結果
| 問題 |
No.3100 Parallel Translated
|
| コンテスト | |
| ユーザー |
 noya2
|
| 提出日時 | 2025-01-28 22:41:21 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 2,000 ms |
| コード長 | 22,521 bytes |
| コンパイル時間 | 3,094 ms |
| コンパイル使用メモリ | 282,696 KB |
| 実行使用メモリ | 7,720 KB |
| 最終ジャッジ日時 | 2025-04-11 20:50:11 |
| 合計ジャッジ時間 | 4,082 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 32 |
ソースコード
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;
#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
for (auto &x : v) is >> x;
return is;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
template<typename T>
void out(const vector<vector<T>> &vv){
int s = (int)vv.size();
for (int i = 0; i < s; i++) out(vv[i]);
}
struct IoSetup {
IoSetup(){
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetup_noya2;
} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{
const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 = 998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";
void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }
} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
namespace noya2{
unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
if (a == 0 || b == 0) return a + b;
int n = __builtin_ctzll(a); a >>= n;
int m = __builtin_ctzll(b); b >>= m;
while (a != b) {
int mm = __builtin_ctzll(a - b);
bool f = a > b;
unsigned long long c = f ? a : b;
b = f ? b : a;
a = (c - b) >> mm;
}
return a << std::min(n, m);
}
template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }
long long sqrt_fast(long long n) {
if (n <= 0) return 0;
long long x = sqrt(n);
while ((x + 1) * (x + 1) <= n) x++;
while (x * x > n) x--;
return x;
}
template<typename T> T floor_div(const T n, const T d) {
assert(d != 0);
return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}
template<typename T> T ceil_div(const T n, const T d) {
assert(d != 0);
return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}
template<typename T> void uniq(std::vector<T> &v){
std::sort(v.begin(),v.end());
v.erase(unique(v.begin(),v.end()),v.end());
}
template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }
template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }
template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }
} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;
namespace noya2{
/* ~ (. _________ . /) */
}
using namespace noya2;
#line 2 "c.cpp"
namespace geometry2d {
template<class Rat>
requires std::constructible_from<Rat, int> && std::totally_ordered<Rat>
constexpr int sign(const Rat &x){
const Rat Rat0 = Rat(0);
return (x < Rat0 ? -1 : x > Rat0 ? 1 : 0);
}
template<class Rat>
struct point {
Rat x, y;
point () {}
point (Rat _x, Rat _y) : x(_x), y(_y) {}
point &operator+=(const point &r){
x += r.x;
y += r.y;
return *this;
}
point &operator-=(const point &r){
x -= r.x;
y -= r.y;
return *this;
}
point operator+() const {
return *this;
}
point operator-() const {
x = -x;
y = -y;
return *this;
}
point &operator*=(const Rat &a){
x *= a;
y *= a;
return *this;
}
point &operator/=(const Rat &a){
x /= a;
y /= a;
return *this;
}
friend point operator+(const point& lhs, const point& rhs){
return point(lhs) += rhs;
}
friend point operator-(const point& lhs, const point& rhs){
return point(lhs) -= rhs;
}
friend point operator*(const point& lhs, const Rat& a){
return point(lhs) *= a;
}
friend point operator*(const Rat& a, const point& rhs){
return point(rhs) *= a;
}
friend point operator/(const point& lhs, const Rat& a){
return point(lhs) /= a;
}
auto operator<=>(const point&) const = default;
friend std::ostream &operator<<(std::ostream &os, const point& p){
return os << p.x << ' ' << p.y;
}
friend std::istream &operator>>(std::istream &is, point &a){
Rat _x, _y; is >> _x >> _y;
a = point(_x, _y);
return (is);
}
friend Rat norm(const point &a) {
return a.x*a.x + a.y*a.y;
}
friend Rat dot(const point &a, const point &b){
return a.x*b.x + a.y*b.y;
}
friend Rat cross(const point &a, const point &b){
return a.x*b.y - a.y*b.x;
}
friend int quadrant_atan2(const point &a){
// not origin point
// ceil ( atan2(y,x) / (pi/2) )
int signx = sign(a.x);
int signy = sign(a.y);
if (signx <= 0 && signy < 0) return -1;
if (signx > 0 && signy <= 0) return 0;
if (signx >= 0 && signy > 0) return 1;
if (signx < 0 && signy >= 0) return 2;
// origin point x == 0 && y == 0
return 0;
}
friend int ccw(const point &a, point b, point c){
b -= a;
c -= a;
int signcr = sign(cross(b, c));
if (signcr > 0){
// ccw
// c
// a --> b
return 1;
}
if (signcr < 0){
// cw
// a --> b
// c
return -1;
}
if (sign(dot(b, c)) < 0){
// c a --> b
return 2;
}
if (norm(b) < norm(c)){
// a --> b c
return -2;
}
// a - c -> b
return 0;
}
friend point rot90(const point &a){
return point(-a.y, a.x);
}
};
template<class Rat>
using vec = point<Rat>;
template<class Rat>
struct arg_less {
constexpr bool operator()(const point<Rat> &l, const point<Rat> &r){
int lq = quadrant_atan2(l);
int rq = quadrant_atan2(r);
if (lq == rq){
return sign(cross(l,r)) > 0;
}
return lq < rq;
}
};
template<class Rat>
void arg_sort(std::vector<point<Rat>> &a){
sort(a.begin(), a.end(), arg_less<Rat>{});
}
template<class Point>
std::vector<int> upper_convex_hull_index(const std::vector<Point> &a){
if (a.empty()) return {};
std::vector<int> ids(a.size()); iota(ids.begin(), ids.end(), 0);
std::sort(ids.begin(), ids.end(), [&](int l, int r){
return a[l] < a[r];
});
std::vector<int> st(a.size());
int ptr = 0;
for (int i : ids){
if (ptr >= 1 && a[st[ptr-1]].x == a[i].x) ptr--;
while (ptr >= 2){
int c = st[ptr-1];
int p = st[ptr-2];
if (sign(cross(a[i] - a[c], a[c] - a[p])) > 0){
break;
}
ptr--;
}
st[ptr++] = i;
}
st.resize(ptr);
return st;
}
template<class Point>
std::vector<int> lower_convex_hull_index(const std::vector<Point> &a){
if (a.empty()) return {};
std::vector<int> ids(a.size()); iota(ids.begin(), ids.end(), 0);
std::sort(ids.begin(), ids.end(), [&](int l, int r){
return a[l] < a[r];
});
std::vector<int> st(a.size());
int ptr = 0;
for (int i : ids){
if (ptr >= 1 && a[st[ptr-1]].x == a[i].x) continue;
while (ptr >= 2){
int c = st[ptr-1];
int p = st[ptr-2];
if (sign(cross(a[c] - a[p], a[i] - a[c])) > 0){
break;
}
ptr--;
}
st[ptr++] = i;
}
st.resize(ptr);
return st;
}
template<class Point>
std::vector<int> convex_hull_index(const std::vector<Point> &a){
if (a.empty()) return {};
auto upper = upper_convex_hull_index(a);
auto lower = lower_convex_hull_index(a);
if (upper.size() == 1u){
// lower.size() == 1u
if (a[upper.front()] == a[lower.front()]){
return {upper.front()};
}
return {lower.front(), upper.front()};
}
if (a[upper.back()] == a[lower.back()]){
lower.pop_back();
}
lower.insert(lower.end(), upper.rbegin(), upper.rend());
if (a[upper.front()] == a[lower.front()]) lower.pop_back();
return lower;
}
template<class Rat>
struct line {
point<Rat> end0, end1;
line (const point<Rat> &_end0, const point<Rat> &_end1) : end0(_end0), end1(_end1) {
assert(end0 != end1);
}
auto operator<=>(const line &) const = default;
bool operator==(const line &that) const {
return is_parallel(*this, that) && has_common_point(*this, that.end0);
}
vec<Rat> direction() const {
return end1 - end0;
}
friend bool has_common_point(const line &a, const point<Rat> &b){
return sign(cross(a.direction(), b - a.end0)) == 0;
}
friend bool has_common_point(const line &a, const line &b){
return !is_parallel(a, b) || has_common_point(a, b.end0);
}
friend point<Rat> common_point(const line &a, const line &b){
// assert(has_common_point(a, b));
if (is_parallel(a, b)){
return a.end0;
}
return a.end0 + a.direction() * cross(b.end0 - a.end0, b.end1 - b.end0) / cross(a.direction(), b.direction());
}
friend point<Rat> projection(const line &a, const point<Rat> &b){
auto dir = a.direction();
return a.end0 + dir * (dot(dir, b - a.end0) / norm(dir));
}
friend point<Rat> reflection(const line &a, const point<Rat> &b){
auto prj = projection(a, b);
return prj + prj - b;
}
};
template<class Rat>
struct segment {
point<Rat> end0, end1;
segment (const point<Rat> &_end0, const point<Rat> &_end1) : end0(_end0), end1(_end1) {
assert(end0 != end1);
}
auto operator<=>(const segment &) const = default;
bool operator==(const segment &that) const {
return (end0 == that.end0 && end1 == that.end1) || (end1 == that.end0 && end0 == that.end1);
}
vec<Rat> direction() const {
return end1 - end0;
}
friend bool has_common_point(const segment &a, const segment &b){
return ccw(a.end0, a.end1, b.end0) * ccw(a.end0, a.end1, b.end1) <= 0
&& ccw(b.end0, b.end1, a.end0) * ccw(b.end0, b.end1, a.end1) <= 0;
}
friend bool has_common_point(const segment &a, const point<Rat> &b){
return ccw(a.end0, a.end1, b) == 0;
}
friend point<Rat> common_point(const segment &a, const segment &b){
// assert(has_common_point(a, b));
if (is_parallel(a, b)){
if (has_common_point(a, b.end0)){
return b.end0;
}
if (has_common_point(a, b.end1)){
return b.end1;
}
return a.end0;
}
return a.end0 + a.direction() * cross(b.end0 - a.end0, b.end1 - b.end0) / cross(a.direction(), b.direction());
}
line<Rat> as_line() const {
return line<Rat>(end0, end1);
}
};
template<class T>
concept hasDirection = requires (T a){
a.direction();
};
template<hasDirection T, hasDirection U>
bool is_parallel(const T &a, const U &b){
return sign(cross(a.direction(), b.direction())) == 0;
}
template<hasDirection T, hasDirection U>
bool is_orthogonal(const T &a, const U &b){
return sign(dot(a.direction(), b.direction())) == 0;
}
} // namespace geometry2d
#line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"
namespace noya2 {
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime_flag = is_prime_constexpr(n);
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u;
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root_flag = primitive_root_constexpr(m);
// constexpr long long primitive_root_constexpr(long long m){
// if (m == (1LL << 47) - (1LL << 24) + 1) return 3;
// return primitive_root_constexpr(static_cast<int>(m));
// }
} // namespace noya2
#line 6 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"
namespace noya2{
struct barrett {
unsigned int _m;
unsigned long long im;
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
unsigned long long z = a;
z *= b;
unsigned long long x = (unsigned long long)((__uint128_t(z) * im) >> 64);
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
template <int m>
struct static_modint {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
constexpr static_modint() : _v(0) {}
template<std::signed_integral T>
constexpr static_modint(T v){
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template<std::unsigned_integral T>
constexpr static_modint(T v){
_v = (unsigned int)(v % umod());
}
constexpr unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
constexpr mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
constexpr mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
constexpr mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (uint)(z % umod());
return *this;
}
constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
constexpr mint operator+() const { return *this; }
constexpr mint operator-() const { return mint() - *this; }
constexpr mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
constexpr mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend constexpr mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend constexpr mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend constexpr mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend constexpr mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend constexpr bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
friend std::ostream &operator<<(std::ostream &os, const mint& p) {
return os << p.val();
}
friend std::istream &operator>>(std::istream &is, mint &a) {
long long t; is >> t;
a = mint(t);
return (is);
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = is_prime_flag<m>;
};
template <int id> struct dynamic_modint {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template<std::signed_integral T>
dynamic_modint(T v){
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template<std::unsigned_integral T>
dynamic_modint(T v){
_v = (unsigned int)(v % umod());
}
uint val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = noya2::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
friend std::ostream &operator<<(std::ostream &os, const mint& p) {
return os << p.val();
}
friend std::istream &operator>>(std::istream &is, mint &a) {
long long t; is >> t;
a = mint(t);
return (is);
}
private:
unsigned int _v;
static barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> noya2::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
template<typename T>
concept Modint = requires (T &a){
T::mod();
a.inv();
a.val();
a.pow(declval<int>());
};
} // namespace noya2
#line 306 "c.cpp"
using mint = modint998244353;
void solve(){
int n; in(n);
using vec = geometry2d::point<ll>;
vector<vec> a(n); in(a);
mint ans = 0;
rep(i,n-2){
ans += abs(cross(a[i+1]-a[0],a[i+2]-a[0]));
}
ans /= 2;
out(ans);
}
int main(){
int t = 1; //in(t);
while (t--) { solve(); }
}