package com.thealgorithms.datastructures.graphs;

// Problem -> Connect all the edges with the minimum cost.
// Possible Solution -> Kruskal Algorithm (KA), KA finds the minimum-spanning-tree, which means, the
// group of edges with the minimum sum of their weights that connect the whole graph.
// The graph needs to be connected, because if there are nodes impossible to reach, there are no
// edges that could connect every node in the graph.
// KA is a Greedy Algorithm, because edges are analysed based on their weights, that is why a
// Priority Queue is used, to take first those less weighted.
// This implementations below has some changes compared to conventional ones, but they are explained
// all along the code.
import java.util.Comparator;
import java.util.HashSet;
import java.util.PriorityQueue;

public class Kruskal {

    // Complexity: O(E log V) time, where E is the number of edges in the graph and V is the number
    // of vertices
    private static class Edge {

        private int from;
        private int to;
        private int weight;

        public Edge(int from, int to, int weight) {
            this.from = from;
            this.to = to;
            this.weight = weight;
        }
    }

    private static void addEdge(HashSet<Edge>[] graph, int from, int to, int weight) {
        graph[from].add(new Edge(from, to, weight));
    }

    public static void main(String[] args) {
        HashSet<Edge>[] graph = new HashSet[7];
        for (int i = 0; i < graph.length; i++) {
            graph[i] = new HashSet<>();
        }
        addEdge(graph, 0, 1, 2);
        addEdge(graph, 0, 2, 3);
        addEdge(graph, 0, 3, 3);
        addEdge(graph, 1, 2, 4);
        addEdge(graph, 2, 3, 5);
        addEdge(graph, 1, 4, 3);
        addEdge(graph, 2, 4, 1);
        addEdge(graph, 3, 5, 7);
        addEdge(graph, 4, 5, 8);
        addEdge(graph, 5, 6, 9);

        System.out.println("Initial Graph: ");
        for (int i = 0; i < graph.length; i++) {
            for (Edge edge : graph[i]) {
                System.out.println(i + " <-- weight " + edge.weight + " --> " + edge.to);
            }
        }

        Kruskal k = new Kruskal();
        HashSet<Edge>[] solGraph = k.kruskal(graph);

        System.out.println("\nMinimal Graph: ");
        for (int i = 0; i < solGraph.length; i++) {
            for (Edge edge : solGraph[i]) {
                System.out.println(i + " <-- weight " + edge.weight + " --> " + edge.to);
            }
        }
    }

    public HashSet<Edge>[] kruskal(HashSet<Edge>[] graph) {
        int nodes = graph.length;
        int[] captain = new int[nodes];
        // captain of i, stores the set with all the connected nodes to i
        HashSet<Integer>[] connectedGroups = new HashSet[nodes];
        HashSet<Edge>[] minGraph = new HashSet[nodes];
        PriorityQueue<Edge> edges = new PriorityQueue<>((Comparator.comparingInt(edge -> edge.weight)));
        for (int i = 0; i < nodes; i++) {
            minGraph[i] = new HashSet<>();
            connectedGroups[i] = new HashSet<>();
            connectedGroups[i].add(i);
            captain[i] = i;
            edges.addAll(graph[i]);
        }
        int connectedElements = 0;
        // as soon as two sets merge all the elements, the algorithm must stop
        while (connectedElements != nodes && !edges.isEmpty()) {
            Edge edge = edges.poll();
            // This if avoids cycles
            if (!connectedGroups[captain[edge.from]].contains(edge.to) && !connectedGroups[captain[edge.to]].contains(edge.from)) {
                // merge sets of the captains of each point connected by the edge
                connectedGroups[captain[edge.from]].addAll(connectedGroups[captain[edge.to]]);
                // update captains of the elements merged
                connectedGroups[captain[edge.from]].forEach(i -> captain[i] = captain[edge.from]);
                // add Edge to minimal graph
                addEdge(minGraph, edge.from, edge.to, edge.weight);
                // count how many elements have been merged
                connectedElements = connectedGroups[captain[edge.from]].size();
            }
        }
        return minGraph;
    }
}
