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input/code.cpp: In function 'int ford_fulkerson(std::vector<std::vector<std::pair<int, int> > >&, int, int, int)':
input/code.cpp:146:27: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  146 |         for (int i = 1; i < path_reversed.size(); i++)
      |                         ~~^~~~~~~~~~~~~~~~~~~~~~

#include <bits/stdc++.h>

#define REP(i, a, b) for (int i = a; i < b; i++)

// Type Aliases for 1D and 2D vectors with initialization
#define vll(n, val) vector<long long>(n, val) // 1D vector of long longs with size n, initialized to val
#define ll long long
#define vvi(n, m, val) vector<vector<int>>(n, vector<int>(m, val))              // 2D vector of ints (n x m), initialized to val
#define vvll(n, m, val) vector<vector<long long>>(n, vector<long long>(m, val)) // 2D vector of long longs (n x m), initialized to val

using namespace std;

void print_vector(vector<int> &x)
{
    for (int v : x)
    {
        cout << v << " ";
    }
    cout << "\n";
}

void print_matrix(vector<vector<int>> &matrix)
{
    cout << "\n"
         << "----------------" << "\n";
    for (vector<int> row : matrix)
    {
        print_vector(row);
    }
    cout << "\n"
         << "----------------" << "\n";
}

int calc_max_digit(int n)
{
    int max_digit = 0;
    while (n > 0 && max_digit < 9)
    {
        int digit = n % 10;
        if (digit > max_digit)
        {
            max_digit = digit;
        }
        n /= 10;
    }
    return max_digit;
}

// edges as edge list for outgoing node as pairs (end, cost)
vector<ll> dijkstras(int start_point, vector<vector<pair<int, int>>> edges)
{
    int n = edges.size();
    vector<bool> processed(n, false);
    vector<ll> distances(n, LLONG_MAX);
    distances[start_point] = 0;
    priority_queue<pair<ll, int>> pq;
    pq.push({0, start_point});
    while (!pq.empty())
    {
        int curr = pq.top().second;
        pq.pop();
        if (processed[curr])
        {
            continue;
        }
        processed[curr] = true;
        ll distance = distances[curr];

        for (pair<int, int> edge : edges[curr])
        {

            if (distance + edge.second < distances[edge.first])
            {
                distances[edge.first] = distance + edge.second;
                pq.push({-distances[edge.first], edge.first});
            }
        }
    }
    return distances;
}

int bfs_edmondson_karp(const vector<vector<pair<int, int>>> &connections,
                       const int source, const int target, vector<int> &path_reversed)
{
    int n = connections.size();

    queue<pair<int, int>> queue;
    queue.push({source, INT_MAX});
    vector<int> predecessor(n, -2);
    predecessor[source] = -1;

    while (!queue.empty())
    {
        int current = queue.front().first;
        int current_bottleneck = queue.front().second;
        queue.pop();
        // cout << "BFS - Current node: " << current << endl;

        if (current == target)
        {
            while (current != -1)
            {
                path_reversed.push_back(current);
                current = predecessor[current];
            }
            // cout << "Found path of capacity" << current_bottleneck << endl;
            return current_bottleneck;
        }

        for (pair<int, int> neigh : connections[current])
        {
            int edge_end = neigh.first, edge_cap = neigh.second;
            if (edge_cap > 0 && predecessor[edge_end] == -2)
            {
                predecessor[edge_end] = current;
                queue.push({edge_end, min(current_bottleneck, edge_cap)});
            }
        }
    }

    return -1;
}

int ford_fulkerson(vector<vector<pair<int, int>>> &residual_graph,
                   const int source, const int target, int starting_capacity)
{
    int n = residual_graph.size();
    int flow = 0;
    bool augmenting_path_exists = true;
    while (augmenting_path_exists)
    {
        vector<int> path_reversed;
        vector<bool> visited(n, false);

        // cout << "Starting BFS" << endl;
        int path_capacity = bfs_edmondson_karp(residual_graph, source, target, path_reversed);
        // cout << "Result " << path_capacity << endl;

        if (path_capacity < 0)
        {
            augmenting_path_exists = false;
            break;
        }

        flow += path_capacity;
        for (int i = 1; i < path_reversed.size(); i++)
        {
            int edge_end = path_reversed[i - 1];
            int edge_start = path_reversed[i];
            // reduce forwards edge
            for (pair<int, int> &edge : residual_graph[edge_start])
            {
                if (edge.first == edge_end)
                {
                    edge.second -= path_capacity;
                    break;
                }
            }
            // add to backwards edge
            for (pair<int, int> &edge : residual_graph[edge_end])
            {
                if (edge.first == edge_start)
                {
                    edge.second += path_capacity;
                    break;
                }
            }
        }
    }
    return flow;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, m;
    cin >> n >> m;

    vector<vector<pair<int, int>>> connections(n + 1, vector<pair<int, int>>(0));
    int max_capacity = 0;
    for (int i = 1; i <= m; i++)
    {
        int start, end, capacity;
        cin >> start >> end >> capacity;
        connections[start].push_back({end, capacity});
        connections[end].push_back({start, 0});
        if (capacity > max_capacity)
        {
            max_capacity = capacity;
        }
    }
    cout << ford_fulkerson(connections, 1, n, max_capacity) << endl;
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: TIME LIMIT EXCEEDED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: TIME LIMIT EXCEEDED

Test 12

Verdict: ACCEPTED