#801842 (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	tokusakurai
提出日時	2022-09-28 18:29:17
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	75 ms / 2,000 ms
コード長	7,194 bytes
コンパイル時間	2,691 ms
コンパイル使用メモリ	220,684 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-06-02 01:36:25
合計ジャッジ時間	4,874 ms
ジャッジサーバーID （参考情報）	judge5 / judge2

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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 6,816 KB
testcase_01	AC	2 ms 6,816 KB
testcase_02	AC	2 ms 6,944 KB
testcase_03	AC	45 ms 6,940 KB
testcase_04	AC	41 ms 6,944 KB
testcase_05	AC	44 ms 6,940 KB
testcase_06	AC	42 ms 6,944 KB
testcase_07	AC	43 ms 6,944 KB
testcase_08	AC	4 ms 6,940 KB
testcase_09	AC	4 ms 6,940 KB
testcase_10	AC	7 ms 6,944 KB
testcase_11	AC	12 ms 6,940 KB
testcase_12	AC	4 ms 6,940 KB
testcase_13	AC	3 ms 6,940 KB
testcase_14	AC	12 ms 6,940 KB
testcase_15	AC	5 ms 6,940 KB
testcase_16	AC	3 ms 6,940 KB
testcase_17	AC	12 ms 6,940 KB
testcase_18	AC	4 ms 6,944 KB
testcase_19	AC	4 ms 6,944 KB
testcase_20	AC	3 ms 6,944 KB
testcase_21	AC	2 ms 6,944 KB
testcase_22	AC	3 ms 6,944 KB
testcase_23	AC	9 ms 6,940 KB
testcase_24	AC	16 ms 6,940 KB
testcase_25	AC	13 ms 6,944 KB
testcase_26	AC	10 ms 6,944 KB
testcase_27	AC	6 ms 6,940 KB
testcase_28	AC	2 ms 6,944 KB
testcase_29	AC	2 ms 6,940 KB
testcase_30	AC	2 ms 6,944 KB
testcase_31	AC	2 ms 6,940 KB
testcase_32	AC	1 ms 6,944 KB
testcase_33	AC	1 ms 6,944 KB
testcase_34	AC	2 ms 6,940 KB
testcase_35	AC	2 ms 6,944 KB
testcase_36	AC	2 ms 6,944 KB
testcase_37	AC	73 ms 6,940 KB
testcase_38	AC	73 ms 6,944 KB
testcase_39	AC	75 ms 6,944 KB
testcase_40	AC	74 ms 6,944 KB
testcase_41	AC	72 ms 6,940 KB
testcase_42	AC	5 ms 6,940 KB
testcase_43	AC	5 ms 6,940 KB
testcase_44	AC	4 ms 6,944 KB

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ソースコード

raw source code

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n)-1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r)-1; i >= (l); i--)
#define each(e, v) for (auto &e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;

template <typename T>
using maxheap = priority_queue<T>;

template <typename T>
bool chmax(T &x, const T &y) {
    return (x < y) ? (x = y, true) : false;
}

template <typename T>
bool chmin(T &x, const T &y) {
    return (x > y) ? (x = y, true) : false;
}

template <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}

template <typename T>
void print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
    if (v.empty()) cout << '\n';
}

template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}

template <typename T>
int lb(const vector<T> &v, T x) {
    return lower_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
int ub(const vector<T> &v, T x) {
    return upper_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
void rearrange(vector<T> &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}

template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}

template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}

template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}

template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}

struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;

const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
// const int MOD = 1000000007;
const int MOD = 998244353;

template <typename F, typename T = F>
struct Primal_Dual {
    struct edge {
        int to;
        F cap;
        T cost;
        int rev;
        edge(int to, F cap, T cost, int rev) : to(to), cap(cap), cost(cost), rev(rev) {}
    };

    vector<vector<edge>> es;
    vector<T> d, h;
    vector<int> pre_v, pre_e;
    bool negative = false;
    const F zero_F, INF_F;
    const T zero_T, INF_T;
    const int n;

    Primal_Dual(int n, F zero_F = 0, F INF_F = numeric_limits<F>::max() / 2, T zero_T = 0, T INF_T = numeric_limits<T>::max() / 2)
        : es(n), d(n), h(n), pre_v(n), pre_e(n), zero_F(zero_F), INF_F(INF_F), zero_T(zero_T), INF_T(INF_T), n(n) {}

    void add_edge(int from, int to, F cap, T cost) {
        es[from].emplace_back(to, cap, cost, (int)es[to].size());
        es[to].emplace_back(from, zero_F, -cost, (int)es[from].size() - 1);
        if (cost < zero_T) negative = true;
    }

    void bellman_ford(int s) {
        fill(begin(h), end(h), INF_T);
        h[s] = zero_T;
        while (true) {
            bool update = false;
            for (int i = 0; i < n; i++) {
                if (h[i] == INF_T) continue;
                for (auto &e : es[i]) {
                    if (e.cap > zero_F && h[i] + e.cost < h[e.to]) {
                        h[e.to] = h[i] + e.cost;
                        update = true;
                    }
                }
            }
            if (!update) break;
        }
    }

    void dag_shortest_path(int s) {
        vector<int> deg(n, 0);
        for (int i = 0; i < n; i++) {
            for (auto &e : es[i]) {
                if (e.cap > zero_F) deg[e.to]++;
            }
        }
        fill(begin(h), end(h), INF_T);
        h[s] = zero_T;
        queue<int> que;
        for (int i = 0; i < n; i++) {
            if (deg[i] == 0) que.push(i);
        }
        while (!que.empty()) {
            int i = que.front();
            que.pop();
            for (auto &e : es[i]) {
                if (e.cap == zero_F) continue;
                h[e.to] = min(h[e.to], h[i] + e.cost);
                if (--deg[e.to] == 0) que.push(e.to);
            }
        }
    }

    void dijkstra(int s) {
        fill(begin(d), end(d), INF_T);
        using P = pair<T, int>;
        priority_queue<P, vector<P>, greater<P>> que;
        que.emplace(d[s] = zero_T, s);
        while (!que.empty()) {
            auto [p, i] = que.top();
            que.pop();
            if (p > d[i]) continue;
            for (int j = 0; j < (int)es[i].size(); j++) {
                edge &e = es[i][j];
                if (e.cap > zero_F && d[i] + e.cost + h[i] - h[e.to] < d[e.to]) {
                    d[e.to] = d[i] + e.cost + h[i] - h[e.to];
                    pre_v[e.to] = i, pre_e[e.to] = j;
                    que.emplace(d[e.to], e.to);
                }
            }
        }
    }

    T min_cost_flow(int s, int t, F flow, bool dag = false) {
        T ret = zero_T;
        if (negative) dag ? dag_shortest_path(s) : bellman_ford(s);
        while (flow > zero_F) {
            dijkstra(s);
            if (d[t] == INF_T) return INF_T;
            for (int i = 0; i < n; i++) {
                if (h[i] == INF_T || d[i] == INF_T) {
                    h[i] = INF_T;
                } else {
                    h[i] += d[i];
                }
            }
            F f = flow;
            for (int now = t; now != s; now = pre_v[now]) f = min(f, es[pre_v[now]][pre_e[now]].cap);
            ret += h[t] * f, flow -= f;
            for (int now = t; now != s; now = pre_v[now]) {
                edge &e = es[pre_v[now]][pre_e[now]];
                e.cap -= f, es[now][e.rev].cap += f;
            }
        }
        return ret;
    }
};

int main() {
    int N, K;
    cin >> N >> K;

    Primal_Dual<ll, ll> G(2 * N + 2);
    int s = 2 * N, t = s + 1;

    vector<int> a(N), b(N);
    rep(i, N) {
        cin >> a[i];
        G.add_edge(s, i, a[i], 0);
    }
    rep(i, N) {
        cin >> b[i];
        G.add_edge(N + i, t, b[i], 0);
    }

    ll ans = 0;
    rep(i, N) {
        rep(j, N) {
            int x;
            cin >> x;
            ans += x * x;
            rep(k, min(a[i], b[j])) G.add_edge(i, N + j, 1, 1 - 2 * (x - k));
        }
    }

    cout << ans + G.min_cost_flow(s, t, K) << '\n';
}

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