Download Speed

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

// Ford-Fulkerson
// https://cp-algorithms.com/graph/edmonds_karp.html

using namespace std;

const int INF = 1e9;

int n;

vector<vector<int>> capacity;
vector<vector<int>> adj;

// Find shortest route with capacity left.
// Path doesnt matter, just that it has flow left
int bfs(int s, int t, vector<int>& parent) {
    fill(parent.begin(), parent.end(), -1);
    parent[s] = -2;
    queue<pair<int, int>> q;
    q.push({s, INF});

    // Go thru paths
    while (!q.empty()) {
        int cur = q.front().first;
        int flow = q.front().second;
        q.pop();

        for (int next : adj[cur]) { // Check if it has flow and we havent been there
            if (parent[next] == -1 && capacity[cur][next]) {
                parent[next] = cur;
                int new_flow = min(flow, capacity[cur][next]);
                if (next == t)
                    return new_flow;
                q.push({next, new_flow});
            }
        }
    }

    return 0;
}

// Keep seaching, while capacity remains.
int maxflow(int s, int t) {
    int flow = 0;
    vector<int> parent(n + 1);
    int new_flow;

    // While new flow exists.
    while ((new_flow = bfs(s, t, parent))) {
        // Increase current flow
        flow += new_flow;

        int cur = t;
        while (cur != s) { // Change flow in tree paths
            int prev = parent[cur];
            capacity[prev][cur] -= new_flow;
            capacity[cur][prev] += new_flow;
            cur = prev;
        }
    }

    return flow;
}

int main() {
    int m;
    cin >> n >> m; // N is global

    // Set capacity vector size
    capacity.assign(n + 1, vector<int>(n + 1, 0));
    adj.assign(n + 1, vector<int>());

    // Create tree
    for (int i = 0; i < m; i++) {
        int u, v, c;
        cin >> u >> v >> c;

        // No duplicates
        if (capacity[u][v] == 0 && capacity[v][u] == 0) {
            adj[u].push_back(v);
            adj[v].push_back(u);
        }

        // Set new capacity from queries
        capacity[u][v] += c;
    }

    // Output
    cout << maxflow(1, n) << "\n";

    return 0;
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: WRONG ANSWER

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: WRONG ANSWER

Test 12

Verdict: ACCEPTED