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:heavy_check_mark: Verify/LC_min_cost_b_flow.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/min_cost_b_flow"

#include "Template/template.hpp"

#include "Graph/mincostflow.hpp"

#include "Utility/fastio.hpp"


namespace std {
string to_string(__int128_t x) {
    if (x == 0)
        return "0";
    __uint128_t k = x;
    if (k == (((__uint128_t)1) << 127))
        return "-170141183460469231731687303715884105728";
    string result;
    if (x < 0) {
        result += "-";
        x *= -1;
    }
    string t;
    while (x) {
        t.push_back('0' + x % 10);
        x /= 10;
    }
    reverse(t.begin(), t.end());
    return result + t;
}
} // namespace std


int main() {
    int n, m;
    read(n, m);
    MinCostFlow<ll, i128> mcf(n);
    rep(i, 0, n) {
        int b;
        read(b);
        mcf.add_excess(i, b);
    }
    rep(i, 0, m) {
        int s, t, l, u, c;
        read(s, t, l, u, c);
        mcf.add_edge(s, t, l, u, c);
    }
    auto [ok, ret] = mcf.run();
    if (!ok) {
        print("infeasible");
        return 0;
    }
    print(to_string(ret));
    rep(i, 0, n) print(to_string(mcf.dual[i]));
    rep(i, 0, m) print(mcf.get_flow(i));
    return 0;
}
#line 1 "Verify/LC_min_cost_b_flow.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/min_cost_b_flow"

#line 1 "Template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b-1); i >= (int)(a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())

using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;

template <typename T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T, typename U> T ceil(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U> T floor(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T> int popcnt(T x) {
    return __builtin_popcountll(x);
}
template <typename T> int topbit(T x) {
    return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <typename T> int lowbit(T x) {
    return (x == 0 ? -1 : __builtin_ctzll(x));
}

#ifdef LOCAL
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define show(...) true
#endif
template <typename T> void _show(int i, T name) {
    cerr << '\n';
}
template <typename T1, typename T2, typename... T3>
void _show(int i, const T1 &a, const T2 &b, const T3 &...c) {
    for (; a[i] != ',' && a[i] != '\0'; i++)
        cerr << a[i];
    cerr << ":" << b << " ";
    _show(i + 1, a, c...);
}
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
    os << "P(" << p.first << ", " << p.second << ")";
    return os;
}
template <typename T, template <class> class C>
ostream &operator<<(ostream &os, const C<T> &v) {
    os << "[";
    for (auto d : v)
        os << d << ", ";
    os << "]";
    return os;
}
#line 2 "Graph/maxflow.hpp"

struct MaxFlow {
    struct Edge {
        int to, rev;
        ll cap;
    };
    int V;
    vector<vector<Edge>> G;
    vector<int> itr, level;
    using P = pair<int, int>;
    vector<P> es;

  public:
    MaxFlow() {}
    MaxFlow(int V) : V(V) {
        G.assign(V, vector<Edge>());
    }
    int add_vertex() {
        G.push_back(vector<Edge>());
        return V++;
    }
    void add_edge(int from, int to, ll cap) {
        int fid = SZ(G[from]), tid = SZ(G[to]);
        if (from == to)
            tid++;
        es.push_back({from, fid});
        G[from].push_back({to, tid, cap});
        G[to].push_back({from, fid, 0});
    }
    struct Type {
        int from, to;
        ll cap, recap;
    };
    Type get_edge(int i) {
        auto [from, pos] = es[i];
        auto e = G[from][pos];
        auto re = G[e.to][e.rev];
        return Type{from, e.to, e.cap, re.cap};
    }
    void bfs(int s) {
        level.assign(V, -1);
        queue<int> q;
        level[s] = 0;
        q.push(s);
        while (!q.empty()) {
            int v = q.front();
            q.pop();
            for (auto &e : G[v]) {
                if (e.cap > 0 && level[e.to] < 0) {
                    level[e.to] = level[v] + 1;
                    q.push(e.to);
                }
            }
        }
    }
    ll dfs(int v, int t, ll f) {
        if (v == t)
            return f;
        for (int &i = itr[v]; i < (int)G[v].size(); i++) {
            Edge &e = G[v][i];
            if (e.cap > 0 && level[v] < level[e.to]) {
                ll d = dfs(e.to, t, min(f, e.cap));
                if (d > 0) {
                    e.cap -= d, G[e.to][e.rev].cap += d;
                    return d;
                }
            }
        }
        return 0;
    }
    ll run(int s, int t) {
        ll ret = 0, f;
        while (bfs(s), level[t] >= 0) {
            itr.assign(V, 0);
            while ((f = dfs(s, t, INF)) > 0)
                ret += f;
        }
        return ret;
    }
    vector<int> cut() {
        vector<int> ret(V);
        rep(v, 0, V) if (level[v] < 0) ret[v] = 1;
        return ret;
    }
};

/**
 * @brief Maximum Flow
 */
#line 3 "Graph/mincostflow.hpp"

// yosupo orz

template <class Cap, class Cost> struct MinCostFlow {
    struct X {
        int from, to;
        Cap lb, ub, flow;
        Cost cost;
    };
    struct Edge {
        int to, rev;
        Cap cap;
        Cost cost;
    };
    using P = pair<int, int>;
    int n, m;
    vector<X> es;
    vector<Cap> exc;
    vector<Cost> dual;
    vector<vector<Edge>> g;
    Cost MX;
    MinCostFlow(int _n) : n(_n), m(0), exc(n), dual(n), g(n), MX(0) {}
    void add_edge(int from, int to, Cap lb, Cap ub, Cost cost) {
        m++;
        chmax(MX, cost);
        chmax(MX, -cost);
        es.push_back({from, to, lb, ub, 0, cost});
    }
    void add_excess(int v, Cap c) { exc[v] += c; }
    pair<bool, Cost> run() {
        MaxFlow mf(n + 2);
        int S = n, T = n + 1;
        Cap psum = 0, nsum = 0;
        for (auto &e : es) {
            exc[e.to] += e.lb;
            exc[e.from] -= e.lb;
            mf.add_edge(e.from, e.to, e.ub - e.lb);
        }
        rep(i, 0, n) {
            if (exc[i] > 0) {
                psum += exc[i];
                mf.add_edge(S, i, exc[i]);
            }
            if (exc[i] < 0) {
                nsum += -exc[i];
                mf.add_edge(i, T, -exc[i]);
            }
        }

        if (psum != nsum or mf.run(S, T) != psum)
            return {false, 0};

        using P = pair<int, int>;
        vector<P> pos;
        rep(i, 0, m) {
            auto e = mf.get_edge(i);
            Cost cost = es[i].cost * n;
            int fid = SZ(g[e.from]), tid = SZ(g[e.to]);
            if (e.from == e.to)
                tid++;
            pos.push_back({e.from, fid});
            g[e.from].push_back({e.to, tid, e.cap, cost});
            g[e.to].push_back({e.from, fid, e.recap, -cost});
        }

        // solve

        Cost eps = MX * n + 1;
        while (eps > 1) {
            eps = max<Cost>(eps >> 2, 1);
            refine(eps);
        }

        Cost ret = 0;
        rep(i, 0, m) {
            auto [from, fid] = pos[i];
            es[i].flow = es[i].ub - g[from][fid].cap;
            ret += es[i].flow * es[i].cost;
        }
        dual.assign(n, 0);
        for (;;) {
            bool upd = 0;
            rep(i, 0, n) {
                for (auto &e : g[i])
                    if (e.cap) {
                        auto cost = dual[i] + e.cost / n;
                        if (chmin(dual[e.to], cost)) {
                            upd = 1;
                        }
                    }
            }
            if (!upd)
                break;
        }
        return {true, ret};
    }
    Cap get_flow(int i) const { return es[i].flow; }

  private:
    void refine(Cost &eps) {
        exc.assign(n, 0);
        vector<int> used(n);
        queue<int> que;
        vector<int> iter(n);

        auto cost = [&](int from, const Edge &e) {
            return e.cost + dual[from] - dual[e.to];
        };
        auto push = [&](int from, Edge &e, Cap cap) {
            exc[from] -= cap;
            exc[e.to] += cap;
            g[e.to][e.rev].cap += cap;
            e.cap -= cap;
        };
        auto relabel = [&](int v) {
            iter[v] = 0;
            Cost down = MX * (n + 1);
            for (auto &e : g[v])
                if (e.cap) {
                    chmin(down, eps + cost(v, e));
                }
            dual[v] -= down;
            que.push(v);
            used[v] = 1;
        };

        rep(i, 0, n) {
            for (auto &e : g[i])
                if (e.cap and cost(i, e) < 0) {
                    push(i, e, e.cap);
                }
        }
        rep(i, 0, n) if (exc[i] > 0) {
            used[i] = 1;
            que.push(i);
        }
        while (!que.empty()) {
            auto v = que.front();
            que.pop();
            used[v] = 0;
            for (int &i = iter[v]; i < SZ(g[v]); i++) {
                auto &e = g[v][i];
                if (e.cap and cost(v, e) < 0) {
                    push(v, e, min(exc[v], e.cap));
                    if (!used[e.to] and exc[e.to] > 0) {
                        used[e.to] = 1;
                        que.push(e.to);
                    }
                    if (exc[v] == 0)
                        break;
                }
            }
            if (exc[v] > 0) {
                relabel(v);
            }
        }
        eps = 0;
        rep(i, 0, n) {
            for (auto &e : g[i])
                if (e.cap) {
                    chmax(eps, -cost(i, e));
                }
        }
    }
};

/**
 * @brief Minimum Cost b-flow
 */
#line 2 "Utility/fastio.hpp"
#include <unistd.h>

namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf


uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
    char num[10000][4];
    constexpr Pre() : num() {
        for (int i = 0; i < 10000; i++) {
            int n = i;
            for (int j = 3; j >= 0; j--) {
                num[i][j] = n % 10 | '0';
                n /= 10;
            }
        }
    }
} constexpr pre;

inline void load() {
    memmove(ibuf, ibuf + pil, pir - pil);
    pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
    pil = 0;
    if (pir < SZ)
        ibuf[pir++] = '\n';
}

inline void flush() {
    fwrite(obuf, 1, por, stdout);
    por = 0;
}

void rd(char &c) {
    do {
        if (pil + 1 > pir)
            load();
        c = ibuf[pil++];
    } while (isspace(c));
}

void rd(string &x) {
    x.clear();
    char c;
    do {
        if (pil + 1 > pir)
            load();
        c = ibuf[pil++];
    } while (isspace(c));
    do {
        x += c;
        if (pil == pir)
            load();
        c = ibuf[pil++];
    } while (!isspace(c));
}

template <typename T> void rd_real(T &x) {
    string s;
    rd(s);
    x = stod(s);
}

template <typename T> void rd_integer(T &x) {
    if (pil + 100 > pir)
        load();
    char c;
    do
        c = ibuf[pil++];
    while (c < '-');
    bool minus = 0;
    if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
        if (c == '-') {
            minus = 1, c = ibuf[pil++];
        }
    }
    x = 0;
    while ('0' <= c) {
        x = x * 10 + (c & 15), c = ibuf[pil++];
    }
    if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
        if (minus)
            x = -x;
    }
}

void rd(int &x) {
    rd_integer(x);
}
void rd(ll &x) {
    rd_integer(x);
}
void rd(i128 &x) {
    rd_integer(x);
}
void rd(uint &x) {
    rd_integer(x);
}
void rd(ull &x) {
    rd_integer(x);
}
void rd(u128 &x) {
    rd_integer(x);
}
void rd(double &x) {
    rd_real(x);
}
void rd(long double &x) {
    rd_real(x);
}

template <class T, class U> void rd(pair<T, U> &p) {
    return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T> void rd_tuple(T &t) {
    if constexpr (N < std::tuple_size<T>::value) {
        auto &x = std::get<N>(t);
        rd(x);
        rd_tuple<N + 1>(t);
    }
}
template <class... T> void rd(tuple<T...> &tpl) {
    rd_tuple(tpl);
}

template <size_t N = 0, typename T> void rd(array<T, N> &x) {
    for (auto &d : x)
        rd(d);
}
template <class T> void rd(vector<T> &x) {
    for (auto &d : x)
        rd(d);
}

void read() {}
template <class H, class... T> void read(H &h, T &...t) {
    rd(h), read(t...);
}

void wt(const char c) {
    if (por == SZ)
        flush();
    obuf[por++] = c;
}
void wt(const string s) {
    for (char c : s)
        wt(c);
}
void wt(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++)
        wt(s[i]);
}

template <typename T> void wt_integer(T x) {
    if (por > SZ - 100)
        flush();
    if (x < 0) {
        obuf[por++] = '-', x = -x;
    }
    int outi;
    for (outi = 96; x >= 10000; outi -= 4) {
        memcpy(out + outi, pre.num[x % 10000], 4);
        x /= 10000;
    }
    if (x >= 1000) {
        memcpy(obuf + por, pre.num[x], 4);
        por += 4;
    } else if (x >= 100) {
        memcpy(obuf + por, pre.num[x] + 1, 3);
        por += 3;
    } else if (x >= 10) {
        int q = (x * 103) >> 10;
        obuf[por] = q | '0';
        obuf[por + 1] = (x - q * 10) | '0';
        por += 2;
    } else
        obuf[por++] = x | '0';
    memcpy(obuf + por, out + outi + 4, 96 - outi);
    por += 96 - outi;
}

template <typename T> void wt_real(T x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << double(x);
    string s = oss.str();
    wt(s);
}

void wt(int x) {
    wt_integer(x);
}
void wt(ll x) {
    wt_integer(x);
}
void wt(i128 x) {
    wt_integer(x);
}
void wt(uint x) {
    wt_integer(x);
}
void wt(ull x) {
    wt_integer(x);
}
void wt(u128 x) {
    wt_integer(x);
}
void wt(double x) {
    wt_real(x);
}
void wt(long double x) {
    wt_real(x);
}

template <class T, class U> void wt(const pair<T, U> val) {
    wt(val.first);
    wt(' ');
    wt(val.second);
}
template <size_t N = 0, typename T> void wt_tuple(const T t) {
    if constexpr (N < std::tuple_size<T>::value) {
        if constexpr (N > 0) {
            wt(' ');
        }
        const auto x = std::get<N>(t);
        wt(x);
        wt_tuple<N + 1>(t);
    }
}
template <class... T> void wt(tuple<T...> tpl) {
    wt_tuple(tpl);
}
template <class T, size_t S> void wt(const array<T, S> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
        if (i)
            wt(' ');
        wt(val[i]);
    }
}
template <class T> void wt(const vector<T> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
        if (i)
            wt(' ');
        wt(val[i]);
    }
}

void print() {
    wt('\n');
}
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
    wt(head);
    if (sizeof...(Tail))
        wt(' ');
    print(forward<Tail>(tail)...);
}
void __attribute__((destructor)) _d() {
    flush();
}
} // namespace fastio


using fastio::flush;
using fastio::print;
using fastio::read;

inline void first(bool i = true) {
    print(i ? "first" : "second");
}
inline void Alice(bool i = true) {
    print(i ? "Alice" : "Bob");
}
inline void yes(bool i = true) {
    print(i ? "yes" : "no");
}
inline void Yes(bool i = true) {
    print(i ? "Yes" : "No");
}
inline void No() {
    print("No");
}
inline void YES(bool i = true) {
    print(i ? "YES" : "NO");
}
inline void NO() {
    print("NO");
}
inline void Yay(bool i = true) {
    print(i ? "Yay!" : ":(");
}
inline void Possible(bool i = true) {
    print(i ? "Possible" : "Impossible");
}
inline void POSSIBLE(bool i = true) {
    print(i ? "POSSIBLE" : "IMPOSSIBLE");
}

/**
 * @brief Fast IO
 */
#line 6 "Verify/LC_min_cost_b_flow.test.cpp"

namespace std {
string to_string(__int128_t x) {
    if (x == 0)
        return "0";
    __uint128_t k = x;
    if (k == (((__uint128_t)1) << 127))
        return "-170141183460469231731687303715884105728";
    string result;
    if (x < 0) {
        result += "-";
        x *= -1;
    }
    string t;
    while (x) {
        t.push_back('0' + x % 10);
        x /= 10;
    }
    reverse(t.begin(), t.end());
    return result + t;
}
} // namespace std


int main() {
    int n, m;
    read(n, m);
    MinCostFlow<ll, i128> mcf(n);
    rep(i, 0, n) {
        int b;
        read(b);
        mcf.add_excess(i, b);
    }
    rep(i, 0, m) {
        int s, t, l, u, c;
        read(s, t, l, u, c);
        mcf.add_edge(s, t, l, u, c);
    }
    auto [ok, ret] = mcf.run();
    if (!ok) {
        print("infeasible");
        return 0;
    }
    print(to_string(ret));
    rep(i, 0, n) print(to_string(mcf.dual[i]));
    rep(i, 0, m) print(mcf.get_flow(i));
    return 0;
}
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