, lz(0) {}
void push(Node &l, Node &r) {
l.add(lz);
r.add(lz);
lz = 0;
}
void merge(const Node &l, const Node &r) {
x[0] = l.x[0] + r.x[0];
x[1] = l.x[1] + r.x[1];
y[0] = l.y[0] + r.y[0];
y[1] = l.y[1] + r.y[1];
y[2] = l.y[2] + r.y[2];
}
void add(int val) {
x[1] += val * x[0];
y[2] += val * (2 * y[1] + val * y[0]);
y[1] += val * y[0];
lz += val;
}
Node getSum() const {
return *this;
}
};
Node getSum(SegmentTreeRange<Node> &seg, int a, int b) {
return seg.get(a, b,
[&](const Node &l, const Node &r) -> Node { Node t; t.merge(l, r); return t; },
[&]() -> Node { return Node(); },
&Node::getSum);
}
int N, M;
vector<int> A;
int main() {
for (; ~scanf("%d%d", &N, &M); ) {
A.resize(N + M);
for (int i = 0; i < N; ++i) {
A[i] = N - 1 - i;
}
for (int i = N; i < N + M; ++i) {
scanf("%d", &A[i]);
--A[i];
}
// cerr<<"A = ";pv(A.begin(),A.end());
if (N == 1) {
printf("%u\n", Mint(M).x);
continue;
}
if (N == 2) {
Mint ans2 = M;
for (int i = N; i < N + M; ++i) {
for (int a = 0; a < 2; ++a) for (int b = 0; b < 2; ++b) if (a != b) {
Mint tmp = 1;
tmp *= ((A[i - 1] == -2) ? Mint(2).inv() : (A[i - 1] == a) ? 1 : 0);
tmp *= ((A[i] == -2) ? Mint(2).inv() : (A[i] == b) ? 1 : 0);
ans2 += tmp;
}
}
printf("%u\n", ans2.x);
continue;
}
vector<int> ls(N + M + 1, 0);
for (int i = 0; i < N + M; ++i) {
ls[i + 1] = ls[i] + ((A[i] == -2) ? 1 : 0);
}
// cerr<<"ls = ";pv(ls.begin(),ls.end());
Mint ans[2][2] = {};
vector<Mint> pw0(N + M + 1), pw1(N + M + 1), pw2(N + M + 1), invPw1(N + M + 1), invPw2(N + M + 1);
pw0[0] = pw1[0] = pw2[0] = invPw1[0] = invPw2[0] = 1;
pw0[1] = Mint(N);
pw1[1] = Mint(N - 1);
pw2[1] = Mint(N - 2);
invPw1[1] = Mint(N - 1).inv();
invPw2[1] = Mint(N - 2).inv();
for (int i = 2; i <= N + M; ++i) {
pw0[i] = pw0[i - 1] * pw0[1];
pw1[i] = pw1[i - 1] * pw1[1];
pw2[i] = pw2[i - 1] * pw2[1];
invPw1[i] = invPw1[i - 1] * invPw1[1];
invPw2[i] = invPw2[i - 1] * invPw2[1];
}
{
vector<int> app(N, 0);
SegmentTreeRange<Node0> seg0(N + M);
SegmentTreeRange<Node> seg(N + M);
for (int i = 0; i < N + M; ++i) {
seg0.at(i).sz = 1;
if (A[i] == -2) {
seg.at(i).x[0] = pw0[ls[i]] * invPw1[ls[i + 1]];
seg.at(i).y[0] = pw0[ls[i]] * invPw2[ls[i + 1]];
}
}
seg0.build();
seg.build();
for (int i = 0; i < N + M; ++i) {
// get
if (i >= N) {
if (A[i] != -2) {
{
const int m = getSum(seg0, app[A[i]], app[A[i]] + 1);
Mint tmp = 0;
tmp += pw1[ls[i] - ls[app[A[i]] + 1]] * Mint(1 + m);
tmp += Mint(N - 1 - m) * (pw1[ls[i] - ls[app[A[i]] + 1]] - pw2[ls[i] - ls[app[A[i]] + 1]]);
tmp *= pw0[ls[app[A[i]]] + (ls[N + M] - ls[i + 1])];
ans[0][0] += tmp;
}
{
const Node res = getSum(seg, app[A[i]], i);
Mint tmp = 0;
tmp += pw1[ls[i]] * (res.x[0] + res.x[1]);
tmp += pw1[ls[i]] * (Mint(N - 1) * res.x[0] - res.x[1])
- pw2[ls[i]] * (Mint(N - 1) * res.y[0] - res.y[1]);
tmp *= pw0[ls[N + M] - ls[i + 1]];
ans[1][0] += tmp;
}
} else {
{
const Node res = getSum(seg, 0, i);
Mint tmp = 0;
tmp += pw1[ls[i]] * (Mint(N) * res.x[0] + Mint(N - 1) * res.x[1]);
tmp += pw1[ls[i]] * (Mint(N) * Mint(N - 1) * res.x[0] - Mint(2 * N - 1) * res.x[1])
- pw2[ls[i]] * (Mint(N) * Mint(N - 1) * res.y[0] - Mint(2 * N - 1) * res.y[1] + res.y[2]);
tmp *= pw0[ls[N + M] - ls[i + 1]];
ans[1][1] += tmp;
}
}
}
// add
if (A[i] != -2) {
seg0.ch(app[A[i]], i, &Node0::add, 1);
seg.ch(app[A[i]], i, &Node::add, 1);
app[A[i]] = i;
}
}
}
{
reverse(A.begin(), A.end());
for (int i = 0; i < N + M; ++i) {
ls[i + 1] = ls[i] + ((A[i] == -2) ? 1 : 0);
}
// cerr<<"A = ";pv(A.begin(),A.end());
// cerr<<"ls = ";pv(ls.begin(),ls.end());
vector<int> app(N, 0);
SegmentTreeRange<Node> seg(N + M);
for (int i = 0; i < N + M; ++i) {
if (A[i] == -2) {
seg.at(i).x[0] = pw0[ls[i]] * invPw1[ls[i + 1]];
seg.at(i).y[0] = pw0[ls[i]] * invPw2[ls[i + 1]];
}
}
seg.build();
for (int i = 0; i < M + N; ++i) {
// get
{
if (A[i] != -2) {
{}
{
const Node res = getSum(seg, app[A[i]], i);
Mint tmp = 0;
tmp += pw1[ls[i]] * (res.x[0] + res.x[1]);
tmp += pw1[ls[i]] * (Mint(N - 1) * res.x[0] - res.x[1])
- pw2[ls[i]] * (Mint(N - 1) * res.y[0] - res.y[1]);
tmp *= pw0[ls[N + M] - ls[i + 1]];
ans[0][1] += tmp;
}
} else {
{}
}
}
// add
if (A[i] != -2) {
seg.ch(app[A[i]], i, &Node::add, 1);
app[A[i]] = i;
}
}
reverse(A.begin(), A.end());
for (int i = 0; i < N + M; ++i) {
ls[i + 1] = ls[i] + ((A[i] == -2) ? 1 : 0);
}
}
printf("%u\n", ((ans[0][0] + ans[0][1] + ans[1][0] + ans[1][1]) / Mint(N).pow(ls[N + M])).x);
#ifdef LOCAL
Mint brt[2][2] = {};
for (int i = 0; i < N + M; ++i) for (int j = N; j < N + M; ++j) {
if (i < j) {
set<int> as(A.begin() + i + 1, A.begin() + j);
as.erase(-2);
const int m = as.size();
Mint tmp = 0;
tmp += Mint(N - 1).pow(ls[j] - ls[i + 1]) * Mint(1 + m);
tmp += Mint(N - 1 - m) * (Mint(N - 1).pow(ls[j] - ls[i + 1]) - Mint(N - 2).pow(ls[j] - ls[i + 1]));
tmp *= Mint(N).pow(ls[i] + (ls[N + M] - ls[j + 1]));
if (A[i] != -2) {
if (A[j] != -2) {
if (A[i] == A[j] && as.find(A[i]) == as.end()) {
brt[0][0] += tmp;
}
} else {
if (as.find(A[i]) == as.end()) {
brt[0][1] += tmp;
}
}
} else {
if (A[j] != -2) {
if (as.find(A[j]) == as.end()) {
brt[1][0] += tmp;
}
} else {
brt[1][1] += Mint(N - m) * tmp;
}
}
}
}
cerr << "brt = " << ((brt[0][0] + brt[0][1] + brt[1][0] + brt[1][1]) / Mint(N).pow(ls[N + M])) << "; "
<< brt[0][0] << " " << brt[0][1] << " " << brt[1][0] << " " << brt[1][1] << endl;
cerr << "ans = " << ((ans[0][0] + ans[0][1] + ans[1][0] + ans[1][1]) / Mint(N).pow(ls[N + M])) << "; "
<< ans[0][0] << " " << ans[0][1] << " " << ans[1][0] << " " << ans[1][1] << endl;
#endif
}
return 0;
}