package GraphAlgorithm;

import java.util.HashSet;
import java.util.Set;

import org.apache.commons.math3.distribution.BinomialDistribution;
import org.apache.commons.math3.distribution.UniformIntegerDistribution;

import network.DisGraph;
import util.StdRandom;

/******************************************************************************
 *  Compilation:  javac GraphGenerator.java
 *  Execution:    java GraphGenerator V E
 *  Dependencies: Graph.java
 *
 *  A graph generator.
 *
 *  For many more graph generators, see
 *  http://networkx.github.io/documentation/latest/reference/generators.html
 *
 ******************************************************************************/

/**
 *  The {@code GraphGenerator} class provides static methods for creating
 *  various graphs, including Erdos-Renyi random graphs, random bipartite
 *  graphs, random k-regular graphs, and random rooted trees.
 *  <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
 */
public class GraphGenerator {
    private static final class Edge implements Comparable<Edge> {
        private int v;
        private int w;

        private Edge(int v, int w) {
            if (v < w) {
                this.v = v;
                this.w = w;
            }
            else {
                this.v = w;
                this.w = v;
            }
        }

        public int compareTo(Edge that) {
            if (this.v < that.v) return -1;
            if (this.v > that.v) return +1;
            if (this.w < that.w) return -1;
            if (this.w > that.w) return +1;
            return 0;
        }
    }

    // this class cannot be instantiated
    private GraphGenerator() { }

    /**
     * Returns a random simple graph containing {@code V} vertices and {@code E} edges.
     * @param V the number of vertices
     * @param E the number of vertices
     * @return a random simple graph on {@code V} vertices, containing a total
     *     of {@code E} edges
     * @throws IllegalArgumentException if no such simple graph exists
     */
    public static DisGraph simple(int V, int E) {
        if (E > (long) V*(V-1)/2) throw new IllegalArgumentException("Too many edges");
        if (E < 0)                throw new IllegalArgumentException("Too few edges");
        DisGraph G = new DisGraph(V);
        Set<Edge> set = new HashSet<Edge>();
        while (G.getEdges() < E) {
            int v = StdRandom.uniform(V);
            int w = StdRandom.uniform(V);
            Edge e = new Edge(v, w);
            if ((v != w) && !set.contains(e)) {
                set.add(e);
                G.addEdge(v, w);
            }
        }
        return G;
    }

    /**
     * Returns a random simple graph on {@code V} vertices, with an 
     * edge between any two vertices with probability {@code p}. This is sometimes
     * referred to as the Erdos-Renyi random graph model.
     * @param V the number of vertices
     * @param p the probability of choosing an edge
     * @return a random simple graph on {@code V} vertices, with an edge between
     *     any two vertices with probability {@code p}
     * @throws IllegalArgumentException if probability is not between 0 and 1
     */
    public static DisGraph simple(int V, double p) {
        if (p < 0.0 || p > 1.0)
            throw new IllegalArgumentException("Probability must be between 0 and 1");
        DisGraph G = new DisGraph(V);
        for (int v = 0; v < V; v++)
            for (int w = v+1; w < V; w++)
                if (StdRandom.bernoulli(p))
                    G.addEdge(v, w);
        return G;
    }

    /**
     * Returns the complete graph on {@code V} vertices.
     * @param V the number of vertices
     * @return the complete graph on {@code V} vertices
     */
    public static DisGraph complete(int V) {
        return simple(V, 1.0);
    }

    /**
     * Returns a complete bipartite graph on {@code V1} and {@code V2} vertices.
     * @param V1 the number of vertices in one partition
     * @param V2 the number of vertices in the other partition
     * @return a complete bipartite graph on {@code V1} and {@code V2} vertices
     * @throws IllegalArgumentException if probability is not between 0 and 1
     */
//    public static DisGraph completeBipartite(int V1, int V2) {
//        return bipartite(V1, V2, V1*V2);
//    }

    /**
     * Returns a random simple bipartite graph on {@code V1} and {@code V2} vertices
     * with {@code E} edges.
     * @param V1 the number of vertices in one partition
     * @param V2 the number of vertices in the other partition
     * @param E the number of edges
     * @return a random simple bipartite graph on {@code V1} and {@code V2} vertices,
     *    containing a total of {@code E} edges
     * @throws IllegalArgumentException if no such simple bipartite graph exists
     */
//    public static DisGraph bipartite(int V1, int V2, int E) {
//        if (E > (long) V1*V2) throw new IllegalArgumentException("Too many edges");
//        if (E < 0)            throw new IllegalArgumentException("Too few edges");
//        DisGraph G = new Graph(V1 + V2);
//
//        int[] vertices = new int[V1 + V2];
//        for (int i = 0; i < V1 + V2; i++)
//            vertices[i] = i;
//        StdRandom.shuffle(vertices);
//
//        SET<Edge> set = new SET<Edge>();
//        while (G.E() < E) {
//            int i = StdRandom.uniform(V1);
//            int j = V1 + StdRandom.uniform(V2);
//            Edge e = new Edge(vertices[i], vertices[j]);
//            if (!set.contains(e)) {
//                set.add(e);
//                G.addEdge(vertices[i], vertices[j]);
//            }
//        }
//        return G;
//    }
//
//    /**
//     * Returns a random simple bipartite graph on {@code V1} and {@code V2} vertices,
//     * containing each possible edge with probability {@code p}.
//     * @param V1 the number of vertices in one partition
//     * @param V2 the number of vertices in the other partition
//     * @param p the probability that the graph contains an edge with one endpoint in either side
//     * @return a random simple bipartite graph on {@code V1} and {@code V2} vertices,
//     *    containing each possible edge with probability {@code p}
//     * @throws IllegalArgumentException if probability is not between 0 and 1
//     */
//    public static Graph bipartite(int V1, int V2, double p) {
//        if (p < 0.0 || p > 1.0)
//            throw new IllegalArgumentException("Probability must be between 0 and 1");
//        int[] vertices = new int[V1 + V2];
//        for (int i = 0; i < V1 + V2; i++)
//            vertices[i] = i;
//        StdRandom.shuffle(vertices);
//        Graph G = new Graph(V1 + V2);
//        for (int i = 0; i < V1; i++)
//            for (int j = 0; j < V2; j++)
//                if (StdRandom.bernoulli(p))
//                    G.addEdge(vertices[i], vertices[V1+j]);
//        return G;
//    }
//
//    /**
//     * Returns a path graph on {@code V} vertices.
//     * @param V the number of vertices in the path
//     * @return a path graph on {@code V} vertices
//     */
//    public static Graph path(int V) {
//        Graph G = new Graph(V);
//        int[] vertices = new int[V];
//        for (int i = 0; i < V; i++)
//            vertices[i] = i;
//        StdRandom.shuffle(vertices);
//        for (int i = 0; i < V-1; i++) {
//            G.addEdge(vertices[i], vertices[i+1]);
//        }
//        return G;
//    }
//
//    /**
//     * Returns a complete binary tree graph on {@code V} vertices.
//     * @param V the number of vertices in the binary tree
//     * @return a complete binary tree graph on {@code V} vertices
//     */
//    public static Graph binaryTree(int V) {
//        Graph G = new Graph(V);
//        int[] vertices = new int[V];
//        for (int i = 0; i < V; i++)
//            vertices[i] = i;
//        StdRandom.shuffle(vertices);
//        for (int i = 1; i < V; i++) {
//            G.addEdge(vertices[i], vertices[(i-1)/2]);
//        }
//        return G;
//    }
//
//    /**
//     * Returns a cycle graph on {@code V} vertices.
//     * @param V the number of vertices in the cycle
//     * @return a cycle graph on {@code V} vertices
//     */
//    public static Graph cycle(int V) {
//        Graph G = new Graph(V);
//        int[] vertices = new int[V];
//        for (int i = 0; i < V; i++)
//            vertices[i] = i;
//        StdRandom.shuffle(vertices);
//        for (int i = 0; i < V-1; i++) {
//            G.addEdge(vertices[i], vertices[i+1]);
//        }
//        G.addEdge(vertices[V-1], vertices[0]);
//        return G;
//    }
//
//    /**
//     * Returns an Eulerian cycle graph on {@code V} vertices.
//     *
//     * @param  V the number of vertices in the cycle
//     * @param  E the number of edges in the cycle
//     * @return a graph that is an Eulerian cycle on {@code V} vertices
//     *         and {@code E} edges
//     * @throws IllegalArgumentException if either {@code V <= 0} or {@code E <= 0}
//     */
//    public static Graph eulerianCycle(int V, int E) {
//        if (E <= 0)
//            throw new IllegalArgumentException("An Eulerian cycle must have at least one edge");
//        if (V <= 0)
//            throw new IllegalArgumentException("An Eulerian cycle must have at least one vertex");
//        Graph G = new Graph(V);
//        int[] vertices = new int[E];
//        for (int i = 0; i < E; i++)
//            vertices[i] = StdRandom.uniform(V);
//        for (int i = 0; i < E-1; i++) {
//            G.addEdge(vertices[i], vertices[i+1]);
//        }
//        G.addEdge(vertices[E-1], vertices[0]);
//        return G;
//    }
//
//    /**
//     * Returns an Eulerian path graph on {@code V} vertices.
//     *
//     * @param  V the number of vertices in the path
//     * @param  E the number of edges in the path
//     * @return a graph that is an Eulerian path on {@code V} vertices
//     *         and {@code E} edges
//     * @throws IllegalArgumentException if either {@code V <= 0} or {@code E < 0}
//     */
//    public static Graph eulerianPath(int V, int E) {
//        if (E < 0)
//            throw new IllegalArgumentException("negative number of edges");
//        if (V <= 0)
//            throw new IllegalArgumentException("An Eulerian path must have at least one vertex");
//        Graph G = new Graph(V);
//        int[] vertices = new int[E+1];
//        for (int i = 0; i < E+1; i++)
//            vertices[i] = StdRandom.uniform(V);
//        for (int i = 0; i < E; i++) {
//            G.addEdge(vertices[i], vertices[i+1]);
//        }
//        return G;
//    }
//
//    /**
//     * Returns a wheel graph on {@code V} vertices.
//     * @param V the number of vertices in the wheel
//     * @return a wheel graph on {@code V} vertices: a single vertex connected to
//     *     every vertex in a cycle on {@code V-1} vertices
//     */
//    public static Graph wheel(int V) {
//        if (V <= 1) throw new IllegalArgumentException("Number of vertices must be at least 2");
//        Graph G = new Graph(V);
//        int[] vertices = new int[V];
//        for (int i = 0; i < V; i++)
//            vertices[i] = i;
//        StdRandom.shuffle(vertices);
//
//        // simple cycle on V-1 vertices
//        for (int i = 1; i < V-1; i++) {
//            G.addEdge(vertices[i], vertices[i+1]);
//        }
//        G.addEdge(vertices[V-1], vertices[1]);
//
//        // connect vertices[0] to every vertex on cycle
//        for (int i = 1; i < V; i++) {
//            G.addEdge(vertices[0], vertices[i]);
//        }
//
//        return G;
//    }
//
//    /**
//     * Returns a star graph on {@code V} vertices.
//     * @param V the number of vertices in the star
//     * @return a star graph on {@code V} vertices: a single vertex connected to
//     *     every other vertex
//     */
//    public static Graph star(int V) {
//        if (V <= 0) throw new IllegalArgumentException("Number of vertices must be at least 1");
//        Graph G = new Graph(V);
//        int[] vertices = new int[V];
//        for (int i = 0; i < V; i++)
//            vertices[i] = i;
//        StdRandom.shuffle(vertices);
//
//        // connect vertices[0] to every other vertex
//        for (int i = 1; i < V; i++) {
//            G.addEdge(vertices[0], vertices[i]);
//        }
//
//        return G;
//    }
//
//    /**
//     * Returns a uniformly random {@code k}-regular graph on {@code V} vertices
//     * (not necessarily simple). The graph is simple with probability only about e^(-k^2/4),
//     * which is tiny when k = 14.
//     *
//     * @param V the number of vertices in the graph
//     * @param k degree of each vertex
//     * @return a uniformly random {@code k}-regular graph on {@code V} vertices.
//     */
//    public static Graph regular(int V, int k) {
//        if (V*k % 2 != 0) throw new IllegalArgumentException("Number of vertices * k must be even");
//        Graph G = new Graph(V);
//
//        // create k copies of each vertex
//        int[] vertices = new int[V*k];
//        for (int v = 0; v < V; v++) {
//            for (int j = 0; j < k; j++) {
//                vertices[v + V*j] = v;
//            }
//        }
//
//        // pick a random perfect matching
//        StdRandom.shuffle(vertices);
//        for (int i = 0; i < V*k/2; i++) {
//            G.addEdge(vertices[2*i], vertices[2*i + 1]);
//        }
//        return G;
//    }
//
//    // http://www.proofwiki.org/wiki/Labeled_Tree_from_Prüfer_Sequence
//    // http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.36.6484&rep=rep1&type=pdf
//    /**
//     * Returns a uniformly random tree on {@code V} vertices.
//     * This algorithm uses a Prufer sequence and takes time proportional to <em>V log V</em>.
//     * @param V the number of vertices in the tree
//     * @return a uniformly random tree on {@code V} vertices
//     */
//    public static Graph tree(int V) {
//        Graph G = new Graph(V);
//
//        // special case
//        if (V == 1) return G;
//
//        // Cayley's theorem: there are V^(V-2) labeled trees on V vertices
//        // Prufer sequence: sequence of V-2 values between 0 and V-1
//        // Prufer's proof of Cayley's theorem: Prufer sequences are in 1-1
//        // with labeled trees on V vertices
//        int[] prufer = new int[V-2];
//        for (int i = 0; i < V-2; i++)
//            prufer[i] = StdRandom.uniform(V);
//
//        // degree of vertex v = 1 + number of times it appers in Prufer sequence
//        int[] degree = new int[V];
//        for (int v = 0; v < V; v++)
//            degree[v] = 1;
//        for (int i = 0; i < V-2; i++)
//            degree[prufer[i]]++;
//
//        // pq contains all vertices of degree 1
//        MinPQ<Integer> pq = new MinPQ<Integer>();
//        for (int v = 0; v < V; v++)
//            if (degree[v] == 1) pq.insert(v);
//
//        // repeatedly delMin() degree 1 vertex that has the minimum index
//        for (int i = 0; i < V-2; i++) {
//            int v = pq.delMin();
//            G.addEdge(v, prufer[i]);
//            degree[v]--;
//            degree[prufer[i]]--;
//            if (degree[prufer[i]] == 1) pq.insert(prufer[i]);
//        }
//        G.addEdge(pq.delMin(), pq.delMin());
//        return G;
//    }
//
//    /**
//     * Unit tests the {@code GraphGenerator} library.
//     *
//     * @param args the command-line arguments
//     */
//    public static void main(String[] args) {
//        int V = Integer.parseInt(args[0]);
//        int E = Integer.parseInt(args[1]);
//        int V1 = V/2;
//        int V2 = V - V1;
//
//        StdOut.println("complete graph");
//        StdOut.println(complete(V));
//        StdOut.println();
//
//        StdOut.println("simple");
//        StdOut.println(simple(V, E));
//        StdOut.println();
//
//        StdOut.println("Erdos-Renyi");
//        double p = (double) E / (V*(V-1)/2.0);
//        StdOut.println(simple(V, p));
//        StdOut.println();
//
//        StdOut.println("complete bipartite");
//        StdOut.println(completeBipartite(V1, V2));
//        StdOut.println();
//
//        StdOut.println("bipartite");
//        StdOut.println(bipartite(V1, V2, E));
//        StdOut.println();
//
//        StdOut.println("Erdos Renyi bipartite");
//        double q = (double) E / (V1*V2);
//        StdOut.println(bipartite(V1, V2, q));
//        StdOut.println();
//
//        StdOut.println("path");
//        StdOut.println(path(V));
//        StdOut.println();
//
//        StdOut.println("cycle");
//        StdOut.println(cycle(V));
//        StdOut.println();
//
//        StdOut.println("binary tree");
//        StdOut.println(binaryTree(V));
//        StdOut.println();
//
//        StdOut.println("tree");
//        StdOut.println(tree(V));
//        StdOut.println();
//
//        StdOut.println("4-regular");
//        StdOut.println(regular(V, 4));
//        StdOut.println();
//
//        StdOut.println("star");
//        StdOut.println(star(V));
//        StdOut.println();
//
//        StdOut.println("wheel");
//        StdOut.println(wheel(V));
//        StdOut.println();
//    }

}