#690758 (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	2021-08-19 00:25:26
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	64 ms / 2,000 ms
コード長	6,287 bytes
コンパイル時間	1,860 ms
コンパイル使用メモリ	146,888 KB
実行使用メモリ	5,672 KB
最終ジャッジ日時	2024-04-20 03:34:11
合計ジャッジ時間	3,243 ms
ジャッジサーバーID （参考情報）	judge2 / judge1

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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 5,248 KB
testcase_01	AC	2 ms 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	36 ms 5,556 KB
testcase_04	AC	45 ms 5,424 KB
testcase_05	AC	34 ms 5,376 KB
testcase_06	AC	42 ms 5,376 KB
testcase_07	AC	39 ms 5,564 KB
testcase_08	AC	6 ms 5,376 KB
testcase_09	AC	4 ms 5,376 KB
testcase_10	AC	9 ms 5,376 KB
testcase_11	AC	14 ms 5,376 KB
testcase_12	AC	4 ms 5,376 KB
testcase_13	AC	3 ms 5,376 KB
testcase_14	AC	15 ms 5,376 KB
testcase_15	AC	8 ms 5,376 KB
testcase_16	AC	2 ms 5,376 KB
testcase_17	AC	10 ms 5,376 KB
testcase_18	AC	4 ms 5,376 KB
testcase_19	AC	3 ms 5,376 KB
testcase_20	AC	3 ms 5,376 KB
testcase_21	AC	2 ms 5,376 KB
testcase_22	AC	3 ms 5,376 KB
testcase_23	AC	6 ms 5,376 KB
testcase_24	AC	17 ms 5,376 KB
testcase_25	AC	9 ms 5,376 KB
testcase_26	AC	12 ms 5,376 KB
testcase_27	AC	5 ms 5,376 KB
testcase_28	AC	2 ms 5,376 KB
testcase_29	AC	1 ms 5,376 KB
testcase_30	AC	2 ms 5,376 KB
testcase_31	AC	2 ms 5,376 KB
testcase_32	AC	1 ms 5,376 KB
testcase_33	AC	2 ms 5,376 KB
testcase_34	AC	2 ms 5,376 KB
testcase_35	AC	2 ms 5,376 KB
testcase_36	AC	2 ms 5,376 KB
testcase_37	AC	43 ms 5,376 KB
testcase_38	AC	40 ms 5,408 KB
testcase_39	AC	45 ms 5,544 KB
testcase_40	AC	64 ms 5,672 KB
testcase_41	AC	34 ms 5,376 KB
testcase_42	AC	5 ms 5,376 KB
testcase_43	AC	5 ms 5,376 KB
testcase_44	AC	5 ms 5,376 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 <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 <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;

// https://people.orie.cornell.edu/dpw/orie633/
template <class Cap, class Cost, int SCALING = 1, int REFINEMENT_ITER = 20> struct mcf_costscaling {
    mcf_costscaling() = default;
    mcf_costscaling(int n) : _n(n), to(n), b(n), p(n) {}

    int _n;
    std::vector<Cap> cap;
    std::vector<Cost> cost;
    std::vector<int> opposite;
    std::vector<std::vector<int>> to;
    std::vector<Cap> b;
    std::vector<Cost> p;

    int add_edge(int from_, int to_, Cap cap_, Cost cost_) {
        assert(0 <= from_ and from_ < _n);
        assert(0 <= to_ and to_ < _n);
        assert(0 <= cap_);
        cost_ *= (_n + 1);
        const int e = int(cap.size());
        to[from_].push_back(e);
        cap.push_back(cap_);
        cost.push_back(cost_);
        opposite.push_back(to_);

        to[to_].push_back(e + 1);
        cap.push_back(0);
        cost.push_back(-cost_);
        opposite.push_back(from_);
        return e / 2;
    }
    void add_supply(int v, Cap supply) { b[v] += supply; }
    void add_demand(int v, Cap demand) { add_supply(v, -demand); }

    template <typename RetCost = Cost> RetCost solve() {
        Cost eps = 1;
        std::vector<int> que;
        for (const auto c : cost) {
            while (eps <= -c) eps <<= SCALING;
        }
        for (; eps >>= SCALING;) {
            auto no_admissible_cycle = [&]() -> bool {
                for (int i = 0; i < _n; i++) {
                    if (b[i]) return false;
                }
                std::vector<Cost> pp = p;
                for (int iter = 0; iter < REFINEMENT_ITER; iter++) {
                    bool flg = false;
                    for (int e = 0; e < int(cap.size()); e++) {
                        if (!cap[e]) continue;
                        int i = opposite[e ^ 1], j = opposite[e];
                        if (pp[j] > pp[i] + cost[e] + eps) pp[j] = pp[i] + cost[e] + eps, flg = true;
                    }
                    if (!flg) return p = pp, true;
                }
                return false;
            };
            if (no_admissible_cycle()) continue; // Refine

            for (int e = 0; e < int(cap.size()); e++) {
                const int i = opposite[e ^ 1], j = opposite[e];
                const Cost cp_ij = cost[e] + p[i] - p[j];
                if (cap[e] and cp_ij < 0) b[i] -= cap[e], b[j] += cap[e], cap[e ^ 1] += cap[e], cap[e] = 0;
            }
            que.clear();
            int qh = 0;
            for (int i = 0; i < _n; i++) {
                if (b[i] > 0) que.push_back(i);
            }
            std::vector<int> iters(_n);
            while (qh < int(que.size())) {
                const int i = que[qh++];
                for (; iters[i] < int(to[i].size()) and b[i]; ++iters[i]) { // Push
                    int e = to[i][iters[i]];
                    if (!cap[e]) continue;
                    int j = opposite[e];
                    Cost cp_ij = cost[e] + p[i] - p[j];
                    if (cp_ij >= 0) continue;
                    Cap f = b[i] > cap[e] ? cap[e] : b[i];
                    if (b[j] <= 0 and b[j] + f > 0) que.push_back(j);
                    b[i] -= f, b[j] += f, cap[e] -= f, cap[e ^ 1] += f;
                }

                if (b[i] > 0) { // Relabel
                    bool flg = false;
                    for (int e : to[i]) {
                        if (!cap[e]) continue;
                        Cost x = p[opposite[e]] - cost[e] - eps;
                        if (!flg or x > p[i]) flg = true, p[i] = x;
                    }
                    que.push_back(i), iters[i] = 0;
                }
            }
        }
        RetCost ret = 0;
        for (int e = 0; e < int(cap.size()); e += 2) ret += RetCost(cost[e]) * cap[e ^ 1];
        return ret / (_n + 1);
    }
    std::vector<Cost> potential() const {
        std::vector<Cost> ret = p, c0 = cost;
        for (auto &x : ret) x /= (_n + 1);
        for (auto &x : c0) x /= (_n + 1);
        while (true) {
            bool flg = false;
            for (int i = 0; i < _n; i++) {
                for (const auto e : to[i]) {
                    if (!cap[e]) continue;
                    int j = opposite[e];
                    auto y = ret[i] + c0[e];
                    if (ret[j] > y) ret[j] = y, flg = true;
                }
            }
            if (!flg) break;
        }
        return ret;
    }
    struct edge {
        int from, to;
        Cap cap, flow;
        Cost cost;
    };
    edge get_edge(int e) const {
        int m = cap.size() / 2;
        assert(e >= 0 and e < m);
        return {opposite[e * 2 + 1], opposite[e * 2], cap[e * 2] + cap[e * 2 + 1], cap[e * 2 + 1], cost[e * 2] / (_n + 1)};
    }
    std::vector<edge> edges() const {
        int m = cap.size() / 2;
        std::vector<edge> result(m);
        for (int i = 0; i < m; i++) result[i] = get_edge(i);
        return result;
    }
};

int main() {
    cin.tie(nullptr), ios::sync_with_stdio(false);
    int N, K;
    cin >> N >> K;
    vector<int> A(N), B(N);
    vector 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;
    mcf_costscaling<int, long long, 2> 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);
        }

    for (int i = 0; i < N; i++) {
        graph.add_edge(gs, i, A[i], 0);
        graph.add_edge(i + N, gt, B[i], 0);
    }
    graph.add_supply(gs, K);
    graph.add_demand(gt, K);
    cout << ret + graph.solve() << '\n';
}

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結果

テストケース

ソースコード