#755455 (C++23) No.1911 Alternately Coloring

提出ソース
結果

問題	No.1911 Alternately Coloring
ユーザー	hitonanode
提出日時	2022-04-22 21:54:43
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	832 ms / 4,000 ms
コード長	14,873 bytes
コンパイル時間	2,495 ms
コンパイル使用メモリ	205,176 KB
実行使用メモリ	6,948 KB
最終ジャッジ日時	2024-06-24 03:02:37
合計ジャッジ時間	16,061 ms
ジャッジサーバーID （参考情報）	judge5 / judge4
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,812 KB
testcase_01	AC	2 ms 6,944 KB
testcase_02	AC	2 ms 6,948 KB
testcase_03	AC	2 ms 6,944 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	734 ms 6,940 KB
testcase_07	AC	556 ms 6,940 KB
testcase_08	AC	550 ms 6,940 KB
testcase_09	AC	695 ms 6,944 KB
testcase_10	AC	535 ms 6,940 KB
testcase_11	AC	675 ms 6,940 KB
testcase_12	AC	710 ms 6,940 KB
testcase_13	AC	662 ms 6,940 KB
testcase_14	AC	472 ms 6,940 KB
testcase_15	AC	599 ms 6,940 KB
testcase_16	AC	591 ms 6,944 KB
testcase_17	AC	604 ms 6,940 KB
testcase_18	AC	485 ms 6,944 KB
testcase_19	AC	551 ms 6,940 KB
testcase_20	AC	615 ms 6,940 KB
testcase_21	AC	520 ms 6,944 KB
testcase_22	AC	676 ms 6,940 KB
testcase_23	AC	832 ms 6,944 KB
testcase_24	AC	2 ms 6,944 KB
testcase_25	AC	2 ms 6,940 KB
testcase_26	AC	2 ms 6,940 KB
testcase_27	AC	638 ms 6,944 KB
testcase_28	AC	267 ms 6,944 KB
testcase_29	AC	593 ms 6,940 KB
testcase_30	AC	2 ms 6,940 KB
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ソースコード

raw source code
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr)
#else
#define dbg(x) 0
#define dbgif(cond, x) 0
#endif

template <typename T, T INF = std::numeric_limits<T>::max() / 2, int INVALID = -1>
struct ShortestPath {
    int V, E;
    bool single_positive_weight;
    T wmin, wmax;
    std::vector<std::vector<std::pair<int, T>>> to;

    ShortestPath(int V = 0) : V(V), E(0), single_positive_weight(true), wmin(0), wmax(0), to(V) {}
    void add_edge(int s, int t, T w) {
        assert(0 <= s and s < V);
        assert(0 <= t and t < V);
        to[s].emplace_back(t, w);
        E++;
        if (w > 0 and wmax > 0 and wmax != w) single_positive_weight = false;
        wmin = std::min(wmin, w);
        wmax = std::max(wmax, w);
    }

    std::vector<T> dist;
    std::vector<int> prev;

    // Dijkstra algorithm
    // Complexity: O(E log E)
    using Pque = std::priority_queue<std::pair<T, int>, std::vector<std::pair<T, int>>,
                                     std::greater<std::pair<T, int>>>;
    template <class Heap = Pque> void Dijkstra(int s) {
        assert(0 <= s and s < V);
        dist.assign(V, INF);
        dist[s] = 0;
        prev.assign(V, INVALID);
        Heap pq;
        pq.emplace(0, s);
        while (!pq.empty()) {
            T d;
            int v;
            std::tie(d, v) = pq.top();
            pq.pop();
            if (dist[v] < d) continue;
            for (auto nx : to[v]) {
                T dnx = d + nx.second;
                if (dist[nx.first] > dnx) {
                    dist[nx.first] = dnx, prev[nx.first] = v;
                    pq.emplace(dnx, nx.first);
                }
            }
        }
    }

    // Dijkstra algorithm, O(V^2 + E)
    void DijkstraVquad(int s) {
        assert(0 <= s and s < V);
        dist.assign(V, INF);
        dist[s] = 0;
        prev.assign(V, INVALID);
        std::vector<char> fixed(V, false);
        while (true) {
            int r = INVALID;
            T dr = INF;
            for (int i = 0; i < V; i++) {
                if (!fixed[i] and dist[i] < dr) r = i, dr = dist[i];
            }
            if (r == INVALID) break;
            fixed[r] = true;
            int nxt;
            T dx;
            for (auto p : to[r]) {
                std::tie(nxt, dx) = p;
                if (dist[nxt] > dist[r] + dx) dist[nxt] = dist[r] + dx, prev[nxt] = r;
            }
        }
    }

    // Bellman-Ford algorithm
    // Complexity: O(VE)
    bool BellmanFord(int s, int nb_loop) {
        assert(0 <= s and s < V);
        dist.assign(V, INF), prev.assign(V, INVALID);
        dist[s] = 0;
        for (int l = 0; l < nb_loop; l++) {
            bool upd = false;
            for (int v = 0; v < V; v++) {
                if (dist[v] == INF) continue;
                for (auto nx : to[v]) {
                    T dnx = dist[v] + nx.second;
                    if (dist[nx.first] > dnx) dist[nx.first] = dnx, prev[nx.first] = v, upd = true;
                }
            }
            if (!upd) return true;
        }
        return false;
    }

    // Bellman-ford algorithm using queue (deque)
    // Complexity: O(VE)
    // Requirement: no negative loop
    void SPFA(int s) {
        assert(0 <= s and s < V);
        dist.assign(V, INF);
        prev.assign(V, INVALID);
        std::deque<int> q;
        std::vector<char> in_queue(V);
        dist[s] = 0;
        q.push_back(s), in_queue[s] = 1;
        while (!q.empty()) {
            int now = q.front();
            q.pop_front(), in_queue[now] = 0;
            for (auto nx : to[now]) {
                T dnx = dist[now] + nx.second;
                int nxt = nx.first;
                if (dist[nxt] > dnx) {
                    dist[nxt] = dnx;
                    if (!in_queue[nxt]) {
                        if (q.size() and dnx < dist[q.front()]) { // Small label first optimization
                            q.push_front(nxt);
                        } else {
                            q.push_back(nxt);
                        }
                        prev[nxt] = now, in_queue[nxt] = 1;
                    }
                }
            }
        }
    }

    void ZeroOneBFS(int s) {
        assert(0 <= s and s < V);
        dist.assign(V, INF), prev.assign(V, INVALID);
        dist[s] = 0;
        std::deque<int> que;
        que.push_back(s);
        while (!que.empty()) {
            int v = que.front();
            que.pop_front();
            for (auto nx : to[v]) {
                T dnx = dist[v] + nx.second;
                if (dist[nx.first] > dnx) {
                    dist[nx.first] = dnx, prev[nx.first] = v;
                    if (nx.second) {
                        que.push_back(nx.first);
                    } else {
                        que.push_front(nx.first);
                    }
                }
            }
        }
    }

    bool dag_solver(int s) {
        assert(0 <= s and s < V);
        std::vector<int> indeg(V, 0);
        std::queue<int> que;
        que.push(s);
        while (que.size()) {
            int now = que.front();
            que.pop();
            for (auto nx : to[now]) {
                indeg[nx.first]++;
                if (indeg[nx.first] == 1) que.push(nx.first);
            }
        }
        dist.assign(V, INF), prev.assign(V, INVALID);
        dist[s] = 0;
        que.push(s);
        while (que.size()) {
            int now = que.front();
            que.pop();
            for (auto nx : to[now]) {
                indeg[nx.first]--;
                if (dist[nx.first] > dist[now] + nx.second)
                    dist[nx.first] = dist[now] + nx.second, prev[nx.first] = now;
                if (indeg[nx.first] == 0) que.push(nx.first);
            }
        }
        return *max_element(indeg.begin(), indeg.end()) == 0;
    }

    // Retrieve a sequence of vertex ids that represents shortest path [s, ..., goal]
    // If not reachable to goal, return {}
    std::vector<int> retrieve_path(int goal) const {
        assert(int(prev.size()) == V);
        assert(0 <= goal and goal < V);
        if (dist[goal] == INF) return {};
        std::vector<int> ret{goal};
        while (prev[goal] != INVALID) {
            goal = prev[goal];
            ret.push_back(goal);
        }
        std::reverse(ret.begin(), ret.end());
        return ret;
    }

    void solve(int s) {
        if (wmin >= 0) {
            if (single_positive_weight) {
                ZeroOneBFS(s);
            } else {
                if ((long long)V * V < (E << 4)) {
                    DijkstraVquad(s);
                } else {
                    Dijkstra(s);
                }
            }
        } else {
            BellmanFord(s, V);
        }
    }

    // Warshall-Floyd algorithm
    // Complexity: O(E + V^3)
    std::vector<std::vector<T>> dist2d;
    void WarshallFloyd() {
        dist2d.assign(V, std::vector<T>(V, INF));
        for (int i = 0; i < V; i++) {
            dist2d[i][i] = 0;
            for (auto p : to[i]) dist2d[i][p.first] = std::min(dist2d[i][p.first], p.second);
        }
        for (int k = 0; k < V; k++) {
            for (int i = 0; i < V; i++) {
                if (dist2d[i][k] == INF) continue;
                for (int j = 0; j < V; j++) {
                    if (dist2d[k][j] == INF) continue;
                    dist2d[i][j] = std::min(dist2d[i][j], dist2d[i][k] + dist2d[k][j]);
                }
            }
        }
    }

    void dump_graphviz(std::string filename = "shortest_path") const {
        std::ofstream ss(filename + ".DOT");
        ss << "digraph{\n";
        for (int i = 0; i < V; i++) {
            for (const auto &e : to[i])
                ss << i << "->" << e.first << "[label=" << e.second << "];\n";
        }
        ss << "}\n";
        ss.close();
        return;
    }
};



// UnionFind Tree (0-indexed), based on size of each disjoint set
struct UnionFind {
    std::vector<int> par, cou;
    UnionFind(int N = 0) : par(N), cou(N, 1) { iota(par.begin(), par.end(), 0); }
    int find(int x) { return (par[x] == x) ? x : (par[x] = find(par[x])); }
    bool unite(int x, int y) {
        x = find(x), y = find(y);
        if (x == y) return false;
        if (cou[x] < cou[y]) std::swap(x, y);
        par[y] = x, cou[x] += cou[y];
        return true;
    }
    int count(int x) { return cou[find(x)]; }
    bool same(int x, int y) { return find(x) == find(y); }
};


int main() {
    int N, M;
    cin >> N >> M;
    vector<vector<int>> to(N);
    UnionFind uf(N * 2);
    REP(e, M) {
        int a, b;
        cin >> a >> b;
        --a, --b;
        to[a].push_back(b);
        to[b].push_back(a);
        uf.unite(a, b + N);
        uf.unite(b, a + N);
    }
    bool notb = false;
    REP(r, N) {
        if (uf.same(r, N + r)) notb = true;
    }

    vector<int> R(N), B(N);
    cin >> R >> B;

    lint ret = 0;

    if (!notb) {
        REP(t, 2) {
            lint tmp = 0;
            REP(i, N) tmp += (uf.same(0, i) ? R[i] : B[i]);
            chmax(ret, tmp);
            swap(R, B);
        }
        cout << ret << '\n';
        return 0;
    }

    lint all_max = 0;
    REP(i, N) all_max += max(R[i], B[i]);
    dbg(all_max);


    REP(_, 2) {
        REP(r, N) {
            ShortestPath<lint> graph(N * 2 + 1);
            REP(i, N) {
                for (auto j : to[i]) {
                    graph.add_edge(i, j + N, max(R[j], B[j]) - R[j]);
                    graph.add_edge(i + N, j, max(R[j], B[j]) - B[j]);
                    if (j == r) {
                        graph.add_edge(i, N * 2, max(R[j], B[j]) - R[j]);
                    }
                }
            }
            graph.solve(r);
            chmax(ret, all_max - graph.dist[N * 2]);
        }
        swap(R, B);
    }
    cout << ret << '\n';
}
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結果

テストケース

ソースコード
