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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#631331 | #8691. Square Root Partitioning | hos_lyric | WA | 29ms | 21864kb | C++14 | 12.0kb | 2024-10-12 00:45:54 | 2024-10-12 00:45:55 |
Judging History
answer
#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 <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#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> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
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; }
#define COLOR(s) ("\x1b[" s "m")
#ifndef LIBRA_OTHER_INT128_H_
#define LIBRA_OTHER_INT128_H_
#include <stdio.h>
#include <iostream>
constexpr unsigned __int128 toUInt128(const char *s) {
unsigned __int128 x = 0;
for (; *s; ++s) x = x * 10 + (*s - '0');
return x;
}
constexpr __int128 toInt128(const char *s) {
if (*s == '-') return -toInt128(s + 1);
__int128 x = 0;
for (; *s; ++s) x = x * 10 + (*s - '0');
return x;
}
unsigned __int128 inUInt128() {
static char buf[41];
scanf("%s", buf);
return toUInt128(buf);
}
__int128 inInt128() {
static char buf[41];
scanf("%s", buf);
return toInt128(buf);
}
void out(unsigned __int128 x) {
static char buf[41];
int len = 0;
do { buf[len++] = '0' + static_cast<int>(x % 10); } while (x /= 10);
for (int i = len; --i >= 0; ) putchar(buf[i]);
}
void out(__int128 x) {
if (x < 0) {
putchar('-');
out(-static_cast<unsigned __int128>(x));
} else {
out(static_cast<unsigned __int128>(x));
}
}
std::ostream &operator<<(std::ostream &os, unsigned __int128 x) {
static char buf[41];
int len = 0;
do { buf[len++] = '0' + static_cast<int>(x % 10); } while (x /= 10);
for (int i = len; --i >= 0; ) os << buf[i];
return os;
}
std::ostream &operator<<(std::ostream &os, __int128 x) {
if (x < 0) {
os << '-' << -static_cast<unsigned __int128>(x);
} else {
os << static_cast<unsigned __int128>(x);
}
return os;
}
#endif // LIBRA_OTHER_INT128_H_
////////////////////////////////////////////////////////////////////////////////
// floor(a b / 2^128)
inline unsigned __int128 mul128High(unsigned __int128 a, unsigned __int128 b) {
const unsigned __int128 a0 = static_cast<unsigned long long>(a), a1 = a >> 64;
const unsigned __int128 b0 = static_cast<unsigned long long>(b), b1 = b >> 64;
return ((((a0 * b0) >> 64) + static_cast<unsigned long long>(a0 * b1) + static_cast<unsigned long long>(a1 * b0)) >> 64) + ((a0 * b1) >> 64) + ((a1 * b0) >> 64) + a1 * b1;
}
// Hold y := (2^128 x) mod M
template <int ID> struct RMModInt128 {
static unsigned __int128 M;
static unsigned __int128 INV_M; // M^-1 mod 2^128
static unsigned __int128 TWO256; // 2^256 mod M
static void setM(unsigned __int128 m) {
assert(m & 1); assert(1 <= m); assert(!(m >> 127));
M = m;
INV_M = (3 * M) ^ 2;
for (int i = 0; i < 5; ++i) INV_M *= (2 - M * INV_M);
TWO256 = (-M) % M;
for (int i = 0; i < 128; ++i) TWO256 = ((TWO256 <<= 1) >= M) ? (TWO256 - M) : TWO256;
}
// (2^-128 a) mod M (0 <= a < 2^128 m)
static inline unsigned __int128 reduce(unsigned __int128 a) {
const unsigned __int128 c = -mul128High(INV_M * a, M);
return (c >= M) ? (c + M) : c;
}
// (2^-128 a b) mod M (0 <= a b < 2^128 m)
static inline unsigned __int128 mulReduce(unsigned __int128 a, unsigned __int128 b) {
const unsigned __int128 c = mul128High(a, b) - mul128High(INV_M * (a * b), M);
return (c >= M) ? (c + M) : c;
}
unsigned __int128 y;
RMModInt128() : y(0U) {}
RMModInt128(unsigned x_) : y(mulReduce(TWO256, x_ % M)) {}
RMModInt128(unsigned long long x_) : y(mulReduce(TWO256, x_ % M)) {}
RMModInt128(unsigned __int128 x_) : y(mulReduce(TWO256, x_ % M)) {}
RMModInt128(int x_) : y(mulReduce(TWO256, ((x_ %= static_cast<__int128>(M)) < 0) ? (x_ + static_cast<__int128>(M)) : x_)) {}
RMModInt128(long long x_) : y(mulReduce(TWO256, ((x_ %= static_cast<__int128>(M)) < 0) ? (x_ + static_cast<__int128>(M)) : x_)) {}
RMModInt128(__int128 x_) : y(mulReduce(TWO256, ((x_ %= static_cast<__int128>(M)) < 0) ? (x_ + static_cast<__int128>(M)) : x_)) {}
unsigned __int128 get() const { return reduce(y); }
RMModInt128 &operator+=(const RMModInt128 &a) { y = ((y += a.y) >= M) ? (y - M) : y; return *this; }
RMModInt128 &operator-=(const RMModInt128 &a) { y = ((y -= a.y) >= M) ? (y + M) : y; return *this; }
RMModInt128 &operator*=(const RMModInt128 &a) { y = mulReduce(y, a.y); return *this; }
RMModInt128 &operator/=(const RMModInt128 &a) { return (*this *= a.inv()); }
template <class T> RMModInt128 pow(T e) const {
if (e < 0) return inv().pow(-e);
for (RMModInt128 a = *this, b = 1U; ; a *= a) { if (e & 1) { b *= a; } if (!(e >>= 1)) { return b; } }
}
RMModInt128 inv() const {
unsigned __int128 a = M, b = reduce(reduce(y)); __int128 u = 0, v = 1;
for (; b; ) { const unsigned __int128 q = a / b; const unsigned __int128 c = a - q * b; a = b; b = c; const __int128 w = u - static_cast<__int128>(q) * v; u = v; v = w; }
assert(a == 1U); RMModInt128 r; r.y = u; r.y = (r.y >= M) ? (r.y + M) : r.y; return r;
}
RMModInt128 operator+() const { return *this; }
RMModInt128 operator-() const { RMModInt128 a; a.y = y ? (M - y) : 0U; return a; }
RMModInt128 operator+(const RMModInt128 &a) const { return (RMModInt128(*this) += a); }
RMModInt128 operator-(const RMModInt128 &a) const { return (RMModInt128(*this) -= a); }
RMModInt128 operator*(const RMModInt128 &a) const { return (RMModInt128(*this) *= a); }
RMModInt128 operator/(const RMModInt128 &a) const { return (RMModInt128(*this) /= a); }
template <class T> friend RMModInt128 operator+(T a, const RMModInt128 &b) { return (RMModInt128(a) += b); }
template <class T> friend RMModInt128 operator-(T a, const RMModInt128 &b) { return (RMModInt128(a) -= b); }
template <class T> friend RMModInt128 operator*(T a, const RMModInt128 &b) { return (RMModInt128(a) *= b); }
template <class T> friend RMModInt128 operator/(T a, const RMModInt128 &b) { return (RMModInt128(a) /= b); }
explicit operator bool() const { return y; }
bool operator==(const RMModInt128 &a) const { return (y == a.y); }
bool operator!=(const RMModInt128 &a) const { return (y != a.y); }
// !
bool operator<(const RMModInt128 &a) const { return (y < a.y); }
friend std::ostream &operator<<(std::ostream &os, const RMModInt128 &a) { return os << a.get(); }
};
template <int ID> unsigned __int128 RMModInt128<ID>::M;
template <int ID> unsigned __int128 RMModInt128<ID>::INV_M;
template <int ID> unsigned __int128 RMModInt128<ID>::TWO256;
////////////////////////////////////////////////////////////////////////////////
using RMM128ForPrime = RMModInt128<-20220617>;
template <class T> vector<T> merge(const vector<T> &a, const vector<T> &b) {
vector<T> c(a.size() + b.size());
std::merge(a.begin(), a.end(), b.begin(), b.end(), c.begin());
return c;
}
int bsf128(__int128 a) {
const long long a64 = a;
return a64 ? __builtin_ctzll(a64) : (64 + __builtin_ctzll(a >> 64));
}
__int128 gcd128(__int128 a, __int128 b) {
if (a < 0) a = -a;
if (b < 0) b = -b;
if (a == 0) return b;
if (b == 0) return a;
const int s = bsf128(a | b);
a >>= bsf128(a);
do {
b >>= bsf128(b);
if (a > b) swap(a, b);
b -= a;
} while (b);
return a << s;
}
// Checks if n is a prime using Miller-Rabin test
bool isPrime128(__int128 n) {
if (n <= 1 || !(n & 1)) return (n == 2);
RMM128ForPrime::setM(n);
const int s = bsf128(n - 1);
const __int128 d = (n - 1) >> s;
// Based on conjectures in Zhang, Two kinds of strong pseudoprimes up to 10^36.
for (const __int128 base : {2, 3, 5, 7, 11, 13, 17, 19, 23, 29,
31, 37, 41, 43, 47, 53, 59, 61, 67, 71}) {
if (base >= n) continue;
RMM128ForPrime a = RMM128ForPrime(base).pow(d);
if (a.get() == 1 || static_cast<__int128>(a.get()) == n - 1) continue;
bool ok = false;
for (int i = 0; i < s - 1; ++i) {
if (static_cast<__int128>((a *= a).get()) == n - 1) {
ok = true;
break;
}
}
if (!ok) return false;
}
return true;
}
#include <chrono>
#ifdef LOCAL
mt19937_64 rng(58);
#else
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
#endif
using INT = __int128;
using Mint = RMModInt128<0>;
using Pair = pair<Mint, Mint>;
Pair operator+(const Pair &a, const Pair &b) { return make_pair(a.first + b.first, a.second + b.second); }
Pair operator-(const Pair &a, const Pair &b) { return make_pair(a.first - b.first, a.second - b.second); }
// Pair operator*(const Pair &a, const Pair &b) { return make_pair(a.first * b.first, a.first * b.second + a.second * b.first); }
Pair operator*(const Pair &a, Mint k) { return make_pair(a.first * k, a.second * k); }
Pair operator*(Mint k, const Pair &a) { return make_pair(k * a.first, k * a.second); }
Pair &operator+=(Pair &a, const Pair &b) { return a = a + b; }
Pair &operator-=(Pair &a, const Pair &b) { return a = a - b; }
// Pair &operator*=(Pair &a, const Pair &b) { return a = a * b; }
Pair &operator*=(Pair &a, Mint k) { return a = a * k; }
// constexpr Pair ZERO(0, 0);
INT rng127() {
return (INT)rng() << 63 ^ rng();
}
INT M;
bool isNonResidue(Mint a) {
return (a && a.pow((M - 1) / 2) != 1);
}
// (b + sqrt(b^2 - a))^((p+1)/2) in F_p(sqrt(b^2 - a))
Mint modSqrt(Mint a) {
Mint b, d;
for (; ; ) {
b = rng127();
d = b * b - a;
if (isNonResidue(d)) break;
}
Mint f0 = b, f1 = 1, g0 = 1, g1 = 0, tmp;
for (INT e = (M + 1) >> 1; e; e >>= 1) {
if (e & 1) {
tmp = (g0 * f0 + d * ((g1 * f1) )) ;
g1 = (g0 * f1 + g1 * f0) ;
g0 = tmp;
}
tmp = (f0 * f0 + d * ((f1 * f1) )) ;
f1 = (2 * f0 * f1) ;
f0 = tmp;
}
assert(g0 * g0 == a);
return g0;
}
int N;
char A[40][100'010];
int main() {
for (; ; ) {
M = ((INT)1<<125) + (rng127() >> 2);
if (isPrime128(M)) break;
}
Mint::setM(M);
// fixed non-residue
Mint R;
for (; ; ) {
R = rng127();
if (isNonResidue(R)) break;
}
cerr<<"M = "<<M<<", R = "<<R<<endl;
for (; ~scanf("%d", &N); ) {
for (int i = 0; i < N; ++i) {
scanf("%s", A[i]);
}
vector<Pair> fs(1 << (N/2)), gs(1 << (N - N/2));
fs[0] = gs[0] = Pair(0, 0);
for (int i = 0; i < N; ++i) {
Mint b = 0;
for (char *a = A[i]; *a; ++a) (b *= 10) += (*a - '0');
Pair c(0, 0);
if (isNonResidue(b)) {
c.second = modSqrt(R * b);
} else {
c.first = modSqrt(b);
}
cerr<<b<<": "<<c<<endl;
if (i < N/2) {
for (int h = 0; h < 1 << i; ++h) {
fs[h | 1 << i] = fs[h] - c;
fs[h] -= c;
}
} else {
for (int h = 0; h < 1 << (i - N/2); ++h) {
gs[h | 1 << (i - N/2)] = gs[h] - c;
gs[h] += c;
}
}
}
sort(fs.begin(), fs.end());
sort(gs.begin(), gs.end());
long long ans = 0;
for (int x = 0, yL = 0, yR = 0; x < (int)fs.size(); ++x) {
for (; yL < (int)gs.size() && gs[yL] < fs[x]; ++yL) {}
for (; yR < (int)gs.size() && gs[yR] <= fs[x]; ++yR) {}
ans += (yR - yL);
}
assert(ans % 2 == 0);
ans /= 2;
printf("%lld\n", ans);
}
return 0;
}
Details
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Test #1:
score: 100
Accepted
time: 1ms
memory: 3836kb
input:
3 2 2 8
output:
1
result:
ok 1 number(s): "1"
Test #2:
score: 0
Accepted
time: 1ms
memory: 5956kb
input:
4 4 9 25 49
output:
0
result:
ok 1 number(s): "0"
Test #3:
score: -100
Wrong Answer
time: 29ms
memory: 21864kb
input:
36 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
output:
2433220608
result:
wrong answer 1st numbers differ - expected: '4537567650', found: '2433220608'