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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 |
---|---|---|---|---|---|---|---|---|---|
#614813 | #9449. New School Term | ucup-team1264# | WA | 0ms | 3936kb | C++20 | 20.5kb | 2024-10-05 16:58:40 | 2024-10-05 16:58:41 |
Judging History
answer
// https://www.youtube.com/watch?v=CrymicX875M
// Angel of mercy
// How did you move me
// Why am I on my feet again
#ifndef ONLINE_JUDGE
#include "templates/debug.hpp"
#else
#define debug(...)
#endif
#include <bits/stdc++.h>
using namespace std;
using i64 = int64_t;
using u64 = uint64_t;
// #define int i64
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#include <utility>
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m < 2^31`
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1)
// < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
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;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
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 = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
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};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
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; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
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 = primitive_root_constexpr(m);
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)> * = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T> * = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T> * = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }
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;
}
mint &operator+=(const mint &rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint &operator-=(const mint &rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint &operator*=(const mint &rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
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 {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
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;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T> * = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T> * = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }
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;
}
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 = internal::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;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
using namespace atcoder;
using Z1 = modint1000000007;
using Z2 = modint998244353;
constexpr int N = 10000 + 5;
Z1 hash1[N + 1];
Z2 hash2[N + 1];
unordered_set<u64> fails;
int fa[N + 1], sz[N + 1], fad[N + 1], c0[N + 1], c1[N + 1];
int diff_sum = 0;
pair<int, int> find(int x) {
if (fa[x] == x) return {x, 0};
auto [f, fv] = find(fa[x]);
fa[x] = f, fad[x] ^= fv;
return {f, fad[x]};
}
int dc(int x) {
if (find(x).first != x) return 0;
return abs(c0[x] - c1[x]);
}
void merge(int x, int y) {
x = find(x).first, y = find(y).first;
if (x == y) return;
if (sz[x] < sz[y]) swap(x, y);
fa[y] = x, sz[x] += sz[y], fad[y] = 1;
c0[x] += c1[y], c1[x] += c0[y];
}
template <typename Z>
struct Comb {
std::vector<Z> fact, inv_fact;
Comb(int n) {
fact.resize(n + 1, Z(1));
inv_fact.resize(n + 1, Z(1));
for (int i = 1; i <= n; i++) {
fact[i] = fact[i - 1] * i;
}
inv_fact[n] = Z{1} / fact[n];
for (int i = n - 1; i >= 0; i--) {
inv_fact[i] = inv_fact[i + 1] * (i + 1);
}
}
Z get(int n, int m) const {
if (n < m || m < 0) return 0;
return fact[n] * inv_fact[m] * inv_fact[n - m];
}
};
Comb<Z1> comb1(N);
Comb<Z2> comb2(N);
using bs = bitset<N + 1>;
void solve() {
int n, m; cin >> n >> m;
n *= 2;
hash1[0] = 1; hash2[0] = 1;
for (int i = 1; i <= n; i++) hash1[i] = rng(), hash2[i] = rng();
Z1 h1 = hash1[1].pow(n); Z2 h2 = hash2[1].pow(n);
diff_sum = n;
for (int i = 1; i <= n; i++) {
fa[i] = i, sz[i] = 1, fad[i] = 0;
c0[i] = 1, c1[i] = 0;
}
vector<Z1> dp1(n + 1);
vector<Z2> dp2(n + 1);
for (int i = 0; i <= n; i++) {
dp1[i] = comb1.get(n, i);
dp2[i] = comb2.get(n, i);
}
auto try_merge = [&](int x, int y, int z) {
auto nh1 = h1 / hash1[x] / hash1[y] * hash1[z];
auto nh2 = h2 / hash2[x] / hash2[y] * hash2[z];
if (fails.contains(u64(nh1.val()) << 32 | nh2.val())) return false;
// rollback dps
// for (int i = n; i >= s1; i--) dp1[i] += dp1[i - s1];
if (x) for (int i = x; i <= n; i++) dp1[i] -= dp1[i - x], dp2[i] -= dp2[i - x];
if (y) for (int i = y; i <= n; i++) dp1[i] -= dp1[i - y], dp2[i] -= dp2[i - y];
if (z) for (int i = n; i >= z; i--) dp1[i] += dp1[i - z], dp2[i] += dp2[i - z];
if (!dp1[diff_sum / 2].val() && !dp2[diff_sum / 2].val()) {
fails.insert(u64(nh1.val()) << 32 | nh2.val());
// rollback again
if (z) for (int i = z; i <= n; i++) dp1[i] -= dp1[i - z], dp2[i] -= dp2[i - z];
if (x) for (int i = n; i >= x; i--) dp1[i] += dp1[i - x], dp2[i] += dp2[i - x];
if (y) for (int i = n; i >= y; i--) dp1[i] += dp1[i - y], dp2[i] += dp2[i - y];
return false;
}
h1 = nh1, h2 = nh2;
return true;
};
vector<pair<int, int>> edges(m);
for (int i = 0; i < m; i++) {
int u, v; cin >> u >> v;
edges[i] = {u, v};
}
reverse(edges.begin(), edges.end());
for (auto [u, v] : edges) {
u = find(u).first, v = find(v).first;
if (u == v) continue;
int diff_add = abs(c0[u] + c1[v] - c0[v] - c1[u]);
diff_sum += diff_add - dc(u) - dc(v);
if (diff_sum % 2 == 0 && try_merge(dc(u), dc(v), diff_add)) {
debug(u, v);
merge(u, v);
} else {
diff_sum -= diff_add - dc(u) - dc(v);
}
}
vector<vector<int>> comp0(n + 1), comp1(n + 1);
for (int i = 1; i <= n; i++) {
auto [f, v] = find(i);
if (v) comp1[f].push_back(i);
else comp0[f].push_back(i);
}
for (int i = 1; i <= n; i++) {
if (c0[i] < c1[i]) swap(comp0[i], comp1[i]), swap(c0[i], c1[i]);
}
// run annother dp to get an construction
vector<bs> dp(n + 1, 0);
dp[0] = 1;
for (int i = 1; i <= n; i++) {
dp[i] = dp[i - 1];
if (dc(i)) {
dp[i] |= (dp[i - 1] << dc(i));
}
}
if (!dp[n][diff_sum / 2]) {
cout << "ERROR\n";
return;
}
string ans(n, '0');
int now = diff_sum / 2;
for (int i = n; i; i--) {
if (now >= dc(i) && dp[i - 1][now - dc(i)]) {
for (int j: comp0[i]) ans[j - 1] = '0';
for (int j: comp1[i]) ans[j - 1] = '1';
now -= dc(i);
} else {
for (int j: comp0[i]) ans[j - 1] = '1';
for (int j: comp1[i]) ans[j - 1] = '0';
}
}
cout << ans << '\n';
}
#undef int
// Make bold hypotheses and verify carefully
int main() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
int t = 1;
// cin >> t;
while (t--) {
solve();
}
}
详细
Test #1:
score: 100
Accepted
time: 0ms
memory: 3936kb
input:
2 4 1 3 2 4 1 4 1 2
output:
0101
result:
ok Output is valid. OK
Test #2:
score: -100
Wrong Answer
time: 0ms
memory: 3904kb
input:
3 7 2 5 1 3 4 6 2 6 4 5 2 4 5 6
output:
001110
result:
wrong answer The division is not minimized.