QOJ.ac
QOJ
ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#564538 | #6188. Elliptic Curve Problem | ucup-team987 | TL | 304ms | 30448kb | C++23 | 18.9kb | 2024-09-15 09:39:18 | 2024-09-15 09:39:18 |
Judging History
answer
/**
* date : 2024-09-15 10:39:02
* author : Nyaan
*/
#define NDEBUG
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tr2/dynamic_bitset>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
constexpr P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
template <typename S>
P &operator*=(const S &r) {
first *= r, second *= r;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
template <typename S>
P operator*(const S &r) const {
return P(*this) *= r;
}
P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
vector<int> mkiota(int n) {
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
T mkrev(const T &v) {
T w{v};
reverse(begin(w), end(w));
return w;
}
template <typename T>
bool nxp(T &v) {
return next_permutation(begin(v), end(v));
}
// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
vector<vector<T>> ret;
vector<T> v;
auto dfs = [&](auto rc, int i) -> void {
if (i == (int)a.size()) {
ret.push_back(v);
return;
}
for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
};
dfs(dfs, 0);
return ret;
}
// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
T res = I;
for (; n; f(a = a * a), n >>= 1) {
if (n & 1) f(res = res * a);
}
return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}
template <typename T>
T Rev(const T &v) {
T res = v;
reverse(begin(res), end(res));
return res;
}
template <typename T>
vector<T> Transpose(const vector<T> &v) {
using U = typename T::value_type;
if(v.empty()) return {};
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
res[j][i] = v[i][j];
}
}
return res;
}
template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
using U = typename T::value_type;
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
if (clockwise) {
res[W - 1 - j][i] = v[i][j];
} else {
res[j][H - 1 - i] = v[i][j];
}
}
}
return res;
}
} // namespace Nyaan
// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
// inout
namespace Nyaan {
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;
}
istream &operator>>(istream &is, __int128_t &x) {
string S;
is >> S;
x = 0;
int flag = 0;
for (auto &c : S) {
if (c == '-') {
flag = true;
continue;
}
x *= 10;
x += c - '0';
}
if (flag) x = -x;
return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
string S;
is >> S;
x = 0;
for (auto &c : S) {
x *= 10;
x += c - '0';
}
return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
if (x == 0) return os << 0;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
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...);
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
} // namespace Nyaan
// debug
#ifdef NyaanDebug
#define trc(...) (void(0))
#else
#define trc(...) (void(0))
#endif
#ifdef NyaanLocal
#define trc2(...) (void(0))
#else
#define trc2(...) (void(0))
#endif
// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
//
using namespace std;
using namespace std;
// x / y (x > 0, y > 0) を管理、デフォルトで 1 / 1
// 入力が互いに素でない場合は gcd を取って格納
// seq : (1, 1) から (x, y) へのパス。右の子が正/左の子が負
template <typename Int>
struct SternBrocotTreeNode {
using Node = SternBrocotTreeNode;
Int lx, ly, x, y, rx, ry;
vector<Int> seq;
SternBrocotTreeNode() : lx(0), ly(1), x(1), y(1), rx(1), ry(0) {}
SternBrocotTreeNode(Int X, Int Y) : SternBrocotTreeNode() {
assert(1 <= X && 1 <= Y);
Int g = gcd(X, Y);
X /= g, Y /= g;
while (min(X, Y) > 0) {
if (X > Y) {
Int d = X / Y;
X -= d * Y;
go_right(d - (X == 0 ? 1 : 0));
} else {
Int d = Y / X;
Y -= d * X;
go_left(d - (Y == 0 ? 1 : 0));
}
}
}
SternBrocotTreeNode(const pair<Int, Int> &xy)
: SternBrocotTreeNode(xy.first, xy.second) {}
SternBrocotTreeNode(const vector<Int> &_seq) : SternBrocotTreeNode() {
for (const Int &d : _seq) {
assert(d != 0);
if (d > 0) go_right(d);
if (d < 0) go_left(d);
}
assert(seq == _seq);
}
// pair<Int, Int> 型で分数を get
pair<Int, Int> get() const { return make_pair(x, y); }
// 区間の下限
pair<Int, Int> lower_bound() const { return make_pair(lx, ly); }
// 区間の上限
pair<Int, Int> upper_bound() const { return make_pair(rx, ry); }
// 根からの深さ
Int depth() const {
Int res = 0;
for (auto &s : seq) res += abs(s);
return res;
}
// 左の子に d 進む
void go_left(Int d = 1) {
if (d <= 0) return;
if (seq.empty() or seq.back() > 0) seq.push_back(0);
seq.back() -= d;
rx += lx * d, ry += ly * d;
x = rx + lx, y = ry + ly;
}
// 右の子に d 進む
void go_right(Int d = 1) {
if (d <= 0) return;
if (seq.empty() or seq.back() < 0) seq.push_back(0);
seq.back() += d;
lx += rx * d, ly += ry * d;
x = rx + lx, y = ry + ly;
}
// 親の方向に d 進む
// d 進めたら true, 進めなかったら false を返す
bool go_parent(Int d = 1) {
if (d <= 0) return true;
while (d != 0) {
if (seq.empty()) return false;
Int d2 = min(d, seq.back() < 0 ? -seq.back() : seq.back());
if (seq.back() > 0) {
x -= rx * d2, y -= ry * d2;
lx = x - rx, ly = y - ry;
seq.back() -= d2;
} else {
x -= lx * d2, y -= ly * d2;
rx = x - lx, ry = y - ly;
seq.back() += d2;
}
d -= d2;
if (seq.back() == 0) seq.pop_back();
if (d2 == Int{0}) break;
}
return true;
}
// SBT 上の LCA
static Node lca(const Node &lhs, const Node &rhs) {
Node n;
for (int i = 0; i < min<int>(lhs.seq.size(), rhs.seq.size()); i++) {
Int val1 = lhs.seq[i], val2 = rhs.seq[i];
if ((val1 < 0) != (val2 < 0)) break;
if (val1 < 0) n.go_left(min(-val1, -val2));
if (val1 > 0) n.go_right(min(val1, val2));
if (val1 != val2) break;
}
return n;
}
friend ostream &operator<<(ostream &os, const Node &rhs) {
os << "\n";
os << "L : ( " << rhs.lx << ", " << rhs.ly << " )\n";
os << "M : ( " << rhs.x << ", " << rhs.y << " )\n";
os << "R : ( " << rhs.rx << ", " << rhs.ry << " )\n";
os << "seq : {";
for (auto &x : rhs.seq) os << x << ", ";
os << "} \n";
return os;
}
friend bool operator<(const Node &lhs, const Node &rhs) {
return lhs.x * rhs.y < rhs.x * lhs.y;
}
friend bool operator==(const Node &lhs, const Node &rhs) {
return lhs.x == rhs.x and lhs.y == rhs.y;
}
};
/**
* @brief Stern-Brocot Tree
*/
// 下向き凸包の頂点列挙
// (xl, yl) 始点, x in [xl, xr]
// inside(x, y) : (x, y) が凸包内部か?
// candicate(x, y, c, d) : (x, y) が凸包外部にあるとする。
// 凸包内部の点 (x + sc, y + sd) が存在すればそのような s を返す
// 存在しなければ任意の値 (-1 でもよい) を返す
template <typename Int>
vector<pair<Int, Int>> enumerate_convex(
Int xl, Int yl, Int xr, const function<bool(Int, Int)>& inside,
const function<Int(Int, Int, Int, Int)>& candicate) {
assert(xl <= xr);
// inside かつ x <= xr
auto f = [&](Int x, Int y) { return x <= xr && inside(x, y); };
// (a, b) から (c, d) 方向に進めるだけ進む
auto go = [&](Int a, Int b, Int c, Int d) -> Int {
assert(f(a, b));
Int r = 1, s = 0;
while (f(a + r * c, b + r * d)) r *= 2;
while ((r /= 2) != 0) {
if (f(a + r * c, b + r * d)) s += r, a += r * c, b += r * d;
}
return s;
};
// (a, b) が out, (a + c * k, b + d * k) が in とする
// out の間進めるだけ進む
auto go2 = [&](Int a, Int b, Int c, Int d, Int k) {
assert(!f(a, b) and f(a + c * k, b + d * k));
Int ok = 0, ng = k;
while (ok + 1 < ng) {
Int m = (ok + ng) / 2;
(f(a + c * m, b + d * m) ? ng : ok) = m;
}
return ok;
};
vector<pair<Int, Int>> ps;
Int x = xl, y = yl;
assert(f(x, y) and go(x, y, 0, -1) == 0);
ps.emplace_back(x, y);
SternBrocotTreeNode<Int> sb;
while (x < xr) {
Int a, b;
if (f(x + 1, y)) {
a = 1, b = 0;
} else {
while (!f(x + sb.lx, y + sb.ly)) {
assert(!sb.seq.empty());
sb.go_parent(sb.seq.back() < 0 ? -sb.seq.back() : sb.seq.back());
}
while (true) {
assert(f(x + sb.lx, y + sb.ly));
assert(!f(x + sb.rx, y + sb.ry));
if (f(x + sb.lx + sb.rx, y + sb.ly + sb.ry)) {
Int s = go(x + sb.lx, y + sb.ly, sb.rx, sb.ry);
assert(s > 0);
sb.go_right(s);
} else {
Int c = candicate(x + sb.rx, y + sb.ry, sb.lx, sb.ly);
Int s = -1;
// 念のため周囲を調べる(フェイルセーフ)
for (Int d = -2; d <= 2; d++) {
Int v = c + d;
if (v > 0 && f(x + sb.lx * v + sb.rx, y + sb.ly * v + sb.ry)) {
s = v;
break;
}
}
if (s <= 0 || !f(x + sb.lx * s + sb.rx, y + sb.ly * s + sb.ry)) {
a = sb.lx, b = sb.ly;
break;
} else {
Int t = go2(x + sb.rx, y + sb.ry, sb.lx, sb.ly, s);
sb.go_left(t);
}
}
}
}
Int s = go(x, y, a, b);
x += a * s, y += b * s;
ps.emplace_back(x, y);
}
return ps;
}
// sum_{0 <= i < N} (ai + b) // m
template <typename T>
T sum_of_floor(T n, T m, T a, T b) {
T ret = 0;
if (a >= m) ret += (n - 1) * n * (a / m) / 2, a %= m;
if (b >= m) ret += n * (b / m), b %= m;
T y = (a * n + b) / m;
if (y == 0) return ret;
T x = y * m - b;
ret += (n - (x + a - 1) / a) * y;
ret += sum_of_floor(y, a, m, (a - x % a) % a);
return ret;
}
// verify www.codechef.com/viewsolution/36222026
// count x : ax + b mod m < yr, 0 <= x < xr
template <typename T>
T mod_affine_range_counting(T a, T b, T m, T xr, T yr) {
assert(0 <= yr && yr <= m);
return sum_of_floor(xr, m, a, b + m) - sum_of_floor(xr, m, a, b + m - yr);
}
//
using namespace Nyaan;
// sum [x=0...(p-1)/2] floor((x^2 + r) / p)
i128 calc(i128 p, i128 r) {
assert(0 <= r);
// y >= (x^2 + r + 1) / p に含まれる頂点を列挙
r++;
auto inside = [&](i128 x, i128 y) { return p * y >= x * x + r; };
auto candicate = [&p](i128 x, i128, i128 c, i128 d) -> i128 {
// p (y + k d) >= (x + k c)^2 + r
// c^2 k^2 - (p d - 2 x c) k + (const) <= 0
i128 numer = p * d - 2 * x * c;
i128 denom = 2 * c * c;
i128 quo = numer / denom, rem = numer % denom;
if (rem < 0) --quo, rem += denom;
if (2 * rem > denom) ++quo, rem -= denom;
return quo;
};
auto ps = enumerate_convex<i128>(0, 1, (p - 1) / 2, inside, candicate);
trc(ps);
auto [xmax, ymax] = ps.back();
i128 res = xmax * ymax;
trc(res);
rep(i, sz(ps) - 1) {
auto [a, b] = ps[i];
auto [c, d] = ps[i + 1];
res -= sum_of_floor<i128>(c - a, c - a, d - b, (ymax - d + 1) * (c - a));
}
return res;
}
i128 naive(i128 p, i128 r) {
vector<long long> v;
rep(x, (p - 1) / 2 + 1) v.push_back((x * x + r) / p);
trc(v);
return Sum(v);
}
void test() {
reg(p, 3, 1000) rep(r, p) {
ll an = naive(p, r);
ll ac = calc(p, r);
trc(p, r, an, ac);
assert(an == ac);
}
trc2("OK");
}
void q() {
// test();
inl(p, l, r);
i128 upper = calc(p, p - l);
i128 lower = calc(p, p - (r + 1));
out(upper - lower);
}
void Nyaan::solve() {
int t = 1;
// in(t);
while (t--) q();
}
详细
Test #1:
score: 100
Accepted
time: 0ms
memory: 3876kb
input:
11 3 8
output:
3
result:
ok 1 number(s): "3"
Test #2:
score: 0
Accepted
time: 304ms
memory: 30448kb
input:
998244353 11451400 919810000
output:
454174074
result:
ok 1 number(s): "454174074"
Test #3:
score: -100
Time Limit Exceeded
input:
96311898227 25437319919 55129361817