結果
| 問題 |
No.1712 Read and Pile
|
| コンテスト | |
| ユーザー |
 hos.lyric
|
| 提出日時 | 2021-10-16 00:12:53 |
| 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 | 14,352 bytes |
| コンパイル時間 | 3,171 ms |
| コンパイル使用メモリ | 153,376 KB |
| 実行使用メモリ | 60,300 KB |
| 最終ジャッジ日時 | 2024-09-17 19:05:44 |
| 合計ジャッジ時間 | 50,102 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 35 TLE * 5 |
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>;
template <class T, class S, class OpTT, class OpST, class OpSS>
struct SegmentTree {
const OpTT opTT;
const OpST opST;
const OpSS opSS;
const T idT;
const S idS;
int n;
vector<T> ts;
vector<S> ss;
SegmentTree(int n_, const OpTT opTT, const OpST opST, const OpSS opSS,
const T &idT, const S &idS)
: opTT(opTT), opST(opST), opSS(opSS), idT(idT), idS(idS) {
for (n = 1; n < n_; n <<= 1) {}
ts.assign(n << 1, idT);
ss.assign(n << 1, idS);
}
T &at(int a) {
return ts[n + a];
}
void build() {
for (int a = n; --a; ) ts[a] = opTT(ts[a << 1], ts[a << 1 | 1]);
}
void update(int a, int b, const S &s) {
update(1, 0, n, a, b, s);
}
T calc(int a, int b) {
return calc(1, 0, n, a, b);
}
private:
void update(int u, int l, int r, int a, int b, const S &s) {
if (a < l) a = l;
if (b > r) b = r;
if (a >= b) return;
if (a == l && b == r) {
ts[u] = opST(s, ts[u], r - l);
ss[u] = opSS(s, ss[u]);
return;
}
const int uL = u << 1, uR = u << 1 | 1;
const int mid = (l + r) >> 1;
// speed-up: if (ss[u] != idS)
if (ss[u])
{
ts[uL] = opST(ss[u], ts[uL], mid - l);
ts[uR] = opST(ss[u], ts[uR], r - mid);
ss[uL] = opSS(ss[u], ss[uL]);
ss[uR] = opSS(ss[u], ss[uR]);
ss[u] = idS;
}
update(uL, l, mid, a, b, s);
update(uR, mid, r, a, b, s);
ts[u] = opTT(ts[uL], ts[uR]);
return;
}
T calc(int u, int l, int r, int a, int b) {
if (a < l) a = l;
if (b > r) b = r;
if (a >= b) return idT;
if (a == l && b == r) {
return ts[u];
}
const int uL = u << 1, uR = u << 1 | 1;
const int mid = (l + r) >> 1;
// speed-up: if (ss[u] != idS)
if (ss[u])
{
ts[uL] = opST(ss[u], ts[uL], mid - l);
ts[uR] = opST(ss[u], ts[uR], r - mid);
ss[uL] = opSS(ss[u], ss[uL]);
ss[uR] = opSS(ss[u], ss[uR]);
ss[u] = idS;
}
const T resL = calc(uL, l, mid, a, b);
const T resR = calc(uR, mid, r, a, b);
ts[u] = opTT(ts[uL], ts[uR]);
return opTT(resL, resR);
}
};
namespace s0 {
using T = Int;
using S = Int;
T opTT(const T &t0, const T &t1) {
return t0 + t1;
}
T opST(const S &s, const T &t, int sz) {
return s * sz + t;
}
S opSS(const S &s0, const S &s1) {
return s0 + s1;
}
constexpr T idT = 0;
constexpr S idS = 0;
using SegTree = SegmentTree<T, S, decltype(&opTT), decltype(&opST), decltype(&opSS)>;
SegTree factory(int n) {
return SegTree(n, &opTT, &opST, &opSS, idT, idS);
}
} // namespace s0
namespace segtree2 {
struct T {
Mint x[2];
T() : x{} {}
};
using S = Mint;
T opTT(const T &t0, const T &t1) {
T tt;
tt.x[0] = t0.x[0] + t1.x[0];
tt.x[1] = t0.x[1] + t1.x[1];
return tt;
}
T opST(const S &s, const T &t, int sz) {
T tt;
tt.x[0] = t.x[0];
tt.x[1] = t.x[1] + s * t.x[0];
return tt;
}
S opSS(const S &s0, const S &s1) {
return s0 + s1;
}
const T idT;
constexpr S idS = 0;
using SegTree = SegmentTree<T, S, decltype(&opTT), decltype(&opST), decltype(&opSS)>;
SegTree factory(int n) {
return SegTree(n, &opTT, &opST, &opSS, idT, idS);
}
} // namespace segtree2
namespace segtree3 {
struct T {
Mint x[3];
T() : x{} {}
};
using S = Mint;
T opTT(const T &t0, const T &t1) {
T tt;
tt.x[0] = t0.x[0] + t1.x[0];
tt.x[1] = t0.x[1] + t1.x[1];
tt.x[2] = t0.x[2] + t1.x[2];
return tt;
}
T opST(const S &s, const T &t, int sz) {
T tt;
tt.x[0] = t.x[0];
tt.x[1] = t.x[1] + s * t.x[0];
tt.x[2] = t.x[2] + s * (2 * t.x[1] + s * t.x[0]);
return tt;
}
S opSS(const S &s0, const S &s1) {
return s0 + s1;
}
const T idT;
constexpr S idS = 0;
using SegTree = SegmentTree<T, S, decltype(&opTT), decltype(&opST), decltype(&opSS)>;
SegTree factory(int n) {
return SegTree(n, &opTT, &opST, &opSS, idT, idS);
}
} // namespace segtree3
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);
auto seg0 = s0::factory(N + M);
auto seg1 = segtree2::factory(N + M);
auto seg2 = segtree3::factory(N + M);
for (int i = 0; i < N + M; ++i) {
if (A[i] == -2) {
seg1.at(i).x[0] = pw0[ls[i]] * invPw1[ls[i + 1]];
seg2.at(i).x[0] = pw0[ls[i]] * invPw2[ls[i + 1]];
}
}
seg1.build();
seg2.build();
for (int i = 0; i < N + M; ++i) {
// get
if (i >= N) {
if (A[i] != -2) {
{
const int m = seg0.calc(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 auto res1 = seg1.calc(app[A[i]], i);
const auto res2 = seg2.calc(app[A[i]], i);
Mint tmp = 0;
tmp += pw1[ls[i]] * (res1.x[0] + res1.x[1]);
tmp += pw1[ls[i]] * (Mint(N - 1) * res1.x[0] - res1.x[1])
- pw2[ls[i]] * (Mint(N - 1) * res2.x[0] - res2.x[1]);
tmp *= pw0[ls[N + M] - ls[i + 1]];
ans[1][0] += tmp;
}
} else {
{
const auto res1 = seg1.calc(0, i);
const auto res2 = seg2.calc(0, i);
Mint tmp = 0;
// tmp += pw1[ls[i]] * (Mint(N) * res1.x[0] + Mint(N - 1) * res1.x[1] - res1.x[2]);
// tmp += pw1[ls[i]] * (Mint(N) * Mint(N - 1) * res1.x[0] - Mint(2 * N - 1) * res1.x[1] + res1.x[2])
tmp += pw1[ls[i]] * (Mint(N) * res1.x[0] + Mint(N - 1) * res1.x[1]);
tmp += pw1[ls[i]] * (Mint(N) * Mint(N - 1) * res1.x[0] - Mint(2 * N - 1) * res1.x[1])
- pw2[ls[i]] * (Mint(N) * Mint(N - 1) * res2.x[0] - Mint(2 * N - 1) * res2.x[1] + res2.x[2]);
tmp *= pw0[ls[N + M] - ls[i + 1]];
ans[1][1] += tmp;
}
}
}
// add
if (A[i] != -2) {
seg0.update(app[A[i]], i, 1);
seg1.update(app[A[i]], i, 1);
seg2.update(app[A[i]], i, 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);
auto seg1 = segtree2::factory(N + M);
auto seg2 = segtree2::factory(N + M);
for (int i = 0; i < N + M; ++i) {
if (A[i] == -2) {
seg1.at(i).x[0] = pw0[ls[i]] * invPw1[ls[i + 1]];
seg2.at(i).x[0] = pw0[ls[i]] * invPw2[ls[i + 1]];
}
}
seg1.build();
seg2.build();
for (int i = 0; i < M + N; ++i) {
// get
{
if (A[i] != -2) {
{}
{
const auto res1 = seg1.calc(app[A[i]], min(i, M));
const auto res2 = seg2.calc(app[A[i]], min(i, M));
Mint tmp = 0;
tmp += pw1[ls[i]] * (res1.x[0] + res1.x[1]);
tmp += pw1[ls[i]] * (Mint(N - 1) * res1.x[0] - res1.x[1])
- pw2[ls[i]] * (Mint(N - 1) * res2.x[0] - res2.x[1]);
tmp *= pw0[ls[N + M] - ls[i + 1]];
ans[0][1] += tmp;
}
} else {
{}
}
}
// add
if (A[i] != -2) {
seg1.update(app[A[i]], i, 1);
seg2.update(app[A[i]], i, 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;
}