結果

問題 No.2250 Split Permutation
ユーザー 👑 emthrmemthrm
提出日時 2023-03-17 22:03:40
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 70 ms / 3,000 ms
コード長 10,517 bytes
コンパイル時間 3,114 ms
コンパイル使用メモリ 259,112 KB
実行使用メモリ 7,168 KB
最終ジャッジ日時 2024-09-18 11:03:33
合計ジャッジ時間 5,083 ms
ジャッジサーバーID
(参考情報)
judge2 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 35
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ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 998244353;
// constexpr int MOD = 1000000007;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U>
inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U>
inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
IOSetup() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
std::cout << fixed << setprecision(20);
}
} iosetup;
#ifndef ARBITRARY_MODINT
# include <cassert>
#endif
#include <compare>
// #include <numeric>
#ifndef ARBITRARY_MODINT
template <int M>
struct MInt {
unsigned int v;
MInt() : v(0) {}
MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {}
static constexpr int get_mod() { return M; }
static void set_mod(const int divisor) { assert(divisor == M); }
static void init(const int x) {
inv<true>(x);
fact(x);
fact_inv(x);
}
template <bool MEMOIZES = false>
static MInt inv(const int n) {
// assert(0 <= n && n < M && std::gcd(n, M) == 1);
static std::vector<MInt> inverse{0, 1};
const int prev = inverse.size();
if (n < prev) return inverse[n];
if constexpr (MEMOIZES) {
// "n!" and "M" must be disjoint.
inverse.resize(n + 1);
for (int i = prev; i <= n; ++i) {
inverse[i] = -inverse[M % i] * (M / i);
}
return inverse[n];
}
int u = 1, v = 0;
for (unsigned int a = n, b = M; b;) {
const unsigned int q = a / b;
std::swap(a -= q * b, b);
std::swap(u -= q * v, v);
}
return u;
}
static MInt fact(const int n) {
static std::vector<MInt> factorial{1};
const int prev = factorial.size();
if (n >= prev) {
factorial.resize(n + 1);
for (int i = prev; i <= n; ++i) {
factorial[i] = factorial[i - 1] * i;
}
}
return factorial[n];
}
static MInt fact_inv(const int n) {
static std::vector<MInt> f_inv{1};
const int prev = f_inv.size();
if (n >= prev) {
f_inv.resize(n + 1);
f_inv[n] = inv(fact(n).v);
for (int i = n; i > prev; --i) {
f_inv[i - 1] = f_inv[i] * i;
}
}
return f_inv[n];
}
static MInt nCk(const int n, const int k) {
if (n < 0 || n < k || k < 0) return 0;
return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
fact_inv(n - k) * fact_inv(k));
}
static MInt nPk(const int n, const int k) {
return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k);
}
static MInt nHk(const int n, const int k) {
return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k));
}
static MInt large_nCk(long long n, const int k) {
if (n < 0 || n < k || k < 0) return 0;
inv<true>(k);
MInt res = 1;
for (int i = 1; i <= k; ++i) {
res *= inv(i) * n--;
}
return res;
}
MInt pow(long long exponent) const {
MInt res = 1, tmp = *this;
for (; exponent > 0; exponent >>= 1) {
if (exponent & 1) res *= tmp;
tmp *= tmp;
}
return res;
}
MInt& operator+=(const MInt& x) {
if (std::cmp_greater_equal(v += x.v, M)) v -= M;
return *this;
}
MInt& operator-=(const MInt& x) {
if (std::cmp_greater_equal(v += M - x.v, M)) v -= M;
return *this;
}
MInt& operator*=(const MInt& x) {
v = static_cast<unsigned long long>(v) * x.v % M;
return *this;
}
MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }
auto operator<=>(const MInt& x) const = default;
MInt& operator++() {
if (std::cmp_equal(++v, M)) v = 0;
return *this;
}
MInt operator++(int) {
const MInt res = *this;
++*this;
return res;
}
MInt& operator--() {
v = (v == 0 ? M - 1 : v - 1);
return *this;
}
MInt operator--(int) {
const MInt res = *this;
--*this;
return res;
}
MInt operator+() const { return *this; }
MInt operator-() const { return MInt(v ? M - v : 0); }
MInt operator+(const MInt& x) const { return MInt(*this) += x; }
MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
MInt operator*(const MInt& x) const { return MInt(*this) *= x; }
MInt operator/(const MInt& x) const { return MInt(*this) /= x; }
friend std::ostream& operator<<(std::ostream& os, const MInt& x) {
return os << x.v;
}
friend std::istream& operator>>(std::istream& is, MInt& x) {
long long v;
is >> v;
x = MInt(v);
return is;
}
};
#else // ARBITRARY_MODINT
template <int ID>
struct MInt {
unsigned int v;
MInt() : v(0) {}
MInt(const long long x) : v(x >= 0 ? x % mod() : x % mod() + mod()) {}
static int get_mod() { return mod(); }
static void set_mod(const int divisor) { mod() = divisor; }
static void init(const int x) {
inv<true>(x);
fact(x);
fact_inv(x);
}
template <bool MEMOIZES = false>
static MInt inv(const int n) {
// assert(0 <= n && n < mod() && std::gcd(x, mod()) == 1);
static std::vector<MInt> inverse{0, 1};
const int prev = inverse.size();
if (n < prev) return inverse[n];
if constexpr (MEMOIZES) {
// "n!" and "M" must be disjoint.
inverse.resize(n + 1);
for (int i = prev; i <= n; ++i) {
inverse[i] = -inverse[mod() % i] * (mod() / i);
}
return inverse[n];
}
int u = 1, v = 0;
for (unsigned int a = n, b = mod(); b;) {
const unsigned int q = a / b;
std::swap(a -= q * b, b);
std::swap(u -= q * v, v);
}
return u;
}
static MInt fact(const int n) {
static std::vector<MInt> factorial{1};
const int prev = factorial.size();
if (n >= prev) {
factorial.resize(n + 1);
for (int i = prev; i <= n; ++i) {
factorial[i] = factorial[i - 1] * i;
}
}
return factorial[n];
}
static MInt fact_inv(const int n) {
static std::vector<MInt> f_inv{1};
const int prev = f_inv.size();
if (n >= prev) {
f_inv.resize(n + 1);
f_inv[n] = inv(fact(n).v);
for (int i = n; i > prev; --i) {
f_inv[i - 1] = f_inv[i] * i;
}
}
return f_inv[n];
}
static MInt nCk(const int n, const int k) {
if (n < 0 || n < k || k < 0) return 0;
return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
fact_inv(n - k) * fact_inv(k));
}
static MInt nPk(const int n, const int k) {
return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k);
}
static MInt nHk(const int n, const int k) {
return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k));
}
static MInt large_nCk(long long n, const int k) {
if (n < 0 || n < k || k < 0) return 0;
inv<true>(k);
MInt res = 1;
for (int i = 1; i <= k; ++i) {
res *= inv(i) * n--;
}
return res;
}
MInt pow(long long exponent) const {
MInt res = 1, tmp = *this;
for (; exponent > 0; exponent >>= 1) {
if (exponent & 1) res *= tmp;
tmp *= tmp;
}
return res;
}
MInt& operator+=(const MInt& x) {
if (std::cmp_greater_equal(v += x.v, mod())) v -= mod();
return *this;
}
MInt& operator-=(const MInt& x) {
if (std::cmp_greater_equal(v += mod() - x.v, mod())) v -= mod();
return *this;
}
MInt& operator*=(const MInt& x) {
v = static_cast<unsigned long long>(v) * x.v % mod();
return *this;
}
MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }
auto operator<=>(const MInt& x) const = default;
MInt& operator++() {
if (std::cmp_equal(++v, mod())) v = 0;
return *this;
}
MInt operator++(int) {
const MInt res = *this;
++*this;
return res;
}
MInt& operator--() {
v = (v == 0 ? mod() - 1 : v - 1);
return *this;
}
MInt operator--(int) {
const MInt res = *this;
--*this;
return res;
}
MInt operator+() const { return *this; }
MInt operator-() const { return MInt(v ? mod() - v : 0); }
MInt operator+(const MInt& x) const { return MInt(*this) += x; }
MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
MInt operator*(const MInt& x) const { return MInt(*this) *= x; }
MInt operator/(const MInt& x) const { return MInt(*this) /= x; }
friend std::ostream& operator<<(std::ostream& os, const MInt& x) {
return os << x.v;
}
friend std::istream& operator>>(std::istream& is, MInt& x) {
long long v;
is >> v;
x = MInt(v);
return is;
}
private:
static int& mod() {
static int divisor = 0;
return divisor;
}
};
#endif // ARBITRARY_MODINT
#include <bit>
template <typename Abelian>
struct FenwickTree {
explicit FenwickTree(const int n, const Abelian ID = 0)
: n(n), ID(ID), data(n, ID) {}
void add(int idx, const Abelian val) {
for (; idx < n; idx |= idx + 1) {
data[idx] += val;
}
}
Abelian sum(int idx) const {
Abelian res = ID;
for (--idx; idx >= 0; idx = (idx & (idx + 1)) - 1) {
res += data[idx];
}
return res;
}
Abelian sum(const int left, const int right) const {
return left < right ? sum(right) - sum(left) : ID;
}
Abelian operator[](const int idx) const { return sum(idx, idx + 1); }
int lower_bound(Abelian val) const {
if (val <= ID) [[unlikely]] return 0;
int res = 0;
for (int mask = std::bit_ceil(static_cast<unsigned int>(n + 1)) >> 1;
mask > 0; mask >>= 1) {
const int idx = res + mask - 1;
if (idx < n && data[idx] < val) {
val -= data[idx];
res += mask;
}
}
return res;
}
private:
const int n;
const Abelian ID;
std::vector<Abelian> data;
};
int main() {
using ModInt = MInt<MOD>;
int n; cin >> n;
vector<int> p(n); REP(i, n) cin >> p[i], --p[i];
vector<int> ord(n);
iota(ALL(ord), 0);
ranges::sort(ord, {}, [&](const int i) -> int { return p[i]; });
vector<ModInt> p2(n, 1);
FOR(i, 1, n) p2[i] = p2[i - 1] * 2;
FenwickTree<int> num(n);
FenwickTree<ModInt> bit(n);
ModInt ans = 0;
for (const int i : ord) {
ans += p2[n - 1] * num.sum(i, n) - bit.sum(i, n) * p2[i];
num.add(i, 1);
bit.add(i, p2[n - 1 - i]);
}
cout << ans << '\n';
return 0;
}
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