prim算法找最小生成树

先定义图类：

class MGraph {
	int verxs;// 表示图的节点个数
	char[] data;// 存放节点数据
	int[][] weight;// 存放边，就是我们的邻接矩阵

	public MGraph(int verxs) {
		this.verxs = verxs;
		data = new char[verxs];
		weight = new int[verxs][verxs];
	}
}

然后是创建最小生成树的类：

//创建最小生成树->村庄的图
class MinTree {
	/**
	 * 创建图的邻接矩阵
	 * @param graph  图对象
	 * @param verxs  图对应的顶点个数
	 * @param data   图的各个顶点的值
	 * @param weight 图的邻接矩阵
	 */
	public void createGraph(MGraph graph, int verxs, char[] data, int[][] weight) {
		int i, j;
		for (i = 0; i < verxs; i++) {// 顶点
			graph.data[i] = data[i];
			for (j = 0; j < verxs; j++) {
				graph.weight[i][j] = weight[i][j];
			}
		}
	}

	// 显示图的邻接矩阵
	public void showGraph(MGraph graph) {
		for (int[] link : graph.weight) {
			System.out.println(Arrays.toString(link));
		}
	}
	
	/**
	 * 编写prim算法，得到最小生成树
	 * @param graph 图
	 * @param v 表示从图的第几个顶点开始生成
	 */
	public void prim(MGraph graph, int v) {
		int[] visited = new int[graph.verxs];//标记节点是否被访问过
		visited[v] = 1;
		//用h1和h2记录两个顶点的下标
		int h1 = -1;
		int h2 = -1;
		int minWeight = 10000;
		for(int k = 1; k < graph.verxs; k++) {
			//确定每一次生成的子图和哪个节点的距离最近
			for(int i = 0; i < graph.verxs; i++) {
				for(int j = 0; j < graph.verxs; j++) {
					if(visited[i] == 1 && visited[j] == 0 && graph.weight[i][j] < minWeight) {
						minWeight = graph.weight[i][j];
						h1 = i;
						h2 = j;
					}
				}
			}
			//找到一条边是最小
			System.out.println("边<" + graph.data[h1] + "," + graph.data[h2] + "> 权值:" + minWeight);
			//将当前这个节点标为已经访问
			visited[h2] = 1;
			//重新设置minWeight为10000
			minWeight = 10000;
		}
	}
}

最后是主类：

public class PrimAlgorithm {
	public static void main(String[] args) {
		char[] data = new char[] {'A','B','C','D','E','F','G'};
		int verxs = data.length;
		int[][] weight = new int[][] {//10000表示两个点不连通
			{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);
	}
}