結果

問題 No.3056 Disconnected Coloring
コンテスト
ユーザー 横山緑
提出日時 2025-03-14 22:22:58
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 198 ms / 2,000 ms
コード長 8,758 bytes
コンパイル時間 4,440 ms
コンパイル使用メモリ 289,728 KB
実行使用メモリ 20,128 KB
最終ジャッジ日時 2025-03-14 22:23:09
合計ジャッジ時間 9,871 ms
ジャッジサーバーID
（参考情報） 		judge1 / 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 * 2
other AC * 34
権限があれば一括ダウンロードができます

ソースコード

diff # 

#line 2 "template.hpp"
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>
using namespace std;
// https://xn--kst.jp/blog/2019/08/29/cpp-comp/
// debug methods
// usage: debug(x,y);
// vector 出力できるように修正
template <typename T>
ostream& debug_print(ostream& os, const vector<T>& v) {
    os << "[";
    for (size_t i = 0; i < v.size(); ++i) {
        os << v[i];
        if (i < v.size() - 1) os << ", ";
    }
    os << "]";
    return os;
}
template <typename T>
ostream& debug_print(ostream& os, const T& var) {
    os << var;
    return os;
}
#define CHOOSE(a) CHOOSE2 a
#define CHOOSE2(a0, a1, a2, a3, a4, x, ...) x
#define debug_1(x1) { cout << #x1 << ": "; debug_print(cout, x1) << endl; }
#define debug_2(x1, x2) { cout << #x1 << ": "; debug_print(cout, x1) << ", " << #x2 << ": "; debug_print(cout, x2) << endl; }
#define debug_3(x1, x2, x3) { cout << #x1 << ": "; debug_print(cout, x1) << ", " << #x2 << ": "; debug_print(cout, x2) << ", " << #x3 << ": "; debug_print(cout, x3) << endl; }
#define debug_4(x1, x2, x3, x4) { cout << #x1 << ": "; debug_print(cout, x1) << ", " << #x2 << ": "; debug_print(cout, x2) << ", " << #x3 << ": "; debug_print(cout, x3) << ", " << #x4 << ": "; debug_print(cout, x4) << endl; }
#define debug_5(x1, x2, x3, x4, x5) { cout << #x1 << ": "; debug_print(cout, x1) << ", " << #x2 << ": "; debug_print(cout, x2) << ", " << #x3 << ": "; debug_print(cout, x3) << ", " << #x4 << ": "; debug_print(cout, x4) << ", " << #x5 << ": "; debug_print(cout, x5) << endl; }

#ifdef LOCAL
#define debug(...) CHOOSE((__VA_ARGS__, debug_5, debug_4, debug_3, debug_2, debug_1, ~))(__VA_ARGS__)
#else
#define debug(...)
#endif

using ll = long long;
using vl = vector<ll>;
using vll = vector<vl>;
using P = pair<ll, ll>;
#define all(v) v.begin(), v.end()
template <typename T> inline bool chmax(T &a, T b) {
    return ((a < b) ? (a = b, true) : (false));
}
template <typename T> inline bool chmin(T &a, T b) {
    return ((a > b) ? (a = b, true) : (false));
}
#define rep1(i, n) for(ll i = 1; i <= ((ll)n); ++i)
// https://trap.jp/post/1224/
template <class... T> constexpr auto min(T... a) {
    return min(initializer_list<common_type_t<T...>>{a...});
}
template <class... T> constexpr auto max(T... a) {
    return max(initializer_list<common_type_t<T...>>{a...});
}
template <class... T> void input(T &...a) { (cin >> ... >> a); }
template <class T> void input(vector<T> &a) {
    for(T &x : a)
        cin >> x;
}
void print() { cout << '\n'; }
template <class T, class... Ts> void print(const T &a, const Ts &...b) {
    cout << a;
    (cout << ... << (cout << ' ', b));
    cout << '\n';
}
void print(const string &s) {
    cout << s << '\n';
}
template <class Container, typename = void>
struct is_container : std::false_type {};
template <class Container>
struct is_container<Container, std::void_t<decltype(std::declval<Container>().begin()), decltype(std::declval<Container>().end())>> : std::true_type {};
template <class Container>
typename enable_if<is_container<Container>::value>::type print(const Container& x) {
    if (!x.empty()) {
        auto it = x.begin();
        for (; it != prev(x.end()); ++it) {
            cout << *it << " ";
        }
        cout << *it << "\n";  // 最後の要素を出力して改行
    }
}
#define INT(...)                                                               \
    int __VA_ARGS__;                                                           \
    input(__VA_ARGS__)
#define LL(...)                                                                \
    long long __VA_ARGS__;                                                     \
    input(__VA_ARGS__)
#define STR(...)                                                               \
    string __VA_ARGS__;                                                        \
    input(__VA_ARGS__)
#define REP1(a) for(ll i = 0; i < a; i++)
#define REP2(i, a) for(ll i = 0; i < a; i++)
#define REP3(i, a, b) for(ll i = a; i < b; i++)
#define REP4(i, a, b, c) for(ll i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)

ll inf = 3e18;
vl dx = {1, -1, 0, 0};
vl dy = {0, 0, 1, -1};
#line 3 "data_structure/union-find.hpp"
struct UnionFind {
    int n;
    vector<int> p;
    UnionFind(int n) : n(n), p(n, -1) {}
    int leader(int x) {
        if(p[x] < 0)
            return x;
        return p[x] = leader(p[x]);
    }
    int merge(int x, int y) {
        x = leader(x), y = leader(y);
        if(x == y)
            return x;
        if(-p[x] < -p[y])
            swap(x, y);
        p[x] += p[y];
        p[y] = x;
        return x;
    }
    int size(int x) { return -p[leader(x)]; }
    bool same(int x, int y) { return leader(x) == leader(y); }
};
#line 3 "graph/graph-template.hpp"
// https://ei1333.github.io/library/graph/graph-template.hpp
template <class T = ll> struct Edge {
    int from, to;
    T cost;
    int idx;
    Edge() = default;
    Edge(int from, int to, T cost = 1, int idx = -1)
        : from(from), to(to), cost(cost), idx(idx) {}
    Edge &operator=(const int &x) {
        to = x;
        return *this;
    }
    operator int() const { return to; }
};
template <class T = ll> struct Graph {
    using cost_type = T;
    vector<vector<Edge<T>>> g;
    int es; // edge_size
    Graph(int n) : g(n), es(0) {};
    int size() const { return ssize(g); }
    void add_directed_edge(int from, int to, T cost = 1) {
        g[from].emplace_back(from, to, cost, es++);
    }
    void add_edge(int from, int to, T cost = 1) {
        g[from].emplace_back(from, to, cost, es);
        g[to].emplace_back(to, from, cost, es++);
    }
    vector<Edge<T>> &operator[](const int &k) { return g[k]; }
    const vector<Edge<T>> &operator[](const int &k) const { return g[k]; }
    void read(int m, int padding = -1, bool weighted = false,
              bool directed = false) {
        rep(i, m) {
            int a, b;
            T c(1);
            cin >> a >> b;
            a += padding;
            b += padding;
            if(weighted)
                cin >> c;
            if(directed)
                add_directed_edge(a, b, c);
            else
                add_edge(a, b, c);
        }
    }
};
#line 4 "/home/y_midori/cp/test/a.cpp"
// #include <atcoder/all>
// using namespace atcoder;
// using mint = modint998244353;
string solve() {
    INT(n, m);
    if(m & 1) {
        return "-1";
    }
    Graph<bool> g(n);
    vector<int> c(m, -1);
    int red = 0, blue = 0;
    string ans;
    g.read(m);
    for(auto to : g[0]) {
        if(to == n - 1) {
            return "-1";
        }
    }
    auto check = [&](char c) {
        UnionFind dsu(n);
        rep(i, n) {
            for(auto to : g[i]) {
                if(ans[to.idx] == c) {
                    dsu.merge(i, to);
                }
            }
        }
        assert(!dsu.same(0, n - 1));
    };
    if(max(g[0].size(), g[n - 1].size()) <= m / 2) {
        for(auto to : g[0]) {
            c[to.idx] = 0;
            red++;
        }
        for(auto to : g[n - 1])
            c[to.idx] = 1;

        rep(i, m) {
            if(c[i] == -1) {
                if(red < m / 2) {
                    c[i] = 0;
                    red++;
                } else
                    c[i] = 1;
            }
            ans.push_back(c[i] ? 'B' : 'R');
        }
        check('B');
        check('R');
        return ans;
        // print(ans);
        // return;
    }
    int s = 0, t = n - 1;
    if(g[s].size() > g[t].size())
        swap(s, t);
    assert(g[t].size() > m / 2);
    UnionFind uf(n);
    rep(i, n) {
        if(i == t)
            continue;
        for(auto to : g[i])
            if(to != t)
                uf.merge(i, to);
    }
    for(auto to : g[t]) {
        if(uf.same(s, to)) {
            c[to.idx] = 1;
            blue++;
        }
    }
    assert(blue <= m / 2);
    for(auto to : g[t]) {
        if(c[to.idx] == -1 and blue < m / 2) {
            c[to.idx] = 1;
            blue++;
        }
    }
    assert(blue == m / 2);
    rep(i, m) {
        if(c[i] == 1)
            ans.push_back('B');
        else
            ans.push_back('R');
    }

    check('B');
    check('R');
    // print(ans);
    return ans;
}
int main() {
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    cout << std::setprecision(16);
    string ans = solve();
    print(ans);
    if(ans != "-1") {
        ll cnt = 0;
        for(auto c : ans) {
            if(c == 'R')
                cnt++;
            else if(c == 'B')
                cnt--;
            else
                exit(1);
        }
        assert(cnt == 0);
    }
}
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