package Prim;
 
import java.util.Arrays;
 
public class PrimAlgorithm {
    public static void main(String[] args) {
        //測(cè)試看看圖是否創(chuàng)建ok
        char[] data = new char[]{'A', 'B', 'C', 'D', 'E', 'F', 'G'};
        int verxs = data.length;
        //鄰接矩陣的關(guān)系使用二維數(shù)組表示,10000這個(gè)大數(shù)，表示兩個(gè)點(diǎn)不聯(lián)通
        int[][] weight = new int[][]{
                {10000, 5, 7, 10000, 10000, 10000, 2},
                {5, 10000, 10000, 9, 10000, 10000, 3},
                {7, 10000, 10000, 10000, 8, 10000, 10000},
                {10000, 9, 10000, 10000, 10000, 4, 10000},
                {10000, 10000, 8, 10000, 10000, 5, 4},
                {10000, 10000, 10000, 4, 5, 10000, 6},
                {2, 3, 10000, 10000, 4, 6, 10000},};
        MGraph mGraph = new MGraph(verxs);
        MinTree minTree = new MinTree();
        minTree.createGraph(mGraph, verxs, data, weight);
        minTree.showGraph(mGraph);
        minTree.Prim(mGraph, 0);
    }
}
 
class MinTree {
    /**
     * 創(chuàng)造圖
     * @param graph  圖對(duì)象
     * @param verxs  圖節(jié)點(diǎn)個(gè)數(shù)
     * @param data   圖每個(gè)頂點(diǎn)的數(shù)據(jù)值
     * @param weight 圖的邊（鄰接矩陣）
     */
    public void createGraph(MGraph graph, int verxs, char[] data, int[][] weight) {
        int i, j;
        for (i = 0; i < verxs; i++) {
            graph.data[i] = data[i];
            for (j = 0; j < verxs; j++) {
                graph.weight[i][j] = weight[i][j];
            }
        }
    }
 
    // 顯示圖的鄰接矩陣
    public void showGraph(MGraph graph) {
        for (int[] link : graph.weight) {
            System.out.println(Arrays.toString(link));
        }
    }
 
    /**
     * 編寫(xiě)prim算法
     *
     * @param graph 圖對(duì)象
     * @param v     從哪個(gè)節(jié)點(diǎn)開(kāi)始生成最小生成樹(shù)
     */
    public void Prim(MGraph graph, int v) {
        //定義一個(gè)數(shù)組，判斷節(jié)點(diǎn)是不是被訪問(wèn)過(guò)了
        int[] visited = new int[graph.verxs];
        //v這個(gè)點(diǎn)已經(jīng)被訪問(wèn)了，從這個(gè)點(diǎn)開(kāi)始訪問(wèn)
        visited[v] = 1;
        //找到節(jié)點(diǎn)下標(biāo)
        int h1 = -1;
        int h2 = -1;
        int minWeight = 10000;//定義初始值為最大值，只要出現(xiàn)小的就會(huì)替換
        int sum = 0;
        // 從1開(kāi)始循環(huán)，相當(dāng)于就是生成graph.verx - 1條邊
        for (int k = 1; k < graph.verxs; k++) {
 
            for (int i = 0; i < graph.verxs; i++) {//遍歷已經(jīng)訪問(wèn)過(guò)的點(diǎn)
                if (visited[i] == 1){
                    for (int j = 0; j < graph.verxs; j++) {//遍歷沒(méi)有訪問(wèn)過(guò)的點(diǎn)
                        //在未訪問(wèn)點(diǎn)中尋找所有與訪問(wèn)過(guò)的點(diǎn)相連的邊中權(quán)值最小值
                        if (visited[i] == 1 && visited[j] == 0 && graph.weight[i][j] < minWeight) {
                            minWeight = graph.weight[i][j];
                            h1 = i;
                            h2 = j;
                        }
                    }
                }
            }
            sum += minWeight; // 求最小生成熟的總權(quán)值
            //此時(shí)已經(jīng)找到一條邊是最小了
            System.out.println("邊<" + graph.data[h1] + "," + graph.data[h2] + "> 權(quán)值:" + minWeight);
            //然后標(biāo)記點(diǎn)
            visited[h2] = 1;
            //將權(quán)值重新變成最大值
            minWeight = 10000;
        }
        System.out.println("最小生成樹(shù)的權(quán)值是:" + sum);
 
    }
}
 
// 圖
class MGraph {
    int verxs; // 表示圖節(jié)點(diǎn)個(gè)數(shù)
    char[] data; // 表示節(jié)點(diǎn)數(shù)據(jù)
    int[][] weight; // 表示邊
 
    public MGraph(int verxs) {
        this.verxs = verxs;
        data = new char[verxs];
        weight = new int[verxs][verxs];
    }
}

package Kruskal;
 
import java.util.Arrays;
 
public class KruskalCase {
 
    private int edgeNum; //邊的個(gè)數(shù)
    private char[] vertexs; //頂點(diǎn)數(shù)組
    private int[][] matrix; //鄰接矩陣
    //使用 INF 表示兩個(gè)頂點(diǎn)不能連通
    private static final int INF = Integer.MAX_VALUE;
 
    public static void main(String[] args) {
        char[] vertexs = {'A', 'B', 'C', 'D', 'E', 'F', 'G'};
        //克魯斯卡爾算法的鄰接矩陣
        int matrix[][] = {
                /*A*//*B*//*C*//*D*//*E*//*F*//*G*/
                /*A*/ {0, 12, INF, INF, INF, 16, 14},
                /*B*/ {12, 0, 10, INF, INF, 7, INF},
                /*C*/ {INF, 10, 0, 3, 5, 6, INF},
                /*D*/ {INF, INF, 3, 0, 4, INF, INF},
                /*E*/ {INF, INF, 5, 4, 0, 2, 8},
                /*F*/ {16, 7, 6, INF, 2, 0, 9},
                /*G*/ {14, INF, INF, INF, 8, 9, 0}};
        //大家可以在去測(cè)試其它的鄰接矩陣，結(jié)果都可以得到最小生成樹(shù).
 
        //創(chuàng)建KruskalCase 對(duì)象實(shí)例
        KruskalCase kruskalCase = new KruskalCase(vertexs, matrix);
        //輸出構(gòu)建的
        kruskalCase.print();
        kruskalCase.kruskal();
 
    }
 
    //構(gòu)造器
    public KruskalCase(char[] vertexs, int[][] matrix) {
        //初始化頂點(diǎn)數(shù)和邊的個(gè)數(shù)
        int vlen = vertexs.length;
 
        //初始化頂點(diǎn), 復(fù)制拷貝的方式
        this.vertexs = new char[vlen];
        for (int i = 0; i < vertexs.length; i++) {
            this.vertexs[i] = vertexs[i];
        }
 
        //初始化邊, 使用的是復(fù)制拷貝的方式
        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];
            }
        }
        //統(tǒng)計(jì)邊的條數(shù)
        for (int i = 0; i < vlen; i++) {
            for (int j = i + 1; j < vlen; j++) {
                if (this.matrix[i][j] != INF) {
                    edgeNum++;
                }
            }
        }
 
    }
 
    public void kruskal() {
        int index = 0; //表示最后結(jié)果數(shù)組的索引
        int[] ends = new int[edgeNum]; //用于保存"已有最小生成樹(shù)" 中的每個(gè)頂點(diǎn)在最小生成樹(shù)中的終點(diǎn)
        //創(chuàng)建結(jié)果數(shù)組, 保存最后的最小生成樹(shù)
        EData[] rets = new EData[edgeNum];
 
        //獲取圖中 所有的邊的集合 ， 一共有12邊
        EData[] edges = getEdges();
        System.out.println("圖的邊的集合=" + Arrays.toString(edges) + " 共" + edges.length); //12
 
        //按照邊的權(quán)值大小進(jìn)行排序(從小到大)
        sortEdges(edges);
 
        //遍歷edges 數(shù)組，將邊添加到最小生成樹(shù)中時(shí)，判斷是準(zhǔn)備加入的邊否形成了回路，如果沒(méi)有，就加入 rets, 否則不能加入
        for (int i = 0; i < edgeNum; i++) {
            //獲取到第i條邊的第一個(gè)頂點(diǎn)(起點(diǎn))
            int p1 = getPosition(edges[i].start); //p1=4
            //獲取到第i條邊的第2個(gè)頂點(diǎn)
            int p2 = getPosition(edges[i].end); //p2 = 5
 
            //獲取p1這個(gè)頂點(diǎn)在已有最小生成樹(shù)中的終點(diǎn)
            int m = getEnd(ends, p1); //m = 4
            //獲取p2這個(gè)頂點(diǎn)在已有最小生成樹(shù)中的終點(diǎn)
            int n = getEnd(ends, p2); // n = 5
            //是否構(gòu)成回路
            if (m != n) { //沒(méi)有構(gòu)成回路
                ends[m] = n; // 設(shè)置m 在"已有最小生成樹(shù)"中的終點(diǎn) <E,F> [0,0,0,0,5,0,0,0,0,0,0,0]
                rets[index++] = edges[i]; //有一條邊加入到rets數(shù)組
            }
        }
        //<E,F> <C,D> <D,E> <B,F> <E,G> <A,B>。
        //統(tǒng)計(jì)并打印 "最小生成樹(shù)", 輸出  rets
        System.out.println("最小生成樹(shù)為");
        for (int i = 0; i < index; i++) {
            System.out.println(rets[i]);
        }
 
 
    }
 
    //打印鄰接矩陣
    public void print() {
        System.out.println("鄰接矩陣為: \n");
        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();//換行
        }
    }
 
    /**
     * 功能：對(duì)邊進(jìn)行排序處理, 冒泡排序
     *
     * @param edges 邊的集合
     */
    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) {//交換
                    EData tmp = edges[j];
                    edges[j] = edges[j + 1];
                    edges[j + 1] = tmp;
                }
            }
        }
    }
 
    /**
     * @param ch 頂點(diǎn)的值，比如'A','B'
     * @return 返回ch頂點(diǎn)對(duì)應(yīng)的下標(biāo)，如果找不到，返回-1
     */
    private int getPosition(char ch) {
        for (int i = 0; i < vertexs.length; i++) {
            if (vertexs[i] == ch) {//找到
                return i;
            }
        }
        //找不到,返回-1
        return -1;
    }
 
    /**
     * 功能: 獲取圖中邊，放到EData[] 數(shù)組中，后面我們需要遍歷該數(shù)組
     * 是通過(guò)matrix 鄰接矩陣來(lái)獲取
     * EData[] 形式 [['A','B', 12], ['B','F',7], .....]
     *
     * @return
     */
    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;
    }
 
    /**
     * 功能: 獲取下標(biāo)為i的頂點(diǎn)的終點(diǎn)(), 用于后面判斷兩個(gè)頂點(diǎn)的終點(diǎn)是否相同
     *
     * @param ends ： 數(shù)組就是記錄了各個(gè)頂點(diǎn)對(duì)應(yīng)的終點(diǎn)是哪個(gè),ends 數(shù)組是在遍歷過(guò)程中，逐步形成
     * @param i    : 表示傳入的頂點(diǎn)對(duì)應(yīng)的下標(biāo)
     * @return 返回的就是 下標(biāo)為i的這個(gè)頂點(diǎn)對(duì)應(yīng)的終點(diǎn)的下標(biāo), 一會(huì)回頭還有來(lái)理解
     */
    private int getEnd(int[] ends, int i) { // i = 4 [0,0,0,0,5,0,0,0,0,0,0,0]
        while (ends[i] != 0) {
            i = ends[i];
        }
        return i;
    }
 
}
 
//創(chuàng)建一個(gè)類EData ，它的對(duì)象實(shí)例就表示一條邊
class EData {
    char start; //邊的一個(gè)點(diǎn)
    char end; //邊的另外一個(gè)點(diǎn)
    int weight; //邊的權(quán)值
 
    //構(gòu)造器
    public EData(char start, char end, int weight) {
        this.start = start;
        this.end = end;
        this.weight = weight;
    }
 
    //重寫(xiě)toString, 便于輸出邊信息
    @Override
    public String toString() {
        return "EData [<" + start + ", " + end + ">= " + weight + "]";
    }
 
 
}