#696911 (C++17) No.1324 Approximate the Matrix

提出ソース

結果

問題	No.1324 Approximate the Matrix
ユーザー	👑 hitonanode
提出日時	2021-09-06 22:43:12
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	99 ms / 2,000 ms
コード長	9,703 bytes
コンパイル時間	1,705 ms
コンパイル使用メモリ	104,664 KB
実行使用メモリ	6,304 KB
最終ジャッジ日時	2023-08-24 13:03:04
合計ジャッジ時間	5,900 ms
ジャッジサーバーID （参考情報）	judge14 / judge12

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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	1 ms 4,380 KB
testcase_01	AC	1 ms 4,384 KB
testcase_02	AC	2 ms 4,380 KB
testcase_03	AC	95 ms 6,128 KB
testcase_04	AC	93 ms 6,128 KB
testcase_05	AC	95 ms 6,176 KB
testcase_06	AC	93 ms 6,212 KB
testcase_07	AC	94 ms 6,284 KB
testcase_08	AC	7 ms 4,380 KB
testcase_09	AC	7 ms 4,384 KB
testcase_10	AC	13 ms 4,380 KB
testcase_11	AC	25 ms 4,440 KB
testcase_12	AC	6 ms 4,380 KB
testcase_13	AC	4 ms 4,380 KB
testcase_14	AC	27 ms 4,648 KB
testcase_15	AC	10 ms 4,384 KB
testcase_16	AC	2 ms 4,384 KB
testcase_17	AC	17 ms 4,380 KB
testcase_18	AC	6 ms 4,384 KB
testcase_19	AC	6 ms 4,380 KB
testcase_20	AC	3 ms 4,380 KB
testcase_21	AC	3 ms 4,384 KB
testcase_22	AC	4 ms 4,384 KB
testcase_23	AC	15 ms 4,384 KB
testcase_24	AC	37 ms 5,028 KB
testcase_25	AC	19 ms 4,380 KB
testcase_26	AC	18 ms 4,380 KB
testcase_27	AC	8 ms 4,384 KB
testcase_28	AC	1 ms 4,380 KB
testcase_29	AC	2 ms 4,384 KB
testcase_30	AC	2 ms 4,384 KB
testcase_31	AC	1 ms 4,384 KB
testcase_32	AC	1 ms 4,380 KB
testcase_33	AC	1 ms 4,380 KB
testcase_34	AC	2 ms 4,380 KB
testcase_35	AC	1 ms 4,384 KB
testcase_36	AC	1 ms 4,380 KB
testcase_37	AC	98 ms 6,104 KB
testcase_38	AC	98 ms 6,132 KB
testcase_39	AC	97 ms 6,304 KB
testcase_40	AC	98 ms 6,100 KB
testcase_41	AC	99 ms 6,124 KB
testcase_42	AC	4 ms 4,384 KB
testcase_43	AC	5 ms 4,384 KB
testcase_44	AC	5 ms 4,380 KB

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ソースコード

raw source code

#line 1 "combinatorial_opt/test/mincostflow.yuki1324.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1324"
#line 2 "data_structure/radix_heap.hpp"
#include <array>
#include <cstddef>
#include <limits>
#include <tuple>
#include <type_traits>
#include <utility>
#include <vector>

// Radix heap for unsigned integer
template <class uint, class label, typename std::enable_if<std::is_unsigned<uint>::value>::type * = nullptr>
class radix_heap {
    int sz;
    uint last;
    std::array<std::vector<std::pair<uint, label>>, std::numeric_limits<uint>::digits + 1> v;

    template <class U, typename std::enable_if<sizeof(U) == 4>::type * = nullptr>
    static inline int bucket(U x) noexcept {
        return x ? 32 - __builtin_ctz(x) : 0;
    }
    template <class U, typename std::enable_if<sizeof(U) == 8>::type * = nullptr>
    static inline int bucket(U x) noexcept {
        return x ? 64 - __builtin_ctzll(x) : 0;
    }

    void pull() {
        if (!v[0].empty()) return;
        int i = 1;
        while (v[i].empty()) ++i;
        last = v[i].back().first;
        for (int j = 0; j < int(v[i].size()); j++) last = std::min(last, v[i][j].first);
        for (int j = 0; j < int(v[i].size()); j++) {
            v[bucket(v[i][j].first ^ last)].emplace_back(std::move(v[i][j]));
        }
        v[i].clear();
    }

public:
    radix_heap() : sz(0), last(0) {}
    std::size_t size() const noexcept { return sz; }
    bool empty() const noexcept { return sz == 0; }
    void push(uint x, const label &val) { ++sz, v[bucket(x ^ last)].emplace_back(x, val); }
    void push(uint x, label &&val) { ++sz, v[bucket(x ^ last)].emplace_back(x, std::move(val)); }
    template <class... Args> void emplace(uint x, Args &&...args) {
        ++sz, v[bucket(x ^ last)].emplace_back(std::piecewise_construct, std::forward_as_tuple(x), std::forward_as_tuple(args...));
    }
    void pop() { pull(), --sz, v[0].pop_back(); }
    std::pair<uint, label> top() { return pull(), v[0].back(); }
    uint top_key() { return pull(), v[0].back().first; }
    label &top_label() { return pull(), v[0].back().second; }
    void clear() {
        sz = 0, last = 0;
        for (auto &vec : v) vec.clear();
    }
    void swap(radix_heap<uint, label> &a) { std::swap(sz, a.sz), std::swap(last, a.last), v.swap(a.v); }
};
#line 3 "combinatorial_opt/mincostflow_nonegativeloop.hpp"
#include <cassert>
#line 5 "combinatorial_opt/mincostflow_nonegativeloop.hpp"
#include <queue>
#line 8 "combinatorial_opt/mincostflow_nonegativeloop.hpp"

// CUT begin
// Minimum cost flow WITH NO NEGATIVE CYCLE (just negative cost edge is allowed)
// Verified:
// - SRM 770 Div1 Medium https://community.topcoder.com/stat?c=problem_statement&pm=15702
// - CodeChef LTIME98 Ancient Magic https://www.codechef.com/problems/ANCT
template <class Cap = long long, class Cost = long long, Cost INF_COST = std::numeric_limits<Cost>::max() / 2>
struct MinCostFlow {
    struct _edge {
        int to, rev;
        Cap cap;
        Cost cost;
        template <class Ostream> friend Ostream &operator<<(Ostream &os, const _edge &e) {
            return os << '(' << e.to << ',' << e.rev << ',' << e.cap << ',' << e.cost << ')';
        }
    };
    bool _is_dual_infeasible;
    int V;
    std::vector<std::vector<_edge>> g;
    std::vector<Cost> dist;
    std::vector<int> prevv, preve;
    std::vector<Cost> dual; // dual[V]: potential
    std::vector<std::pair<int, int>> pos;

    bool _initialize_dual_dag() {
        std::vector<int> deg_in(V);
        for (int i = 0; i < V; i++) {
            for (const auto &e : g[i]) deg_in[e.to] += (e.cap > 0);
        }
        std::vector<int> st;
        st.reserve(V);
        for (int i = 0; i < V; i++) {
            if (!deg_in[i]) st.push_back(i);
        }
        for (int n = 0; n < V; n++) {
            if (int(st.size()) == n) return false; // Not DAG
            int now = st[n];
            for (const auto &e : g[now]) {
                if (!e.cap) continue;
                deg_in[e.to]--;
                if (deg_in[e.to] == 0) st.push_back(e.to);
                if (dual[e.to] >= dual[now] + e.cost) dual[e.to] = dual[now] + e.cost;
            }
        }
        return true;
    }

    bool _initialize_dual_spfa() { // Find feasible dual's when negative cost edges exist
        dual.assign(V, 0);
        std::queue<int> q;
        std::vector<int> in_queue(V);
        std::vector<int> nvis(V);
        for (int i = 0; i < V; i++) q.push(i), in_queue[i] = true;
        while (q.size()) {
            int now = q.front();
            q.pop(), in_queue[now] = false;
            if (nvis[now] > V) return false; // Negative cycle exists
            nvis[now]++;
            for (const auto &e : g[now]) {
                if (!e.cap) continue;
                if (dual[e.to] > dual[now] + e.cost) {
                    dual[e.to] = dual[now] + e.cost;
                    if (!in_queue[e.to]) in_queue[e.to] = true, q.push(e.to);
                }
            }
        }
        return true;
    }

    bool initialize_dual() {
        return !_is_dual_infeasible or _initialize_dual_dag() or _initialize_dual_spfa();
    }

    void _dijkstra(int s) { // O(ElogV)
        prevv.assign(V, -1);
        preve.assign(V, -1);
        dist.assign(V, INF_COST);
        dist[s] = 0;
        typedef typename std::make_unsigned<Cost>::type UCost;
        using P = std::pair<UCost, int>;
        // radix_heap<UCost, int> q;
        std::priority_queue<P, std::vector<P>, std::greater<P>> q;
        q.emplace(0, s);
        while (!q.empty()) {
            P p = q.top();
            q.pop();
            int v = p.second;
            if (dist[v] < p.first) continue;
            for (int i = 0; i < (int)g[v].size(); i++) {
                _edge &e = g[v][i];
                UCost c = dist[v] + e.cost + dual[v] - dual[e.to];
                if (e.cap > 0 and dist[e.to] > c) {
                    dist[e.to] = c, prevv[e.to] = v, preve[e.to] = i;
                    assert(dist[e.to] >= 0);
                    q.emplace(dist[e.to], e.to);
                }
            }
        }
    }

    MinCostFlow(int V = 0) : _is_dual_infeasible(false), V(V), g(V), dual(V, 0) {
        static_assert(INF_COST > 0, "INF_COST must be positive");
    }

    int add_edge(int from, int to, Cap cap, Cost cost) {
        assert(0 <= from and from < V);
        assert(0 <= to and to < V);
        assert(cap >= 0);
        if (cost < 0) _is_dual_infeasible = true;
        pos.emplace_back(from, g[from].size());
        g[from].push_back({to, (int)g[to].size() + (from == to), cap, cost});
        g[to].push_back({from, (int)g[from].size() - 1, (Cap)0, -cost});
        return int(pos.size()) - 1;
    }

    // Flush flow f from s to t. Graph must not have negative cycle.
    std::pair<Cap, Cost> flow(int s, int t, const Cap &flow_limit) {
        if (!initialize_dual()) throw; // Fail to find feasible dual
        Cost cost = 0;
        Cap flow_rem = flow_limit;
        while (flow_rem > 0) {
            _dijkstra(s);
            if (dist[t] == INF_COST) break;
            for (int v = 0; v < V; v++) dual[v] = std::min(dual[v] + dist[v], INF_COST);
            Cap d = flow_rem;
            for (int v = t; v != s; v = prevv[v]) d = std::min(d, g[prevv[v]][preve[v]].cap);
            flow_rem -= d;
            cost += d * (dual[t] - dual[s]);
            for (int v = t; v != s; v = prevv[v]) {
                _edge &e = g[prevv[v]][preve[v]];
                e.cap -= d;
                g[v][e.rev].cap += d;
            }
        }
        return std::make_pair(flow_limit - flow_rem, cost);
    }

    struct edge {
        int from, to;
        Cap cap, flow;
        Cost cost;
        template <class Ostream> friend Ostream &operator<<(Ostream &os, const edge &e) {
            return os << '(' << e.from << "->" << e.to << ',' << e.flow << '/' << e.cap << ",$" << e.cost << ')';
        }
    };

    edge get_edge(int edge_id) const {
        int m = int(pos.size());
        assert(0 <= edge_id and edge_id < m);
        auto _e = g[pos[edge_id].first][pos[edge_id].second];
        auto _re = g[_e.to][_e.rev];
        return {pos[edge_id].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost};
    }
    std::vector<edge> edges() const {
        std::vector<edge> ret(pos.size());
        for (int i = 0; i < int(pos.size()); i++) ret[i] = get_edge(i);
        return ret;
    }

    template <class Ostream> friend Ostream &operator<<(Ostream &os, const MinCostFlow &mcf) {
        os << "[MinCostFlow]V=" << mcf.V << ":";
        for (int i = 0; i < mcf.V; i++) {
            for (auto &e : mcf.g[i]) os << "\n" << i << "->" << e.to << ":cap" << e.cap << ",$" << e.cost;
        }
        return os;
    }
};
#line 3 "combinatorial_opt/test/mincostflow.yuki1324.test.cpp"
#include <iostream>
#line 5 "combinatorial_opt/test/mincostflow.yuki1324.test.cpp"
using namespace std;

int main() {
    cin.tie(nullptr), ios::sync_with_stdio(false);
    int N, K;
    cin >> N >> K;
    vector<int> A(N), B(N);
    vector<vector<int>> P(N, vector<int>(N));
    for (auto &x : A) cin >> x;
    for (auto &x : B) cin >> x;
    for (auto &v : P) {
        for (auto &x : v) cin >> x;
    }

    const int gs = N * 2, gt = gs + 1;
    MinCostFlow<int, long long> graph(gt + 1);
    long long ret = 0;
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            ret += P[i][j] * P[i][j];
            for (int a = 0; a < A[i]; a++) graph.add_edge(i, j + N, 1, 2 * (a - P[i][j]) + 1);
        }
        graph.add_edge(gs, i, A[i], 0);
        graph.add_edge(i + N, gt, B[i], 0);
    }
    cout << ret + graph.flow(gs, gt, K).second << '\n';
}