QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#614813#9449. New School Termucup-team1264#WA 0ms3936kbC++2020.5kb2024-10-05 16:58:402024-10-05 16:58:41

Judging History

你现在查看的是最新测评结果

  • [2024-10-05 16:58:41]
  • 评测
  • 测评结果:WA
  • 用时:0ms
  • 内存:3936kb
  • [2024-10-05 16:58:40]
  • 提交

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();
    }
}

Details

Tip: Click on the bar to expand more detailed information

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.