CC.h

#ifndef CH4_CC_H
#define CH4_CC_H

// TODO: add EdgeWeightedGraph
#include "../head/Graph.h"

/**
 *  The {@code CC} class represents a data type for
 *  determining the connected components in an undirected graph.
 *  The <em>id</em> operation determines in which connected component
 *  a given vertex lies; the <em>connected</em> operation
 *  determines whether two vertices are in the same connected component;
 *  the <em>count</em> operation determines the number of connected
 *  components; and the <em>size</em> operation determines the number
 *  of vertices in the connect component containing a given vertex.

 *  The <em>component identifier</em> of a connected component is one of the
 *  vertices in the connected component: two vertices have the same component
 *  identifier if and only if they are in the same connected component.

 *  <p>
 *  This implementation uses depth-first search.
 *  The constructor takes time proportional to <em>V</em> + <em>E</em>
 *  (in the worst case),
 *  where <em>V</em> is the number of vertices and <em>E</em> is the number of edges.
 *  Afterwards, the <em>id</em>, <em>count</em>, <em>connected</em>,
 *  and <em>size</em> operations take constant time.
 *  <p>
 *  For additional documentation, see <a href="https://algs4.cs.princeton.edu/41graph">Section 4.1</a>
 *  of <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
 *
 *  @author Robert Sedgewick
 *  @author Kevin Wayne
 */
class CC {
public:
    /**
     * Computes the connected components of the undirected graph {@code G}.
     *
     * @param G the undirected graph
     */
    CC(Graph &G) : marked(G.getV()), id(G.getV()), size(G.getV()), count(0) {
        for (int v = 0; v < G.getV(); v++) {
            if (!marked[v]) {
                dfs(G, v);
                count++;
            }
        }
    }

    /**
     * Returns the component id of the connected component containing vertex {@code v}.
     *
     * @param  v the vertex
     * @return the component id of the connected component containing vertex {@code v}
     * @throws IllegalArgumentException unless {@code 0 <= v < V}
     */
    int getid(int v) {
        validateVertex(v);
        return id[v];
    }

    /**
     * Returns the number of vertices in the connected component containing vertex {@code v}.
     *
     * @param  v the vertex
     * @return the number of vertices in the connected component containing vertex {@code v}
     * @throws IllegalArgumentException unless {@code 0 <= v < V}
     */
    int getsize(int v) {
        validateVertex(v);
        return size[id[v]];
    }

    /**
    * Returns the number of connected components in the graph {@code G}.
    *
    * @return the number of connected components in the graph {@code G}
    */
    int getcount() {
        return count;
    }

    /**
     * Returns true if vertices {@code v} and {@code w} are in the same
     * connected component.
     *
     * @param  v one vertex
     * @param  w the other vertex
     * @return {@code true} if vertices {@code v} and {@code w} are in the same
     *         connected component; {@code false} otherwise
     * @throws IllegalArgumentException unless {@code 0 <= v < V}
     * @throws IllegalArgumentException unless {@code 0 <= w < V}
     */
    bool connected(int v, int w) {
        validateVertex(v);
        validateVertex(w);
        return getid(v) == getid(w);
    }



private:
    // depth-first search for a Graph
    void dfs(Graph G, int v) {
        marked[v] = true;
        id[v] = count;
        size[count]++;
        for (int w : G.getadj(v)) {
            if (!marked[w]) {
                dfs(G, w);
            }
        }
    }

    // throw an IllegalArgumentException unless {@code 0 <= v < V}
    void validateVertex(int v) {
        int V = marked.size();
        if (v < 0 || v >= V)
            throw runtime_error("vertex " + to_string(v) + " is not between 0 and " + to_string(V - 1));
    }


private:
    vector<bool> marked;   // marked[v] = has vertex v been marked?
    vector<int> id;        // id[v] = id of connected component containing v
    vector<int> size;      // size[id] = number of vertices in given component
    int count;             // number of connected components
};

#endif //CH4_CC_H