結果

問題 No.2294 Union Path Query (Easy)
ユーザー Forested
提出日時 2023-05-05 21:56:49
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
TLE  
実行時間 -
コード長 10,970 bytes
コンパイル時間 1,522 ms
コンパイル使用メモリ 130,088 KB
最終ジャッジ日時 2025-02-12 18:07:28
ジャッジサーバーID
（参考情報） 		judge4 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 43 TLE * 3
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ソースコード

diff #
プレゼンテーションモードにする

#ifndef LOCAL
#define FAST_IO
#endif
// ============
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32)(n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
template <typename T>
using Vec = vector<T>;
template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
Vec<tuple<i32, i32, T>> runlength(const Vec<T> &a) {
    if (a.empty()) {
        return Vec<tuple<i32, i32, T>>();
    }
    Vec<tuple<i32, i32, T>> ret;
    i32 prv = 0;
    REP(i, 1, a.size()) {
        if (a[i - 1] != a[i]) {
            ret.emplace_back(prv, i, a[i - 1]);
            prv = i;
        }
    }
    ret.emplace_back(prv, (i32)a.size(), a.back());
    return ret;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
istream &operator>>(istream &is, i128 &x) {
    i64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, i128 x) {
    os << (i64)x;
    return os;
}
istream &operator>>(istream &is, u128 &x) {
    u64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, u128 x) {
    os << (u64)x;
    return os;
}
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
// ============
#ifdef DEBUGF
#else
#define DBG(x) (void)0
#endif
// ============
#include <cassert>
#include <iostream>
#include <type_traits>
// ============
constexpr bool is_prime(unsigned n) {
    if (n == 0 || n == 1) {
        return false;
    }
    for (unsigned i = 2; i * i <= n; ++i) {
        if (n % i == 0) {
            return false;
        }
    }
    return true;
}
constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
    unsigned ret = 1, self = x;
    while (y != 0) {
        if (y & 1) {
            ret = (unsigned) ((unsigned long long) ret * self % mod);
        }
        self = (unsigned) ((unsigned long long) self * self % mod);
        y /= 2;
    }
    return ret;
}
template <unsigned mod>
constexpr unsigned primitive_root() {
    static_assert(is_prime(mod), "`mod` must be a prime number.");
    if (mod == 2) {
        return 1;
    }
    unsigned primes[32] = {};
    int it = 0;
    {
        unsigned m = mod - 1;
        for (unsigned i = 2; i * i <= m; ++i) {
            if (m % i == 0) {
                primes[it++] = i;
                while (m % i == 0) {
                    m /= i;
                }
            }
        }
        if (m != 1) {
            primes[it++] = m;
        }
    }
    for (unsigned i = 2; i < mod; ++i) {
        bool ok = true;
        for (int j = 0; j < it; ++j) {
            if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
                ok = false;
                break;
            }
        }
        if (ok)
            return i;
    }
    return 0;
}
// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
    x %= y;
    if (x < 0) {
        x += y;
    }
    return x;
}
// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return x / y;
    } else {
        return -((-x + y - 1) / y);
    }
}
// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return (x + y - 1) / y;
    } else {
        return -(-x / y);
    }
}
// ============
template <unsigned mod>
class ModInt {
    static_assert(mod != 0, "`mod` must not be equal to 0.");
    static_assert(
        mod < (1u << 31),
        "`mod` must be less than (1u << 31) = 2147483648.");
    unsigned val;
public:
    static constexpr unsigned get_mod() {
        return mod;
    }
    
    constexpr ModInt() : val(0) {}
    template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) ((long long) x % (long long) mod + (x < 0 ? mod : 0))) {}
    template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) (x % mod)) {}
    static constexpr ModInt raw(unsigned x) {
        ModInt<mod> ret;
        ret.val = x;
        return ret;
    }
    constexpr unsigned get_val() const {
        return val;
    }
    constexpr ModInt operator+() const {
        return *this;
    }
    constexpr ModInt operator-() const {
        return ModInt<mod>(0u) - *this;
    }
    constexpr ModInt &operator+=(const ModInt &rhs) {
        val += rhs.val;
        if (val >= mod)
            val -= mod;
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt &rhs) {
        if (val < rhs.val)
            val += mod;
        val -= rhs.val;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.val % mod;
        return *this;
    }
    constexpr ModInt &operator/=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.inv().val % mod;
        return *this;
    }
    friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) += rhs;
    }
    friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) -= rhs;
    }
    friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) *= rhs;
    }
    friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) /= rhs;
    }
    constexpr ModInt pow(unsigned long long x) const {
        ModInt<mod> ret = ModInt<mod>::raw(1);
        ModInt<mod> self = *this;
        while (x != 0) {
            if (x & 1)
                ret *= self;
            self *= self;
            x >>= 1;
        }
        return ret;
    }
    constexpr ModInt inv() const {
        static_assert(is_prime(mod), "`mod` must be a prime number.");
        assert(val != 0);
        return this->pow(mod - 2);
    }
    friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
        long long val;
        is >> val;
        x.val = val % mod + (val < 0 ? mod : 0);
        return is;
    }
    friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
        os << x.val;
        return os;
    }
    friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val == rhs.val;
    }
    
    friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val != rhs.val;
    }
};
[[maybe_unused]] constexpr unsigned mod998244353 = 998244353;
[[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007;
// ============
class StrangeUf {
    i32 n;
    Vec<i32> par;
    Vec<i32> sz;
    Vec<i64> comp;
    Vec<i32> xor_0;
    Vec<i32> xor_1;
    Vec<i32> wt;
    
    i32 root(i32 v) const {
        if (par[v] < 0) {
            return v;
        } else {
            return root(par[v]);
        }
    }
    
    i32 root_xor(i32 v) const {
        i32 xo = 0;
        while (par[v] != -1) {
            xo ^= wt[v];
            v = par[v];
        }
        return xo;
    }
    
public:
    StrangeUf() = default;
    StrangeUf(i32 n) : n(n), par(n, -1), sz(n, 1), comp(n, 0), xor_0(n, 1), xor_1(n, 0), wt(n, 0) {}
    
    void unite(i32 u, i32 v, i32 w) {
        i32 xu = root_xor(u);
        u = root(u);
        i32 xv = root_xor(v);
        v = root(v);
        w ^= xu ^ xv;
        if (sz[u] > sz[v]) {
            swap(u, v);
        }
        par[u] = v;
        sz[v] += sz[u];
        comp[v] += comp[u];
        if (w) {
            comp[v] += (i64)xor_0[u] * xor_0[v];
            comp[v] += (i64)xor_1[u] * xor_1[v];
        } else {
            comp[v] += (i64)xor_1[u] * xor_0[v];
            comp[v] += (i64)xor_0[u] * xor_1[v];
        }
        if (w) {
            xor_0[v] += xor_1[u];
            xor_1[v] += xor_0[u];
        } else {
            xor_0[v] += xor_0[u];
            xor_1[v] += xor_1[u];
        }
        wt[u] = w;
    }
    
    i64 get_comp(i32 v) const {
        v = root(v);
        return comp[v];
    }
    
    i32 get_path(i32 u, i32 v) const {
        i32 xo = 0;
        while (u != v) {
            if (sz[u] < sz[v]) {
                xo ^= wt[u];
                u = par[u];
            } else {
                xo ^= wt[v];
                v = par[v];
            }
        }
        return xo;
    }
    
    bool same(i32 u, i32 v) const {
        return root(u) == root(v);
    }
    
    void trc() {
        DBG(par);
        DBG(sz);
    }
};
int main() {
    using Mint = ModInt<mod998244353>;
    i32 n, x, q;
    cin >> n >> x >> q;
    array<StrangeUf, 30> ufs;
    REP(i, 30) {
        ufs[i] = StrangeUf(n);
    }
    array<Mint, 30> pow2;
    pow2[0] = Mint(1);
    REP(i, 29) {
        pow2[i + 1] = pow2[i] * Mint(2);
    }
    REP(qi, q) {
        i32 type;
        cin >> type;
        if (type == 1) {
            i32 u, w;
            cin >> u >> w;
            REP(d, 30) {
                i32 f = (w >> d) & 1;
                ufs[d].unite(u, x, f);
            }
        } else if (type == 2) {
            i32 u, v;
            cin >> u >> v;
            if (!ufs[0].same(u, v)) {
                cout << -1 << '\n';
            } else {
                i32 ans = 0;
                REP(d, 30) {
                    ans ^= ufs[d].get_path(u, v) << d;
                }
                cout << ans << '\n';
                x = (x + ans) % n;
            }
        } else if (type == 3) {
            i32 v;
            cin >> v;
            Mint ans;
            REP(d, 30) {
                ans += pow2[d] * Mint(ufs[d].get_comp(v));
            }
            cout << ans << '\n';
        } else {
            i32 v;
            cin >> v;
            x = (x + v) % n;
        }
        DBG(qi);
        REP(d, 3) {
            ufs[d].trc();
        }
    }
}
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