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linear_algebra_matrix/test/upper_trinaglular_matrix.yuki3530.test.cpp
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- Last update: 2026-05-06 21:05:36+09:00
- Problem: https://yukicoder.me/problems/no/3530
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Code
#define PROBLEM "https://yukicoder.me/problems/no/3530"
#include "../upper_triangular_matrix.hpp"
#include "../../modint.hpp"
#include <algorithm>
#include <iostream>
#include <map>
#include <utility>
#include <vector>
#include <atcoder/segtree>
using namespace std;
using S = UpperTriangular3d<ModInt998244353>;
S op(const S &l, const S &r) { return l * r; }
S e() { return S{1, 0, 0, 1, 0, 1}; }
S GenR() { return S{ModInt998244353(3) / 4, ModInt998244353(1) / 4, 0, 1, 0, 1}; }
S GenL() { return S{1, 0, 0, ModInt998244353(3) / 4, ModInt998244353(1) / 4, 1}; }
ModInt998244353 Solve(vector<pair<int, int>> ps) {
vector<tuple<int, int, int>> yxis;
for (int i = 0; i < (int)ps.size(); ++i) {
auto [x, y] = ps.at(i);
yxis.emplace_back(y, x, i);
}
sort(yxis.begin(), yxis.end());
const auto L = GenL(), R = GenR();
const vector<S> init(ps.size(), R);
atcoder::segtree<S, op, e> seg(init);
int last_x = -1e9;
ModInt998244353 ret = 0;
map<int, vector<pair<int, int>>> x2yis;
for (int i = 0; i < (int)ps.size(); ++i) {
auto [x, y] = ps.at(i);
x2yis[x].emplace_back(y, i);
}
for (auto [x, yis] : x2yis) {
const ModInt998244353 dx = x - last_x;
ret += dx * seg.all_prod().a02;
for (auto [y, i] : yis) {
const int idx =
lower_bound(yxis.begin(), yxis.end(), make_tuple(y, x, i)) - yxis.begin();
seg.set(idx, L);
}
last_x = x;
}
return ret;
}
int main() {
int N;
cin >> N;
vector<pair<int, int>> xy(N);
for (auto &[x, y] : xy) cin >> x >> y;
const ModInt998244353 coeff = ModInt998244353(4).pow(N);
ModInt998244353 ret1 = Solve(xy) * coeff;
for (auto &[x, y] : xy) swap(x, y);
ModInt998244353 ret2 = Solve(xy) * coeff;
cout << (ret1 + ret2) * 2 << '\n';
}#line 1 "linear_algebra_matrix/test/upper_trinaglular_matrix.yuki3530.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/3530"
#line 2 "linear_algebra_matrix/upper_triangular_matrix.hpp"
template <class T> struct UpperTriangular3d {
static T explicit_init_required() = delete;
T a00 = this->explicit_init_required(), a01 = this->explicit_init_required(),
a02 = this->explicit_init_required();
T a11 = this->explicit_init_required(), a12 = this->explicit_init_required();
T a22 = this->explicit_init_required();
UpperTriangular3d operator*(const UpperTriangular3d &r) const {
return UpperTriangular3d{
.a00 = this->a00 * r.a00,
.a01 = this->a00 * r.a01 + this->a01 * r.a11,
.a02 = this->a00 * r.a02 + this->a01 * r.a12 + this->a02 * r.a22,
.a11 = this->a11 * r.a11,
.a12 = this->a11 * r.a12 + this->a12 * r.a22,
.a22 = this->a22 * r.a22,
};
}
UpperTriangular3d operator-() const {
return UpperTriangular3d{
.a00 = -this->a00,
.a01 = -this->a01,
.a02 = -this->a02,
.a11 = -this->a11,
.a12 = -this->a12,
.a22 = -this->a22,
};
}
UpperTriangular3d operator+(const UpperTriangular3d &r) const {
return UpperTriangular3d{
.a00 = this->a00 + r.a00,
.a01 = this->a01 + r.a01,
.a02 = this->a02 + r.a02,
.a11 = this->a11 + r.a11,
.a12 = this->a12 + r.a12,
.a22 = this->a22 + r.a22,
};
}
auto operator<=>(const UpperTriangular3d &) const = default;
};
#line 2 "modint.hpp"
#include <cassert>
#include <iostream>
#include <set>
#include <vector>
template <int md> struct ModInt {
static_assert(md > 1);
using lint = long long;
constexpr static int mod() { return md; }
static int get_primitive_root() {
static int primitive_root = 0;
if (!primitive_root) {
primitive_root = [&]() {
std::set<int> fac;
int v = md - 1;
for (lint i = 2; i * i <= v; i++)
while (v % i == 0) fac.insert(i), v /= i;
if (v > 1) fac.insert(v);
for (int g = 1; g < md; g++) {
bool ok = true;
for (auto i : fac)
if (ModInt(g).pow((md - 1) / i) == 1) {
ok = false;
break;
}
if (ok) return g;
}
return -1;
}();
}
return primitive_root;
}
int val_;
int val() const noexcept { return val_; }
constexpr ModInt() : val_(0) {}
constexpr ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }
constexpr ModInt(lint v) { _setval(v % md + md); }
constexpr explicit operator bool() const { return val_ != 0; }
constexpr ModInt operator+(const ModInt &x) const {
return ModInt()._setval((lint)val_ + x.val_);
}
constexpr ModInt operator-(const ModInt &x) const {
return ModInt()._setval((lint)val_ - x.val_ + md);
}
constexpr ModInt operator*(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.val_ % md);
}
constexpr ModInt operator/(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.inv().val() % md);
}
constexpr ModInt operator-() const { return ModInt()._setval(md - val_); }
constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt(a) + x; }
friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt(a) - x; }
friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt(a) * x; }
friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt(a) / x; }
constexpr bool operator==(const ModInt &x) const { return val_ == x.val_; }
constexpr bool operator!=(const ModInt &x) const { return val_ != x.val_; }
constexpr bool operator<(const ModInt &x) const {
return val_ < x.val_;
} // To use std::map<ModInt, T>
friend std::istream &operator>>(std::istream &is, ModInt &x) {
lint t;
return is >> t, x = ModInt(t), is;
}
constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) {
return os << x.val_;
}
constexpr ModInt pow(lint n) const {
ModInt ans = 1, tmp = *this;
while (n) {
if (n & 1) ans *= tmp;
tmp *= tmp, n >>= 1;
}
return ans;
}
static constexpr int cache_limit = std::min(md, 1 << 21);
static std::vector<ModInt> facs, facinvs, invs;
constexpr static void _precalculation(int N) {
const int l0 = facs.size();
if (N > md) N = md;
if (N <= l0) return;
facs.resize(N), facinvs.resize(N), invs.resize(N);
for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;
facinvs[N - 1] = facs.back().pow(md - 2);
for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);
for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];
}
constexpr ModInt inv() const {
if (this->val_ < cache_limit) {
if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0};
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return invs[this->val_];
} else {
return this->pow(md - 2);
}
}
constexpr static ModInt fac(int n) {
assert(n >= 0);
if (n >= md) return ModInt(0);
while (n >= int(facs.size())) _precalculation(facs.size() * 2);
return facs[n];
}
constexpr static ModInt facinv(int n) {
assert(n >= 0);
if (n >= md) return ModInt(0);
while (n >= int(facs.size())) _precalculation(facs.size() * 2);
return facinvs[n];
}
constexpr static ModInt doublefac(int n) {
assert(n >= 0);
if (n >= md) return ModInt(0);
long long k = (n + 1) / 2;
return (n & 1) ? ModInt::fac(k * 2) / (ModInt(2).pow(k) * ModInt::fac(k))
: ModInt::fac(k) * ModInt(2).pow(k);
}
constexpr static ModInt nCr(int n, int r) {
assert(n >= 0);
if (r < 0 or n < r) return ModInt(0);
return ModInt::fac(n) * ModInt::facinv(r) * ModInt::facinv(n - r);
}
constexpr static ModInt nPr(int n, int r) {
assert(n >= 0);
if (r < 0 or n < r) return ModInt(0);
return ModInt::fac(n) * ModInt::facinv(n - r);
}
static ModInt binom(long long n, long long r) {
static long long bruteforce_times = 0;
if (r < 0 or n < r) return ModInt(0);
if (n <= bruteforce_times or n < (int)facs.size()) return ModInt::nCr(n, r);
r = std::min(r, n - r);
assert((int)r == r);
ModInt ret = ModInt::facinv(r);
for (int i = 0; i < r; ++i) ret *= n - i;
bruteforce_times += r;
return ret;
}
// Multinomial coefficient, (k_1 + k_2 + ... + k_m)! / (k_1! k_2! ... k_m!)
// Complexity: O(sum(ks))
// Verify: https://yukicoder.me/problems/no/3178
template <class Vec> static ModInt multinomial(const Vec &ks) {
ModInt ret{1};
int sum = 0;
for (int k : ks) {
assert(k >= 0);
ret *= ModInt::facinv(k), sum += k;
}
return ret * ModInt::fac(sum);
}
template <class... Args> static ModInt multinomial(Args... args) {
int sum = (0 + ... + args);
ModInt result = (1 * ... * ModInt::facinv(args));
return ModInt::fac(sum) * result;
}
// Catalan number, C_n = binom(2n, n) / (n + 1) = # of Dyck words of length 2n
// C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, ...
// https://oeis.org/A000108
// Complexity: O(n)
static ModInt catalan(int n) {
if (n < 0) return ModInt(0);
return ModInt::fac(n * 2) * ModInt::facinv(n + 1) * ModInt::facinv(n);
}
ModInt sqrt() const {
if (val_ == 0) return 0;
if (md == 2) return val_;
if (pow((md - 1) / 2) != 1) return 0;
ModInt b = 1;
while (b.pow((md - 1) / 2) == 1) b += 1;
int e = 0, m = md - 1;
while (m % 2 == 0) m >>= 1, e++;
ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
x *= (*this);
ModInt z = b.pow(m);
while (y != 1) {
int j = 0;
ModInt t = y;
while (t != 1) j++, t *= t;
z = z.pow(1LL << (e - j - 1));
x *= z, z *= z, y *= z;
e = j;
}
return ModInt(std::min(x.val_, md - x.val_));
}
};
template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};
using ModInt998244353 = ModInt<998244353>;
// using mint = ModInt<998244353>;
// using mint = ModInt<1000000007>;
#line 4 "linear_algebra_matrix/test/upper_trinaglular_matrix.yuki3530.test.cpp"
#include <algorithm>
#line 7 "linear_algebra_matrix/test/upper_trinaglular_matrix.yuki3530.test.cpp"
#include <map>
#include <utility>
#line 10 "linear_algebra_matrix/test/upper_trinaglular_matrix.yuki3530.test.cpp"
#include <atcoder/segtree>
using namespace std;
using S = UpperTriangular3d<ModInt998244353>;
S op(const S &l, const S &r) { return l * r; }
S e() { return S{1, 0, 0, 1, 0, 1}; }
S GenR() { return S{ModInt998244353(3) / 4, ModInt998244353(1) / 4, 0, 1, 0, 1}; }
S GenL() { return S{1, 0, 0, ModInt998244353(3) / 4, ModInt998244353(1) / 4, 1}; }
ModInt998244353 Solve(vector<pair<int, int>> ps) {
vector<tuple<int, int, int>> yxis;
for (int i = 0; i < (int)ps.size(); ++i) {
auto [x, y] = ps.at(i);
yxis.emplace_back(y, x, i);
}
sort(yxis.begin(), yxis.end());
const auto L = GenL(), R = GenR();
const vector<S> init(ps.size(), R);
atcoder::segtree<S, op, e> seg(init);
int last_x = -1e9;
ModInt998244353 ret = 0;
map<int, vector<pair<int, int>>> x2yis;
for (int i = 0; i < (int)ps.size(); ++i) {
auto [x, y] = ps.at(i);
x2yis[x].emplace_back(y, i);
}
for (auto [x, yis] : x2yis) {
const ModInt998244353 dx = x - last_x;
ret += dx * seg.all_prod().a02;
for (auto [y, i] : yis) {
const int idx =
lower_bound(yxis.begin(), yxis.end(), make_tuple(y, x, i)) - yxis.begin();
seg.set(idx, L);
}
last_x = x;
}
return ret;
}
int main() {
int N;
cin >> N;
vector<pair<int, int>> xy(N);
for (auto &[x, y] : xy) cin >> x >> y;
const ModInt998244353 coeff = ModInt998244353(4).pow(N);
ModInt998244353 ret1 = Solve(xy) * coeff;
for (auto &[x, y] : xy) swap(x, y);
ModInt998244353 ret2 = Solve(xy) * coeff;
cout << (ret1 + ret2) * 2 << '\n';
}