test/data_structure/aoj_dsl_1_b.test.cpp

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• Last update: 2024-08-13 15:38:35+09:00
• Problem: https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DSL_1_B&lang=ja

Depends on

• data_structure/potentialized_dsu.hpp
• misc/concepts.hpp
• misc/monoids.hpp
• template/const.hpp
• template/inout_old.hpp
• template/template.hpp
• template/utils.hpp

Code

#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DSL_1_B&lang=ja"

#include"../../template/template.hpp"
#include"../../data_structure/potentialized_dsu.hpp"
#include"../../misc/monoids.hpp"

int main(){
    int n, q; in(n,q);
    potentialized_dsu<plus_group<ll>> d(n);
    while (q--){
        int t; in(t);
        if (t == 0){
            int u, v; in(u,v);
            ll w; in(w);
            d.merge(u,v,w);
        }
        else {
            int u, v; in(u,v);
            if (d.same(u,v)){
                out(d.diff(u,v));
            }
            else {
                out('?');
            }
        }
    }
}

#line 1 "test/data_structure/aoj_dsl_1_b.test.cpp"
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DSL_1_B&lang=ja"

#line 2 "template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "template/inout_old.hpp"
namespace noya2 {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "template/utils.hpp"

#line 6 "template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "data_structure/potentialized_dsu.hpp"

#line 6 "data_structure/potentialized_dsu.hpp"

#line 2 "misc/concepts.hpp"

#include<concepts>

namespace noya2 {

template<class monoid>
concept Monoid = requires {
    typename monoid::value_type;
    {monoid::op(declval<typename monoid::value_type>(),declval<typename monoid::value_type>())} -> std::same_as<typename monoid::value_type>;
    {monoid::e()} -> std::same_as<typename monoid::value_type>;
};

template<class group>
concept Group = requires {
    requires Monoid<group>;
    {group::inv(declval<typename group::value_type>())} -> std::same_as<typename group::value_type>;
};

} // namespace noya2
#line 8 "data_structure/potentialized_dsu.hpp"

namespace noya2 {

template<Group G>
struct potentialized_dsu {
    using T = typename G::value_type;
    potentialized_dsu (int n = 0) : _n(n), parent_or_size(n,-1), pot(n, G::e()) {}
    // p[u] = op(p[v], d), u is higher than v by d
    int merge(int u, int v, T d){
        int x = leader(u), y = leader(v);
        if (x == y){
            if (diff(u, v) == d) return x;
            else return -1;
        }
        d = G::op(potential(u), G::inv(G::op(potential(v), d)));
        if (-parent_or_size[x] < -parent_or_size[y]){
            d = G::inv(d);
            std::swap(x, y);
        }
        parent_or_size[x] += parent_or_size[y];
        parent_or_size[y] = x;
        pot[y] = d;
        return x;
    }
    int leader(int v){
        assert(0 <= v && v < _n);
        if (parent_or_size[v] < 0) return v;
        int l = leader(parent_or_size[v]);
        pot[v] = G::op(pot[parent_or_size[v]], pot[v]);
        return parent_or_size[v] = l;
    }
    bool same(int u, int v){
        return leader(u) == leader(v);
    }
    int size(int v){
        return -parent_or_size[leader(v)];
    }
    T potential(int v){
        leader(v);
        return pot[v];
    }
    // p[u] = op(p[v], d)
    // d = op(inv(p[v]), p[u])
    T diff(int u, int v){
        return G::op(G::inv(potential(v)), potential(u));
    }
    std::vector<std::vector<int>> groups() {
        std::vector<int> leader_buf(_n), group_size(_n);
        for (int i = 0; i < _n; i++) {
            leader_buf[i] = leader(i);
            group_size[leader_buf[i]]++;
        }
        std::vector<std::vector<int>> result(_n);
        for (int i = 0; i < _n; i++) {
            result[i].reserve(group_size[i]);
        }
        for (int i = 0; i < _n; i++) {
            result[leader_buf[i]].push_back(i);
        }
        result.erase(
            std::remove_if(result.begin(), result.end(),
                           [&](const std::vector<int>& v) { return v.empty(); }),
            result.end());
        return result;
    }
  private:
    int _n;
    std::vector<int> parent_or_size;
    std::vector<T> pot;
};

} // namespace noya2
#line 2 "misc/monoids.hpp"

#line 4 "misc/monoids.hpp"

namespace noya2{

template<typename T>
struct max_monoid {
    using value_type = T;
    static constexpr T op(const T &a, const T &b){ return max(a,b); }
    static constexpr T e(){ return std::numeric_limits<T>::min(); }
    static constexpr T inv(const T &a){ return e(); }
};
template<typename T>
struct min_monoid {
    using value_type = T;
    static constexpr T op(const T &a, const T &b){ return min(a,b); }
    static constexpr T e(){ return std::numeric_limits<T>::max(); }
    static constexpr T inv(const T &a){ return e(); }
};
template<typename T>
struct plus_group {
    using value_type = T;
    static constexpr T op(const T &a, const T &b){ return a + b; }
    static constexpr T e(){ return T(0); }
    static constexpr T inv(const T &a){ return -a; }
};
template<typename T>
struct xor_group {
    using value_type = T;
    static constexpr T op(const T &a, const T &b){ return a ^ b; }
    static constexpr T e(){ return T(0); }
    static constexpr T inv(const T &a){ return a; }
};
    
} // namespace noya2
#line 6 "test/data_structure/aoj_dsl_1_b.test.cpp"

int main(){
    int n, q; in(n,q);
    potentialized_dsu<plus_group<ll>> d(n);
    while (q--){
        int t; in(t);
        if (t == 0){
            int u, v; in(u,v);
            ll w; in(w);
            d.merge(u,v,w);
        }
        else {
            int u, v; in(u,v);
            if (d.same(u,v)){
                out(d.diff(u,v));
            }
            else {
                out('?');
            }
        }
    }
}

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