Download Speed

#include <iostream>
#include <vector>
#include <queue>
#include <climits>
#include <cstring>
 
using namespace std;
 
const int MAXN = 505; // Maximum number of nodes
int capacity[MAXN][MAXN]; // Capacity matrix
vector<int> adj[MAXN]; // Adjacency list
 
// Perform BFS to find an augmenting path, and record the path in 'parent'
int bfs(int s, int t, vector<int>& parent) {
    fill(parent.begin(), parent.end(), -1);
    parent[s] = s;
    queue<pair<int, int>> q;
    q.push({s, INT_MAX});
 
    while (!q.empty()) {
        int u = q.front().first;
        int flow = q.front().second;
        q.pop();
 
        // Traverse all neighbors of u
        for (int v : adj[u]) {
            // If the node is not yet visited and the capacity is greater than 0
            if (parent[v] == -1 && capacity[u][v] > 0) {
                parent[v] = u;
                int new_flow = min(flow, capacity[u][v]);
 
                // If we reached the sink, return the flow
                if (v == t)
                    return new_flow;
 
                q.push({v, new_flow});
            }
        }
    }
 
    return 0; // No path found
}
 
// Edmonds-Karp algorithm to compute the maximum flow
int edmonds_karp(int s, int t, int n) {
    int flow = 0;
    vector<int> parent(n + 1);
 
    while (int new_flow = bfs(s, t, parent)) {
        flow += new_flow;
 
        // Update the capacities of the edges in the augmenting path
        int cur = t;
        while (cur != s) {
            int prev = parent[cur];
            capacity[prev][cur] -= new_flow;
            capacity[cur][prev] += new_flow;
            cur = prev;
        }
    }
 
    return flow;
}
 
int main() {
    int n, m;
    cin >> n >> m;
 
    // Initialize the capacity matrix and adjacency list
    memset(capacity, 0, sizeof(capacity));
 
    // Read the edges and build the graph
    for (int i = 0; i < m; i++) {
        int a, b, c;
        cin >> a >> b >> c;
        capacity[a][b] += c;
        capacity[b][a] += c; // Since the graph is undirected, both directions have the same capacity
        adj[a].push_back(b);
        adj[b].push_back(a);
    }
 
    // Run the Edmonds-Karp algorithm to find the maximum flow from node 1 to node n
    int result = edmonds_karp(1, n, n);
    cout << result << endl;
 
    return 0;
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: WRONG ANSWER

Test 5

Verdict: WRONG ANSWER

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: WRONG ANSWER

Test 10

Verdict: ACCEPTED

Test 11

Verdict: WRONG ANSWER

Test 12

Verdict: ACCEPTED