QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#433857 | #8786. The Whole World | ucup-team008# | WA | 1ms | 3760kb | C++17 | 20.3kb | 2024-06-08 13:42:02 | 2024-06-08 13:42:03 |
Judging History
answer
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <complex>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <unordered_map>
#include <vector>
using namespace std;
// BEGIN NO SAD
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define trav(a, x) for(auto& a : x)
#define all(x) x.begin(), x.end()
#define sz(x) (int)(x).size()
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
typedef vector<int> vi;
#define f first
#define s second
#define derr if(0) cerr
void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}
template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ", "; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? ", " : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#define debug(x...) cerr << "\e[91m"<<__func__<<":"<<__LINE__<<" [" << #x << "] = ["; _print(x); cerr << "\e[39m" << flush;
// END NO SAD
template<class Fun>
class y_combinator_result {
Fun fun_;
public:
template<class T>
explicit y_combinator_result(T &&fun): fun_(std::forward<T>(fun)) {}
template<class ...Args>
decltype(auto) operator()(Args &&...args) {
return fun_(std::ref(*this), std::forward<Args>(args)...);
}
};
template<class Fun>
decltype(auto) y_combinator(Fun &&fun) {
return y_combinator_result<std::decay_t<Fun>>(std::forward<Fun>(fun));
}
template<class T>
bool updmin(T& a, T b) {
if(b < a) {
a = b;
return true;
}
return false;
}
template<class T>
bool updmax(T& a, T b) {
if(b > a) {
a = b;
return true;
}
return false;
}
typedef int64_t ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef array<array<int, 2>, 2> matrix;
using cpx = complex<double>;
const double PI = acos(-1);
vector<cpx> roots = {{0, 0},
{1, 0}};
void ensure_capacity(int min_capacity) {
for (int len = roots.size(); len < min_capacity; len *= 2) {
for (int i = len >> 1; i < len; i++) {
roots.emplace_back(roots[i]);
double angle = 2 * PI * (2 * i + 1 - len) / (len * 2);
roots.emplace_back(cos(angle), sin(angle));
}
}
}
void fft(vector<cpx> &z, bool inverse) {
int n = z.size();
assert((n & (n - 1)) == 0);
ensure_capacity(n);
for (unsigned i = 1, j = 0; i < n; i++) {
int bit = n >> 1;
for (; j >= bit; bit >>= 1)
j -= bit;
j += bit;
if (i < j)
swap(z[i], z[j]);
}
for (int len = 1; len < n; len <<= 1) {
for (int i = 0; i < n; i += len * 2) {
for (int j = 0; j < len; j++) {
cpx root = inverse ? conj(roots[j + len]) : roots[j + len];
cpx u = z[i + j];
cpx v = z[i + j + len] * root;
z[i + j] = u + v;
z[i + j + len] = u - v;
}
}
}
if (inverse)
for (int i = 0; i < n; i++)
z[i] /= n;
}
vector<int> multiply_bigint(const vector<int> &a, const vector<int> &b, int base) {
int need = a.size() + b.size();
int n = 1;
while (n < need) n <<= 1;
vector<cpx> p(n);
for (size_t i = 0; i < n; i++) {
p[i] = cpx(i < a.size() ? a[i] : 0, i < b.size() ? b[i] : 0);
}
fft(p, false);
// a[w[k]] = (p[w[k]] + conj(p[w[n-k]])) / 2
// b[w[k]] = (p[w[k]] - conj(p[w[n-k]])) / (2*i)
vector<cpx> ab(n);
cpx r(0, -0.25);
for (int i = 0; i < n; i++) {
int j = (n - i) & (n - 1);
ab[i] = (p[i] * p[i] - conj(p[j] * p[j])) * r;
}
fft(ab, true);
vector<int> result(need);
long long carry = 0;
for (int i = 0; i < need; i++) {
long long d = (long long) (ab[i].real() + 0.5) + carry;
carry = d / base;
result[i] = d % base;
}
return result;
}
vector<int> multiply_mod(const vector<int> &a, const vector<int> &b, int m) {
int need = a.size() + b.size() - 1;
int n = 1;
while (n < need) n <<= 1;
vector<cpx> A(n);
for (size_t i = 0; i < a.size(); i++) {
int x = (a[i] % m + m) % m;
A[i] = cpx(x & ((1 << 15) - 1), x >> 15);
}
fft(A, false);
vector<cpx> B(n);
for (size_t i = 0; i < b.size(); i++) {
int x = (b[i] % m + m) % m;
B[i] = cpx(x & ((1 << 15) - 1), x >> 15);
}
fft(B, false);
vector<cpx> fa(n);
vector<cpx> fb(n);
for (int i = 0, j = 0; i < n; i++, j = n - i) {
cpx a1 = (A[i] + conj(A[j])) * cpx(0.5, 0);
cpx a2 = (A[i] - conj(A[j])) * cpx(0, -0.5);
cpx b1 = (B[i] + conj(B[j])) * cpx(0.5, 0);
cpx b2 = (B[i] - conj(B[j])) * cpx(0, -0.5);
fa[i] = a1 * b1 + a2 * b2 * cpx(0, 1);
fb[i] = a1 * b2 + a2 * b1;
}
fft(fa, true);
fft(fb, true);
vector<int> res(need);
for (int i = 0; i < need; i++) {
long long aa = (long long) (fa[i].real() + 0.5);
long long bb = (long long) (fb[i].real() + 0.5);
long long cc = (long long) (fa[i].imag() + 0.5);
res[i] = (aa % m + (bb % m << 15) + (cc % m << 30)) % m;
}
return res;
}
constexpr int digits(int base) noexcept {
return base <= 1 ? 0 : 1 + digits(base / 10);
}
constexpr int base = 1000'000'000;
constexpr int base_digits = digits(base);
constexpr int fft_base = 10'000; // fft_base^2 * n / fft_base_digits <= 10^15 for double
constexpr int fft_base_digits = digits(fft_base);
struct bigint {
// value == 0 is represented by empty z
vector<int> z; // digits
// sign == 1 <==> value >= 0
// sign == -1 <==> value < 0
int sign;
bigint(long long v = 0) {
*this = v;
}
bigint &operator=(long long v) {
sign = v < 0 ? -1 : 1;
v *= sign;
z.clear();
for (; v > 0; v = v / base)
z.push_back((int) (v % base));
return *this;
}
bigint(const string &s) {
read(s);
}
bigint &operator+=(const bigint &other) {
if (sign == other.sign) {
for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
if (i == z.size())
z.push_back(0);
z[i] += carry + (i < other.z.size() ? other.z[i] : 0);
carry = z[i] >= base;
if (carry)
z[i] -= base;
}
} else if (other != 0 /* prevent infinite loop */) {
*this -= -other;
}
return *this;
}
friend bigint operator+(bigint a, const bigint &b) {
a += b;
return a;
}
bigint &operator-=(const bigint &other) {
if (sign == other.sign) {
if ((sign == 1 && *this >= other) || (sign == -1 && *this <= other)) {
for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
z[i] -= carry + (i < other.z.size() ? other.z[i] : 0);
carry = z[i] < 0;
if (carry)
z[i] += base;
}
trim();
} else {
*this = other - *this;
this->sign = -this->sign;
}
} else {
*this += -other;
}
return *this;
}
friend bigint operator-(bigint a, const bigint &b) {
a -= b;
return a;
}
bigint &operator*=(int v) {
if (v < 0)
sign = -sign, v = -v;
for (int i = 0, carry = 0; i < z.size() || carry; ++i) {
if (i == z.size())
z.push_back(0);
long long cur = (long long) z[i] * v + carry;
carry = (int) (cur / base);
z[i] = (int) (cur % base);
}
trim();
return *this;
}
bigint operator*(int v) const {
return bigint(*this) *= v;
}
friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
int norm = base / (b1.z.back() + 1);
bigint a = a1.abs() * norm;
bigint b = b1.abs() * norm;
bigint q, r;
q.z.resize(a.z.size());
for (int i = (int) a.z.size() - 1; i >= 0; i--) {
r *= base;
r += a.z[i];
int s1 = b.z.size() < r.z.size() ? r.z[b.z.size()] : 0;
int s2 = b.z.size() - 1 < r.z.size() ? r.z[b.z.size() - 1] : 0;
int d = (int) (((long long) s1 * base + s2) / b.z.back());
r -= b * d;
while (r < 0)
r += b, --d;
q.z[i] = d;
}
q.sign = a1.sign * b1.sign;
r.sign = a1.sign;
q.trim();
r.trim();
return {q, r / norm};
}
friend bigint sqrt(const bigint &a1) {
bigint a = a1;
while (a.z.empty() || a.z.size() % 2 == 1)
a.z.push_back(0);
int n = a.z.size();
int firstDigit = (int) ::sqrt((double) a.z[n - 1] * base + a.z[n - 2]);
int norm = base / (firstDigit + 1);
a *= norm;
a *= norm;
while (a.z.empty() || a.z.size() % 2 == 1)
a.z.push_back(0);
bigint r = (long long) a.z[n - 1] * base + a.z[n - 2];
firstDigit = (int) ::sqrt((double) a.z[n - 1] * base + a.z[n - 2]);
int q = firstDigit;
bigint res;
for (int j = n / 2 - 1; j >= 0; j--) {
for (;; --q) {
bigint r1 = (r - (res * 2 * base + q) * q) * base * base +
(j > 0 ? (long long) a.z[2 * j - 1] * base + a.z[2 * j - 2] : 0);
if (r1 >= 0) {
r = r1;
break;
}
}
res *= base;
res += q;
if (j > 0) {
int d1 = res.z.size() + 2 < r.z.size() ? r.z[res.z.size() + 2] : 0;
int d2 = res.z.size() + 1 < r.z.size() ? r.z[res.z.size() + 1] : 0;
int d3 = res.z.size() < r.z.size() ? r.z[res.z.size()] : 0;
q = (int) (((long long) d1 * base * base + (long long) d2 * base + d3) / (firstDigit * 2));
}
}
res.trim();
return res / norm;
}
bigint operator/(const bigint &v) const {
return divmod(*this, v).first;
}
bigint operator%(const bigint &v) const {
return divmod(*this, v).second;
}
bigint &operator/=(int v) {
if (v < 0)
sign = -sign, v = -v;
for (int i = (int) z.size() - 1, rem = 0; i >= 0; --i) {
long long cur = z[i] + rem * (long long) base;
z[i] = (int) (cur / v);
rem = (int) (cur % v);
}
trim();
return *this;
}
bigint operator/(int v) const {
return bigint(*this) /= v;
}
int operator%(int v) const {
if (v < 0)
v = -v;
int m = 0;
for (int i = (int) z.size() - 1; i >= 0; --i)
m = (int) ((z[i] + m * (long long) base) % v);
return m * sign;
}
bigint &operator*=(const bigint &v) {
*this = *this * v;
return *this;
}
bigint &operator/=(const bigint &v) {
*this = *this / v;
return *this;
}
bigint &operator%=(const bigint &v) {
*this = *this % v;
return *this;
}
bool operator<(const bigint &v) const {
if (sign != v.sign)
return sign < v.sign;
if (z.size() != v.z.size())
return z.size() * sign < v.z.size() * v.sign;
for (int i = (int) z.size() - 1; i >= 0; i--)
if (z[i] != v.z[i])
return z[i] * sign < v.z[i] * sign;
return false;
}
bool operator>(const bigint &v) const {
return v < *this;
}
bool operator<=(const bigint &v) const {
return !(v < *this);
}
bool operator>=(const bigint &v) const {
return !(*this < v);
}
bool operator==(const bigint &v) const {
return !(*this < v) && !(v < *this);
}
bool operator!=(const bigint &v) const {
return *this < v || v < *this;
}
void trim() {
while (!z.empty() && z.back() == 0)
z.pop_back();
if (z.empty())
sign = 1;
}
bool isZero() const {
return z.empty();
}
friend bigint operator-(bigint v) {
if (!v.z.empty())
v.sign = -v.sign;
return v;
}
bigint abs() const {
return sign == 1 ? *this : -*this;
}
long long longValue() const {
long long res = 0;
for (int i = (int) z.size() - 1; i >= 0; i--)
res = res * base + z[i];
return res * sign;
}
friend bigint gcd(const bigint &a, const bigint &b) {
return b.isZero() ? a : gcd(b, a % b);
}
friend bigint lcm(const bigint &a, const bigint &b) {
return a / gcd(a, b) * b;
}
void read(const string &s) {
sign = 1;
z.clear();
int pos = 0;
while (pos < s.size() && (s[pos] == '-' || s[pos] == '+')) {
if (s[pos] == '-')
sign = -sign;
++pos;
}
for (int i = (int) s.size() - 1; i >= pos; i -= base_digits) {
int x = 0;
for (int j = max(pos, i - base_digits + 1); j <= i; j++)
x = x * 10 + s[j] - '0';
z.push_back(x);
}
trim();
}
friend istream &operator>>(istream &stream, bigint &v) {
string s;
stream >> s;
v.read(s);
return stream;
}
friend ostream &operator<<(ostream &stream, const bigint &v) {
if (v.sign == -1)
stream << '-';
stream << (v.z.empty() ? 0 : v.z.back());
for (int i = (int) v.z.size() - 2; i >= 0; --i)
stream << setw(base_digits) << setfill('0') << v.z[i];
return stream;
}
static vector<int> convert_base(const vector<int> &a, int old_digits, int new_digits) {
vector<long long> p(max(old_digits, new_digits) + 1);
p[0] = 1;
for (int i = 1; i < p.size(); i++)
p[i] = p[i - 1] * 10;
vector<int> res;
long long cur = 0;
int cur_digits = 0;
for (int v : a) {
cur += v * p[cur_digits];
cur_digits += old_digits;
while (cur_digits >= new_digits) {
res.push_back(int(cur % p[new_digits]));
cur /= p[new_digits];
cur_digits -= new_digits;
}
}
res.push_back((int) cur);
while (!res.empty() && res.back() == 0)
res.pop_back();
return res;
}
bigint operator*(const bigint &v) const {
if (min(z.size(), v.z.size()) < 200)
return mul_simple(v);
bigint res;
res.sign = sign * v.sign;
res.z = multiply_bigint(convert_base(z, base_digits, fft_base_digits),
convert_base(v.z, base_digits, fft_base_digits), fft_base);
res.z = convert_base(res.z, fft_base_digits, base_digits);
res.trim();
return res;
}
bigint mul_simple(const bigint &v) const {
bigint res;
res.sign = sign * v.sign;
res.z.resize(z.size() + v.z.size());
for (int i = 0; i < z.size(); ++i)
if (z[i])
for (int j = 0, carry = 0; j < v.z.size() || carry; ++j) {
long long cur = res.z[i + j] + (long long) z[i] * (j < v.z.size() ? v.z[j] : 0) + carry;
carry = (int) (cur / base);
res.z[i + j] = (int) (cur % base);
}
res.trim();
return res;
}
};
int phi(int n) {
int r = n;
for(int i = 2; i <= n; i++) {
if(n%i==0) {
while(n%i==0) n /= i;
r -= r/i;
}
}
return r;
}
const array<int, 2> ZERO = {0, 0};
vector<int> primes;
bool isprime(int n) {
if(n < 2) return false;
for(int i = 2; i*i <= n; i++) {
if(n%i == 0) return false;
}
return true;
}
ll modpow(ll b, ll e, ll m) {
ll ret = 1;
for(; e; e >>= 1) {
if(e & 1) ret = 1LL * ret * b % m;
b = 1LL * b * b % m;
}
return ret;
}
void rsolve() {
int n;
cin >> n;
vector<array<int, 2>> v(n);
for(auto& x: v) cin >> x[0] >> x[1];
sort(all(v));
int x = v[0][0];
int y = v[0][1];
for(auto& z: v) {
z[0] -= x;
z[1] -= y;
}
{
bool allzero = true;
for(auto [x, y]: v) {
if(y != 0) allzero = false;
}
if(allzero) {
cout << "0\n";
return;
}
}
v.erase(v.begin());
for(int d = 1; d <= v.back()[0]; d++) {
bool valid = true;
for(int candp: primes) {
vector<vector<ll>> mat(sz(v));
for(auto& x: mat) x.resize(d+1);
for(int i = 0; i < sz(v); i++) {
for(int j = 0; j < d; j++) {
bigint curr = 1;
for(int a = 0; a <= j; a++) {
curr *= v[i][0] - j + a;
}
for(int a = 2; a <= j+1; a++) {
curr /= a;
}
mat[i][j] = curr % candp;
}
mat[i].back() = v[i][1] % candp;
}
int rnk = 0;
int col = 0;
while(col < d && rnk < sz(mat)) {
for(int i = rnk; i < sz(mat); i++) {
if(mat[i][col]) {
if(i != rnk) {
swap(mat[rnk], mat[i]);
}
}
}
if(mat[rnk][col] == 0) {
col++;
continue;
}
// normalize
int other = mat[rnk][col] / gcd(mat[rnk][col], candp);
int invscale = modpow(other, phi(candp) - 1, candp);
for(int j = 0; j < sz(mat[rnk]); j++) {
mat[rnk][j] *= invscale;
mat[rnk][j] %= candp;
}
// not guaranteed
// assert(mat[rnk][col] == 1);
for(int i = 0; i < sz(mat); i++) {
if(i == rnk) continue;
ll scale = -mat[i][col];
for(int j = 0; j < sz(mat[i]); j++) {
mat[i][j] += scale * mat[rnk][j];
mat[i][j] %= candp;
if(mat[i][j] < 0) mat[i][j] += candp;
}
// also not guaranteed
// assert(mat[i][col] == 0);
}
rnk++;
}
for(int i = rnk; valid && i < sz(mat); i++) {
for(int j = 0; valid && j < sz(mat[i]); j++) {
if(j + 1 < sz(mat[i])) {
assert(mat[i][j] == 0);
}
else if(mat[i][j] != 0) {
assert(j == sz(mat[i]) - 1);
valid = false;
}
}
}
if(!valid) break;
}
if(valid) {
cout << d << "\n";
return;
}
}
cout << (v.back()[0]+1) << "\n";
}
void solve() {
for(int i = 2; i <= 29; i++) if(isprime(i)) {
ll curr = 1;
while(true) {
curr *= i;
if(curr > 1e9) break;
primes.pb(curr);
}
}
int t;
cin >> t;
while(t--) rsolve();
}
// what would chika do
// are there edge cases (N=1?)
// are array sizes proper (scaled by proper constant, for example 2* for koosaga tree)
// integer overflow?
// DS reset properly between test cases
// are you doing geometry in floating points
// are you not using modint when you should
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
solve();
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 1ms
memory: 3760kb
input:
2 2 1 0 4 1 3 1 1 4 4 6 6
output:
3 1
result:
ok 2 number(s): "3 1"
Test #2:
score: -100
Wrong Answer
time: 1ms
memory: 3636kb
input:
2 2 1 0 4 1 3 1 0 3 0 5 4
output:
3 2
result:
wrong answer 2nd numbers differ - expected: '3', found: '2'