結果

問題 No.1324 Approximate the Matrix
ユーザー keijakkeijak
提出日時 2020-12-28 22:56:52
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 38 ms / 2,000 ms
コード長 6,800 bytes
コンパイル時間 2,695 ms
コンパイル使用メモリ 227,508 KB
実行使用メモリ 6,276 KB
最終ジャッジ日時 2024-10-04 02:22:04
合計ジャッジ時間 4,400 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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
5,248 KB
testcase_01 AC 1 ms
5,248 KB
testcase_02 AC 2 ms
5,248 KB
testcase_03 AC 28 ms
5,248 KB
testcase_04 AC 25 ms
5,248 KB
testcase_05 AC 28 ms
5,248 KB
testcase_06 AC 27 ms
5,248 KB
testcase_07 AC 27 ms
5,248 KB
testcase_08 AC 4 ms
5,248 KB
testcase_09 AC 3 ms
5,248 KB
testcase_10 AC 5 ms
5,248 KB
testcase_11 AC 9 ms
5,248 KB
testcase_12 AC 4 ms
5,248 KB
testcase_13 AC 2 ms
5,248 KB
testcase_14 AC 9 ms
5,248 KB
testcase_15 AC 5 ms
5,248 KB
testcase_16 AC 3 ms
5,248 KB
testcase_17 AC 9 ms
5,248 KB
testcase_18 AC 4 ms
5,248 KB
testcase_19 AC 5 ms
5,248 KB
testcase_20 AC 3 ms
5,248 KB
testcase_21 AC 2 ms
5,248 KB
testcase_22 AC 3 ms
5,248 KB
testcase_23 AC 8 ms
5,248 KB
testcase_24 AC 12 ms
5,248 KB
testcase_25 AC 9 ms
5,248 KB
testcase_26 AC 7 ms
5,248 KB
testcase_27 AC 6 ms
5,248 KB
testcase_28 AC 2 ms
5,248 KB
testcase_29 AC 2 ms
5,248 KB
testcase_30 AC 2 ms
5,248 KB
testcase_31 AC 2 ms
5,248 KB
testcase_32 AC 2 ms
5,248 KB
testcase_33 AC 2 ms
5,248 KB
testcase_34 AC 2 ms
5,248 KB
testcase_35 AC 2 ms
5,248 KB
testcase_36 AC 2 ms
5,248 KB
testcase_37 AC 38 ms
6,272 KB
testcase_38 AC 31 ms
6,276 KB
testcase_39 AC 35 ms
6,156 KB
testcase_40 AC 33 ms
6,276 KB
testcase_41 AC 36 ms
6,164 KB
testcase_42 AC 5 ms
5,248 KB
testcase_43 AC 5 ms
5,248 KB
testcase_44 AC 5 ms
5,248 KB
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ソースコード

diff # 

#include <bits/stdc++.h>


#include <algorithm>
#include <cassert>
#include <limits>
#include <queue>
#include <vector>

namespace atcoder {

template <class Cap, class Cost> struct mcf_graph {
  public:
    mcf_graph() {}
    mcf_graph(int n) : _n(n), g(n) {}

    int add_edge(int from, int to, Cap cap, Cost cost) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        assert(0 <= cap);
        assert(0 <= cost);
        int m = int(pos.size());
        pos.push_back({from, int(g[from].size())});
        int from_id = int(g[from].size());
        int to_id = int(g[to].size());
        if (from == to) to_id++;
        g[from].push_back(_edge{to, to_id, cap, cost});
        g[to].push_back(_edge{from, from_id, 0, -cost});
        return m;
    }

    struct edge {
        int from, to;
        Cap cap, flow;
        Cost cost;
    };

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

    std::pair<Cap, Cost> flow(int s, int t) {
        return flow(s, t, std::numeric_limits<Cap>::max());
    }
    std::pair<Cap, Cost> flow(int s, int t, Cap flow_limit) {
        return slope(s, t, flow_limit).back();
    }
    std::vector<std::pair<Cap, Cost>> slope(int s, int t) {
        return slope(s, t, std::numeric_limits<Cap>::max());
    }
    std::vector<std::pair<Cap, Cost>> slope(int s, int t, Cap flow_limit) {
        assert(0 <= s && s < _n);
        assert(0 <= t && t < _n);
        assert(s != t);
        // variants (C = maxcost):
        // -(n-1)C <= dual[s] <= dual[i] <= dual[t] = 0
        // reduced cost (= e.cost + dual[e.from] - dual[e.to]) >= 0 for all edge
        std::vector<Cost> dual(_n, 0), dist(_n);
        std::vector<int> pv(_n), pe(_n);
        std::vector<bool> vis(_n);
        auto dual_ref = [&]() {
            std::fill(dist.begin(), dist.end(),
                      std::numeric_limits<Cost>::max());
            std::fill(pv.begin(), pv.end(), -1);
            std::fill(pe.begin(), pe.end(), -1);
            std::fill(vis.begin(), vis.end(), false);
            struct Q {
                Cost key;
                int to;
                bool operator<(Q r) const { return key > r.key; }
            };
            std::priority_queue<Q> que;
            dist[s] = 0;
            que.push(Q{0, s});
            while (!que.empty()) {
                int v = que.top().to;
                que.pop();
                if (vis[v]) continue;
                vis[v] = true;
                if (v == t) break;
                // dist[v] = shortest(s, v) + dual[s] - dual[v]
                // dist[v] >= 0 (all reduced cost are positive)
                // dist[v] <= (n-1)C
                for (int i = 0; i < int(g[v].size()); i++) {
                    auto e = g[v][i];
                    if (vis[e.to] || !e.cap) continue;
                    // |-dual[e.to] + dual[v]| <= (n-1)C
                    // cost <= C - -(n-1)C + 0 = nC
                    Cost cost = e.cost - dual[e.to] + dual[v];
                    if (dist[e.to] - dist[v] > cost) {
                        dist[e.to] = dist[v] + cost;
                        pv[e.to] = v;
                        pe[e.to] = i;
                        que.push(Q{dist[e.to], e.to});
                    }
                }
            }
            if (!vis[t]) {
                return false;
            }

            for (int v = 0; v < _n; v++) {
                if (!vis[v]) continue;
                // dual[v] = dual[v] - dist[t] + dist[v]
                //         = dual[v] - (shortest(s, t) + dual[s] - dual[t]) + (shortest(s, v) + dual[s] - dual[v])
                //         = - shortest(s, t) + dual[t] + shortest(s, v)
                //         = shortest(s, v) - shortest(s, t) >= 0 - (n-1)C
                dual[v] -= dist[t] - dist[v];
            }
            return true;
        };
        Cap flow = 0;
        Cost cost = 0, prev_cost_per_flow = -1;
        std::vector<std::pair<Cap, Cost>> result;
        result.push_back({flow, cost});
        while (flow < flow_limit) {
            if (!dual_ref()) break;
            Cap c = flow_limit - flow;
            for (int v = t; v != s; v = pv[v]) {
                c = std::min(c, g[pv[v]][pe[v]].cap);
            }
            for (int v = t; v != s; v = pv[v]) {
                auto& e = g[pv[v]][pe[v]];
                e.cap -= c;
                g[v][e.rev].cap += c;
            }
            Cost d = -dual[s];
            flow += c;
            cost += c * d;
            if (prev_cost_per_flow == d) {
                result.pop_back();
            }
            result.push_back({flow, cost});
            prev_cost_per_flow = d;
        }
        return result;
    }

  private:
    int _n;

    struct _edge {
        int to, rev;
        Cap cap;
        Cost cost;
    };

    std::vector<std::pair<int, int>> pos;
    std::vector<std::vector<_edge>> g;
};

}  // namespace atcoder


#define REP_(i, a_, b_, a, b, ...) \
  for (int i = (a), N_##i = (b); i < N_##i; ++i)
#define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define ALL(x) std::begin(x), std::end(x)
using i64 = long long;
using u64 = unsigned long long;

template <typename T>
std::istream &operator>>(std::istream &is, std::vector<T> &a) {
  for (auto &x : a) is >> x;
  return is;
}

using namespace std;

i64 solve() {
  int n, k;
  cin >> n >> k;
  vector<int> a(n), b(n);
  cin >> a >> b;
  vector p(n, vector(n, 0));
  i64 p_norm = 0;
  REP(i, n) REP(j, n) {
    cin >> p[i][j];
    p_norm += p[i][j] * p[i][j];
  }

  atcoder::mcf_graph<int, i64> g(n * 2 + 2);
  const int v_source = n * 2;
  const int v_sink = n * 2 + 1;

  REP(i, n) { g.add_edge(v_source, i, a[i], 0); }
  REP(i, n) { g.add_edge(n + i, v_sink, b[i], 0); }
  const i64 BASE_COST = 600;
  REP(i, n) REP(j, n) {
    for (i64 x = 1; x <= min(a[i], b[j]); ++x) {
      // (x - p)^2 - (x - 1 - p)^2
      // = (x^2 - 2px + p^2) - (x^2 + 1 + p^2 - 2x + 2p - 2px)
      // = 2x - 2p - 1
      i64 cost = 2 * x - 2 * p[i][j] - 1 + BASE_COST;
      g.add_edge(i, n + j, 1, cost);
    }
  }
  auto [maxflow, mincost] = g.flow(v_source, v_sink, k);
  // if (maxflow == 0) {
  //   return p_norm;
  // }
  assert(maxflow == k);
  return mincost - k * BASE_COST + p_norm;
}

int main() {
  std::ios::sync_with_stdio(false), cin.tie(nullptr);
  cout << solve() << "\n";
}
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