克鲁斯卡尔算法（Kruskal）

同样是求最小生成树克鲁斯卡尔算法的思想则转变了一下，以边为目标去生成最小数

这种感觉就像是结果等于10式子2*5也行，20/2也行，方式不同只看最后的结果

思想：按照权值的大小从小到大排序，选择n-1条边，并且不构成回路

过程：构造一个只含有n个节点的森林，然后从权值最小到最大选择边加入到森林中，使之不产生回路，直到森林变成树为止

import java.util.Arrays;

public class KruskalCase {

    private int edgeNum;//边
    private char[] vertexs;//顶点
    private int[][] matrix;//邻接矩阵
    private static final int INF = Integer.MAX_VALUE;//顶点不相同

    public static void main(String[] args) {
        char[] vertexs = {'A', 'B', 'C', 'D', 'E', 'F', 'G'};
        int[][] matrix = {
                {0, 12, INF, INF, INF, 16, 14},
                {12, 0, 10, INF, INF, 7, INF,},
                {INF, 10, 0, 3, 5, 6, INF,},
                {INF, INF, 3, 0, 4, INF, INF},
                {INF, INF, 5, 4, 0, 2, 8},
                {16, 7, 6, INF, 2, 0, 9},
                {14, INF, INF, INF, 8, 9, 0}
        };
        KruskalCase kruskalCase = new KruskalCase(vertexs, matrix);
//        kruskalCase.print();
        EData[] edges = kruskalCase.getEdges();
        System.out.println(Arrays.toString(edges));
        kruskalCase.sortEdges(edges);
        System.out.println(Arrays.toString(edges));
        kruskalCase.kruskal();
    }

    public KruskalCase(char[] vertexs, int[][] matrix) {
        int vlen = vertexs.length;
        this.vertexs = new char[vlen];
        for (int i = 0; i < vertexs.length; i++) {
            this.vertexs[i] = vertexs[i];
        }
        this.matrix = new int[vlen][vlen];
        for (int i = 0; i < vlen; i++) {
            for (int j = 0; j < vlen; j++) {
                this.matrix[i][j] = matrix[i][j];
            }
        }
        for (int i = 0; i < vlen; i++) {
            for (int j = i + 1; j < vlen; j++) {
                if (this.matrix[i][j] != INF) {
                    edgeNum++;
                }
            }
        }
    }

    public void print() {
        for (int i = 0; i < vertexs.length; i++) {
            for (int j = 0; j < vertexs.length; j++) {
                System.out.printf("%12d", matrix[i][j]);
            }
            System.out.println();
        }
    }

    //排序
    private void sortEdges(EData[] edges) {
        for (int i = 0; i < edges.length - 1; i++) {
            for (int j = 0; j < edges.length - 1 - i; j++) {
                if (edges[j].weight > edges[j + 1].weight) {
                    EData tmp = edges[j];
                    edges[j] = edges[j + 1];
                    edges[j + 1] = tmp;
                }
            }
        }
    }

    private int getPosition(char ch) {
        for (int i = 0; i < vertexs.length; i++) {
            if (vertexs[i] == ch) {
                return i;
            }
        }
        return -1;
    }

    private EData[] getEdges() {
        int index = 0;
        EData[] edges = new EData[edgeNum];
        for (int i = 0; i < vertexs.length; i++) {
            for (int j = i + 1; j < vertexs.length; j++) {
                if (matrix[i][j] != INF) {
                    edges[index++] = new EData(vertexs[i], vertexs[j], matrix[i][j]);
                }
            }
        }
        return edges;
    }

    /**
     * 判断终点是否相同
     *
     * @param ends 记录各个顶点对应的终点是哪个 遍历中形成
     * @param i    传入顶点对应的下标
     * @return
     */
    private int getEnd(int[] ends, int i) {
        while (ends[i] != 0) {
            i = ends[i];
        }
        return i;
    }

    public void kruskal() {
        int index = 0;//最后结果数组索引
        int[] ends = new int[edgeNum];//保存顶点的终点
        EData[] rets = new EData[edgeNum];//保存最后结果
        EData[] edges = getEdges();//所有边的集合 12
        sortEdges(edges);
        for (int i= 0;i<edgeNum;i++){
            int p1 = getPosition(edges[i].start);
            int p2 = getPosition(edges[i].end);

            int m = getEnd(ends, p1);
            int n = getEnd(ends, p2);
            if (m != n){
                ends[m] = n;//设置 m 在最小生成树的终点
                rets[index++] = edges[i];//一条边确认
            }
        }
        for (int i = 0; i < index; i++) {
            System.out.println(rets[i]);
        }
    }
}

class EData {
    char start;
    char end;
    int weight;

    public EData(char start, char end, int weight) {
        this.start = start;
        this.end = end;
        this.weight = weight;
    }

    @Override
    public String toString() {
        return "EData[" +
                "<" + start +
                "," + end +
                "> = " + weight +
                ']';
    }
}