Language: C++

/*あかん*/


#pragma GCC optimize ("O3")
#pragma GCC target ("avx")
#include "bits/stdc++.h" // define macro "/D__MAI"

using namespace std;
typedef long long int ll;

#define xprintf(fmt,...) fprintf(stderr,fmt,__VA_ARGS__)
#define debugv(v) {printf("L%d %s => ",__LINE__,#v);for(auto e:v){cout<<e<<" ";}cout<<endl;}
#define debugm(m) {printf("L%d %s is..\n",__LINE__,#m);for(auto v:m){for(auto e:v){cout<<e<<" ";}cout<<endl;}}
#define debuga(m,w) {printf("L%d %s is => ",__LINE__,#m);for(int x=0;x<(w);x++){cout<<(m)[x]<<" ";}cout<<endl;}
#define debugaa(m,w,h) {printf("L%d %s is..\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){cout<<(m)[x][y]<<" ";}cout<<endl;}}
#define debugaar(m,w,h) {printf("L%d %s is..\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){cout<<(m)[y][x]<<" ";}cout<<endl;}}
#define ALL(v) (v).begin(),(v).end()
#define repeat(l) for(auto cnt=0;cnt<(l);++cnt)
#define iterate(b,e) for(auto cnt=(b);cnt!=(e);++cnt)
#define MD 1000000007ll
#define PI 3.1415926535897932384626433832795
template<typename T1, typename T2>
ostream& operator <<(ostream &o, const pair<T1, T2> p) { o << "(" << p.first << ":" << p.second << ")"; return o; }

mt19937 mt(8901016);
inline int rand_int(int l, int h) {
    return uniform_int_distribution<>(l, h)(mt);
}

#ifdef __MAI
#define getchar_unlocked getchar
#define putchar_unlocked putchar
#endif
#ifdef __VSCC
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#endif
namespace {
#define isvisiablechar(c) (0x21<=(c)&&(c)<=0x7E)
    class MaiScanner {
    public:
        template<typename T> void input_integer(T& var) {
            var = 0;
            T sign = 1;
            int cc = getchar_unlocked();
            for (; cc<'0' || '9'<cc; cc = getchar_unlocked())
                if (cc == '-') sign = -1;
            for (; '0' <= cc&&cc <= '9'; cc = getchar_unlocked())
                var = (var << 3) + (var << 1) + cc - '0';
            var = var*sign;
        }
        inline int c() { return getchar_unlocked(); }
        inline MaiScanner& operator>>(int& var) {
            input_integer<int>(var);
            return *this;
        }
        inline MaiScanner& operator>>(long long& var) {
            input_integer<long long>(var);
            return *this;
        }
        inline MaiScanner& operator>>(string& var) {
            int cc = getchar_unlocked();
            for (; !isvisiablechar(cc); cc = getchar_unlocked());
            for (; isvisiablechar(cc); cc = getchar_unlocked())
                var.push_back(cc);
        }
        template<typename IT> void in(IT begin, IT end) {
            for (auto it = begin; it != end; ++it) *this >> *it;
        }
    };
}
MaiScanner scanner;


class Flow {
public:
    size_t n;
    struct Arrow {
        int from, to;
        int left;
        int cap;

        Arrow(int from = 0, int to = 0, int w = 1) :from(from), to(to), left(w), cap(w) {}
        bool operator<(const Arrow& a) const { return (from<a.from) | (to<a.to) | (left<a.left) | (cap<a.cap); }
        bool operator==(const Arrow& a) const { return (from == a.from) && (to == a.to) && (left == a.left) && (cap == a.cap); }
    };
    vector<vector<int>> vertex_to;
    vector<vector<int>> vertex_from;
    vector<Arrow> arrow;

    Flow(int n, int m = 5010) :n(n), vertex_to(n), vertex_from(n) { arrow.reserve(m); }

    void connect(int from, int to, int left) {
        vertex_to[from].push_back(arrow.size()); // toto
        vertex_from[to].push_back(arrow.size()); // fromfrom
        arrow.emplace_back(from, to, left);
    }
    size_t degree(int v) {
        return vertex_to[v].size() + vertex_from[v].size();
    }
    size_t degree_in(int v) {
        return vertex_from[v].size();
    }
    size_t degree_out(int v) {
        return vertex_to[v].size();
    }
};

int _dinic_path_dfs(Flow& flow, vector<int>& result, vector<int>& flag, const vector<int>& dist, int u, int i_sink, int mini) {
    // TODO: 経路再利用
    if (i_sink == u) return mini;
    if (flag[u]) return -1;
    flag[u] = true;

    int sumw = 0;
    bool term = true;
    for (int e : flow.vertex_to[u]) {
        Flow::Arrow& a = flow.arrow[e];
        if (a.left > 0 && dist[u]>dist[a.to]) {
            int w;
            if (mini < 0)
                w = a.left;
            else
                w = min(a.left, mini);

            w = _dinic_path_dfs(flow, result, flag, dist, a.to, i_sink, w);
            if (w == -1) continue;
            a.left -= w;
            result[a.to] += w;

            sumw += w;
            mini -= w;
            term = false;
            flag[u] = false; // TODO: 末尾では? 

            if (mini == 0) return term ? -1 : sumw;
        }
    }
    for (int e : flow.vertex_from[u]) {
        Flow::Arrow& a = flow.arrow[e];
        if (a.cap>a.left && dist[u]>dist[a.from]) {
            int w;
            if (mini < 0)
                w = a.cap - a.left;
            else
                w = min(a.cap - a.left, mini);

            w = _dinic_path_dfs(flow, result, flag, dist, a.from, i_sink, w);
            if (w == -1) continue;
            a.left += w;
            result[a.to] -= w;

            sumw += w;
            mini -= w;
            term = false;
            flag[u] = false;
            if (mini == 0) return term ? -1 : sumw;
        }
    }
    return term ? -1 : sumw;
}

// flowは書き換えられる．
void dinic(Flow &flow, vector<int>& result, int i_source, int i_sink) {
    assert(i_source != i_sink);

    result.resize(flow.n);

    int distbegin = 0;
    vector<int> dist(flow.n);
    queue<int> q;
    vector<int> flag(flow.n);
    for (int distbegin = 0; ; distbegin += flow.n) {

        q.emplace(i_sink); // bfsはsinkからsourceへの距離を計算．
        dist[i_sink] = distbegin + 1;
        while (!q.empty()) {
            int v = q.front();
            q.pop();
            for (int ie : flow.vertex_from[v]) {
                const Flow::Arrow& e = flow.arrow[ie];
                if (0<e.left && dist[e.from] <= distbegin) {
                    dist[e.from] = dist[v] + 1;
                    q.emplace(e.from);
                }
            }
            for (int ie : flow.vertex_to[v]) {
                const Flow::Arrow& e = flow.arrow[ie];
                if (e.left<e.cap && dist[e.to] <= distbegin) {
                    dist[e.to] = dist[v] + 1;
                    q.emplace(e.to);
                }
            }
        }
        //debugv(dist);
        fill(ALL(flag), false);

        if (dist[i_source] <= distbegin) {
            break;
        }
        else {
            result[i_source] += _dinic_path_dfs(flow, result, flag, dist, i_source, i_sink, -1);
        }
    }

}

ll n, m;

int main() {

    scanner >> n >> m;

    Flow graph_orig(n);
    Flow graph(n);

    map<int, int> link;

    repeat(m) {
        int a, b, c;

        scanner >> a >> b >> c;
        --a; --b;

        int ia, ib;
        ia = graph.arrow.size();
        graph.connect(a, b, c);
        ib = graph.arrow.size();
        graph.connect(b, a, c);

        link[ia] = ib;
        link[ib] = ia;

        graph_orig.connect(a, b, c);
    }


    vector<int> result;
    dinic(graph, result, 0, n - 1);

    int fl = 0;
    int high = 0;

    for (int i = 0; i < graph.arrow.size();++i) {
        auto& a = graph.arrow[i];
        auto di = link[i];
        auto& d = graph.arrow[di];
        
        if (di < i) continue;

        if (a.left != a.cap && d.left != d.cap) {
            high = max(high, a.cap);
            fl += a.cap;
            //graph.arrow[di].cap = a.ca;
        }
    }

    cout << (fl - high) << endl;

    return 0;
}

Compiler output:
a.cc: In member function '{anonymous}::MaiScanner& {anonymous}::MaiScanner::operator>>(std::string&)':
a.cc:66:9: warning: no return statement in function returning non-void [-Wreturn-type]
   66 |         }
      |         ^
In file included from /usr/include/c++/14/string:43,
                 from /usr/include/c++/14/bitset:52,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:52,
                 from a.cc:6:
/usr/include/c++/14/bits/allocator.h: In destructor 'std::_Vector_base<std::vector<int>, std::allocator<std::vector<int> > >::_Vector_impl::~_Vector_impl()':
/usr/include/c++/14/bits/allocator.h:182:7: error: inlining failed in call to 'always_inline' 'std::allocator< <template-parameter-1-1> >::~allocator() noexcept [with _Tp = std::vector<int>]': target specific option mismatch
  182 |       ~allocator() _GLIBCXX_NOTHROW { }
      |       ^
In file included from /usr/include/c++/14/vector:66,
                 from /usr/include/c++/14/functional:64,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:53:
/usr/include/c++/14/bits/stl_vector.h:132:14: note: called from here
  132 |       struct _Vector_impl
      |              ^~~~~~~~~~~~