/C++/Shortest path in unweighted graph bfs

Shortest path in unweighted graph bfs

// CPP code for printing shortest path between
// two vertices of unweighted graph
#include <bits/stdc++.h>
using namespace std;
 
// utility function to form edge between two vertices
// source and dest
void add_edge(vector<int> adj[], int src, int dest)
{
    adj[src].push_back(dest);
    adj[dest].push_back(src);
}
 
// a modified version of BFS that stores predecessor
// of each vertex in array p
// and its distance from source in array d
bool BFS(vector<int> adj[], int src, int dest, int v,
         int pred[], int dist[])
{
    // a queue to maintain queue of vertices whose
    // adjacency list is to be scanned as per normal
    // DFS algorithm
    list<int> queue;
 
    // boolean array visited[] which stores the
    // information whether ith vertex is reached
    // at least once in the Breadth first search
    bool visited[v];
 
    // initially all vertices are unvisited
    // so v[i] for all i is false
    // and as no path is yet constructed
    // dist[i] for all i set to infinity
    for (int i = 0; i < v; i++) {
        visited[i] = false;
        dist[i] = INT_MAX;
        pred[i] = -1;
    }
 
    // now source is first to be visited and
    // distance from source to itself should be 0
    visited[src] = true;
    dist[src] = 0;
    queue.push_back(src);
 
    // standard BFS algorithm
    while (!queue.empty()) {
        int u = queue.front();
        queue.pop_front();
        for (int i = 0; i < adj[u].size(); i++) {
            if (visited[adj[u][i]] == false) {
                visited[adj[u][i]] = true;
                dist[adj[u][i]] = dist[u] + 1;
                pred[adj[u][i]] = u;
                queue.push_back(adj[u][i]);
 
                // We stop BFS when we find
                // destination.
                if (adj[u][i] == dest)
                    return true;
            }
        }
    }
 
    return false;
}
 
// utility function to print the shortest distance
// between source vertex and destination vertex
void printShortestDistance(vector<int> adj[], int s,
                           int dest, int v)
{
    // predecessor[i] array stores predecessor of
    // i and distance array stores distance of i
    // from s
    int pred[v], dist[v];
 
    if (BFS(adj, s, dest, v, pred, dist) == false) {
        cout << "Given source and destination"
             << " are not connected";
        return;
    }
 
    // vector path stores the shortest path
    vector<int> path;
    int crawl = dest;
    path.push_back(crawl);
    while (pred[crawl] != -1) {
        path.push_back(pred[crawl]);
        crawl = pred[crawl];
    }
 
    // distance from source is in distance array
    cout << "Shortest path length is : "
         << dist[dest];
 
    // printing path from source to destination
    cout << "\nPath is::\n";
    for (int i = path.size() - 1; i >= 0; i--)
        cout << path[i] << " ";
}
 
// Driver program to test above functions
int main()
{
    // no. of vertices
    int v = 8;
 
    // array of vectors is used to store the graph
    // in the form of an adjacency list
    vector<int> adj[v];
 
    // Creating graph given in the above diagram.
    // add_edge function takes adjacency list, source
    // and destination vertex as argument and forms
    // an edge between them.
    add_edge(adj, 0, 1);
    add_edge(adj, 0, 3);
    add_edge(adj, 1, 2);
    add_edge(adj, 3, 4);
    add_edge(adj, 3, 7);
    add_edge(adj, 4, 5);
    add_edge(adj, 4, 6);
    add_edge(adj, 4, 7);
    add_edge(adj, 5, 6);
    add_edge(adj, 6, 7);
    int source = 0, dest = 7;
    printShortestDistance(adj, source, dest, v);
    return 0;
}

Source: geeksforgeeks.org

Shortest path in unweighted graph bfs

Input: source vertex = 0 and destination vertex is = 7.
Output: Shortest path length is:2
        Path is::
        0 3 7

Input: source vertex is = 2 and destination vertex is = 6.
Output: Shortest path length is:5
        Path is::
        2 1 0 3 4 6

Source: geeksforgeeks.org

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