Sem_2_Task_8

#include <iostream>
#include <vector>
#include <algorithm>
#include <unordered_map>
#include <queue>

struct Edge;

const int64_t INF = int64_t(1e15);

namespace {
    using NumsVec = std::vector<int64_t>;
    using VecNumsVec = std::vector<NumsVec>;
    using BoolVec = std::vector<bool>;
    using EdgeVec = std::vector<Edge>;
    using VecEdgeVec = std::vector<EdgeVec>;
    using UnMapNumEdge = std::unordered_map<int64_t, Edge>;
}

struct Edge {
    Edge() = default;
    Edge(std::pair<size_t, size_t> edge) : from(edge.first), to(edge.second) {};
    Edge(size_t i, size_t j, size_t w) : from(i), to(j), c(w) {};

    bool operator==(const Edge& other) const {
        return from == other.from && to == other.to;
    }

    Edge Reverse() {
        return Edge(to, from, c);
    }

    size_t from = 0;
    size_t to = 0;
    int64_t c = 0;
};

std::istream& operator>>(std::istream& input, Edge& edge) {
    input >> edge.from >> edge.to >> edge.c;
    --edge.from;
    --edge.to;
    return input;
}

void InputEdges(std::vector<Edge>& edges) {
    for (auto& edge : edges) {
        std::cin >> edge;
    }
}

template<>
struct std::hash<Edge> {
    size_t operator()(const Edge& p) const {
        return p.from * p.to;
    }
};

std::ostream& operator<<(std::ostream& output, NumsVec& vec) {
    for (auto elem : vec) {
        std::cout << elem + 1 << " ";
    }
    return output;
}

struct Graph {
    Graph(size_t n) : size(n), neighbours(n), visited(n, false), color(n, 0),
    top_sort(n, 0), top_sort_pos(n - 1), d(n, INF) {};

    Graph(size_t n, EdgeVec& edges) : size(n), h(n, 0), e(n, 0), flow(n, NumsVec(n, 0)), neighbours(n) {
        for (auto edge : edges) {
            auto& edge_direct = neighbours[edge.from][edge.to];
            edge_direct.from = edge.from;
            edge_direct.to = edge.to;
            edge_direct.c += edge.c;
            auto& edge_back = neighbours[edge.to][edge.from];
            edge_back.to = edge.from;
            edge_back.from = edge.to;
        }
    };

    size_t size = 0;
    bool cycle = false;

    std::vector<UnMapNumEdge> neighbours;
    VecNumsVec matrix;
    VecNumsVec flow;
    BoolVec visited;
    NumsVec color;
    NumsVec top_sort;
    NumsVec d;
    NumsVec e;
    NumsVec h;
    EdgeVec route;
    size_t max_flow = 0;
    size_t sum_w = 0;
    size_t top_sort_pos = 0;
};

void Push(Graph& g, size_t u, Edge edge) {
    size_t v = edge.to;
    int64_t flow = std::min(g.e[u], edge.c - g.flow[u][v]);
    g.flow[u][v] += flow;
    g.flow[v][u] = -g.flow[u][v];
    g.e[u] -= flow;
    g.e[v] += flow;
}

void Lift(Graph& g, size_t u) {
    g.h[u] = INF;
    for (auto [v, edge] : g.neighbours[u]) {
        if (edge.c - g.flow[u][v] > 0) {
            g.h[u] = std::min(g.h[u], g.h[v] + 1);
        }
    }
}

void ChangeFlow(Graph& g, size_t u) {
    for (auto [v, edge] : g.neighbours[u]) {
        if (edge.c - g.flow[u][v] > 0 && g.h[u] == g.h[v] + 1) {
            Push(g, u, edge);
            return;
        }
    }
    Lift(g, u);
}

size_t FindOverflowing(Graph& g, size_t s, size_t t) {
    for (size_t v = 0; v < g.size; ++v) {
        if (v != s && v != t && g.e[v] > 0) {
            return v;
        }
    }
    return t;
}

void GenericPreflowPush(Graph& g, size_t s, size_t t) {
    g.h[s] = g.size;
    for (auto [v, edge] : g.neighbours[s]) {
        g.e[v] += edge.c;
        g.flow[s][v] = edge.c;
        g.flow[v][s] = -edge.c;
    }
    size_t u;
    while ((u = FindOverflowing(g, s, t)) != t) {
        ChangeFlow(g, u);
    }
    for (auto [v, edge] : g.neighbours[s]) {
        g.max_flow += g.flow[s][v];
    }
}

int main() {
    size_t n, m;
    std::cin >> n >> m;
    EdgeVec edges(m);
    InputEdges(edges);
    Graph g(n, edges);
    GenericPreflowPush(g, 0, n - 1);
    std::cout << g.max_flow;
}