#656504 (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	2021-05-13 19:28:38
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	90 ms / 2,000 ms
コード長	9,754 bytes
コンパイル時間	1,797 ms
コンパイル使用メモリ	157,516 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-09-25 07:44:36
合計ジャッジ時間	3,995 ms
ジャッジサーバーID （参考情報）	judge1 / judge5

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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 6,820 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	AC	86 ms 6,944 KB
testcase_04	AC	85 ms 6,940 KB
testcase_05	AC	87 ms 6,944 KB
testcase_06	AC	85 ms 6,940 KB
testcase_07	AC	86 ms 6,944 KB
testcase_08	AC	7 ms 6,940 KB
testcase_09	AC	7 ms 6,944 KB
testcase_10	AC	13 ms 6,944 KB
testcase_11	AC	22 ms 6,940 KB
testcase_12	AC	5 ms 6,940 KB
testcase_13	AC	4 ms 6,944 KB
testcase_14	AC	25 ms 6,944 KB
testcase_15	AC	9 ms 6,940 KB
testcase_16	AC	2 ms 6,944 KB
testcase_17	AC	16 ms 6,940 KB
testcase_18	AC	6 ms 6,940 KB
testcase_19	AC	6 ms 6,944 KB
testcase_20	AC	4 ms 6,940 KB
testcase_21	AC	3 ms 6,940 KB
testcase_22	AC	3 ms 6,944 KB
testcase_23	AC	15 ms 6,944 KB
testcase_24	AC	34 ms 6,940 KB
testcase_25	AC	18 ms 6,944 KB
testcase_26	AC	17 ms 6,944 KB
testcase_27	AC	8 ms 6,944 KB
testcase_28	AC	2 ms 6,944 KB
testcase_29	AC	2 ms 6,944 KB
testcase_30	AC	2 ms 6,944 KB
testcase_31	AC	2 ms 6,944 KB
testcase_32	AC	2 ms 6,940 KB
testcase_33	AC	2 ms 6,940 KB
testcase_34	AC	2 ms 6,944 KB
testcase_35	AC	2 ms 6,944 KB
testcase_36	AC	2 ms 6,944 KB
testcase_37	AC	90 ms 6,940 KB
testcase_38	AC	89 ms 6,940 KB
testcase_39	AC	86 ms 6,940 KB
testcase_40	AC	88 ms 6,940 KB
testcase_41	AC	87 ms 6,944 KB
testcase_42	AC	5 ms 6,944 KB
testcase_43	AC	5 ms 6,940 KB
testcase_44	AC	5 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 <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;
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) { if (m < q) {m = q; return true;} else return false; }
template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return 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::lower_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) { 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
#else
#define dbg(x) (x)
#endif

/*
MinCostFlow: Minimum-cost flow problem solver WITH NO NEGATIVE CYCLE (just negative cost edge is allowed)
Verified by SRM 770 Div1 Medium <https://community.topcoder.com/stat?c=problem_statement&pm=15702>
*/
template <typename CAP = long long, typename COST = long long> struct MinCostFlow {
    const COST INF_COST = std::numeric_limits<COST>::max() / 2;
    struct edge {
        int to, rev;
        CAP cap;
        COST cost;
        friend std::ostream &operator<<(std::ostream &os, const edge &e) {
            os << '(' << e.to << ',' << e.rev << ',' << e.cap << ',' << e.cost << ')';
            return os;
        }
    };
    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 _calc_distance_bellman_ford(int s) { // O(VE), able to detect negative cycle
        dist.assign(V, INF_COST);
        dist[s] = 0;
        bool upd = true;
        int cnt = 0;
        while (upd) {
            upd = false;
            cnt++;
            if (cnt > V) return false; // Negative cycle existence
            for (int v = 0; v < V; v++)
                if (dist[v] != INF_COST) {
                    for (int i = 0; i < (int)g[v].size(); i++) {
                        edge &e = g[v][i];
                        COST 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;
                            upd = true;
                        }
                    }
                }
        }
        return true;
    }

    bool _calc_distance_dijkstra(int s) { // O(ElogV)
        dist.assign(V, INF_COST);
        dist[s] = 0;
        using P = std::pair<COST, int>;
        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];
                COST 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;
                    q.emplace(dist[e.to], e.to);
                }
            }
        }
        return true;
    }

    MinCostFlow(int V = 0) : V(V), g(V) {}

    void add_edge(int from, int to, CAP cap, COST cost) {
        assert(0 <= from and from < V);
        assert(0 <= to and to < V);
        pos.emplace_back(from, g[from].size());
        g[from].emplace_back(edge{to, (int)g[to].size() + (from == to), cap, cost});
        g[to].emplace_back(edge{from, (int)g[from].size() - 1, (CAP)0, -cost});
    }

    std::pair<CAP, COST> flow(int s, int t, const CAP &f) {
        /*
        Flush amount of `f` from `s` to `t` using the Dijkstra's algorithm
        works for graph with no negative cycles (negative cost edges are allowed)
        retval: (flow, cost)
        */
        COST ret = 0;
        dual.assign(V, 0);
        prevv.assign(V, -1);
        preve.assign(V, -1);
        CAP frem = f;
        while (frem > 0) {
            _calc_distance_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 = frem;
            for (int v = t; v != s; v = prevv[v]) { d = std::min(d, g[prevv[v]][preve[v]].cap); }
            frem -= d;
            ret += d * dual[t];
            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(f - frem, ret);
    }

    friend std::ostream &operator<<(std::ostream &os, const MinCostFlow &mcf) {
        os << "[MinCostFlow]V=" << mcf.V << ":";
        for (int i = 0; i < (int)mcf.g.size(); i++)
            for (auto &e : mcf.g[i]) { os << "\n" << i << "->" << e.to << ": cap=" << e.cap << ", cost=" << e.cost; }
        return os;
    }
};


int main() {
    int N, K;
    cin >> N >> K;
    vector<int> A(N), B(N);
    vector P(N, vector<int>(N));
    cin >> A >> B >> P;

    const int gs = N * 2, gt = gs + 1;
    MinCostFlow<int, lint> graph(gt + 1);

    lint ret = 0;
    REP(i, N) REP(j, N) {
        ret += P[i][j] * P[i][j];
        REP(a, A[i]) graph.add_edge(i, j + N, 1, 2 * (a - P[i][j]) + 1);
    }
    
    REP(i, N) {
        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';
}

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結果

テストケース

ソースコード