数据结构01-最小生成树-Prim算法

import java.util.Arrays;

public class PrimAlgorithm {
	
	public static void main(String[] args) {
		char[] data = new char[] { 'A', 'B', 'C', 'D', 'E', 'F', 'G' };
		int verNum = data.length;
		int[][] weight = new int[][] { // 1024表示无边
				{ 1024, 5, 7, 1024, 1024, 1024, 2 },
				{ 5, 1024, 1024, 9, 1024, 1024, 3 },
				{ 7, 1024, 1024, 1024, 8, 1024, 1024 }, 
				{ 1024, 9, 1024, 1024, 1024, 4, 1024 },
				{ 1024, 1024, 8, 1024, 1024, 5, 4 },
				{ 1024, 1024, 1024, 4, 5, 1024, 6 },
				{ 2, 3, 1024, 1024, 4, 6, 1024 } };
		// 创建MGraph对象
		MGraph graph = new MGraph(verNum);
		// 创建MinTree对象
		MinTree minTree = new MinTree();
		minTree.creatGraph(graph, verNum, data, weight);
		minTree.showGraph(graph);
		// 测试prim算法
		System.out.println("-----从" + data[0] + "开始的最小生成树-----");
		minTree.prim(graph, 0);	
	}
}

//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 verNum 图的节点个数
	 * @param data   图的各个节点的值
	 * @param weight 图的邻接矩阵
	 */
	public void creatGraph(MGraph graph, int verNum, char[] data, int[][] weight) {
		for (int i = 0; i < verNum; i++) {// 顶点
			graph.data[i] = data[i];
			for (int j = 0; j < verNum; j++) {// 边
				graph.weight[i][j] = weight[i][j];
			}
		}
	}

	// 显式图的邻接矩阵
	public void showGraph(MGraph graph) {
		for (int i = 0; i < graph.verNum; i++) {
			System.out.print("    " + graph.data[i]);
		}
		System.out.println();
		int j = 0;
		for (int[] link : graph.weight) {
			System.out.println(graph.data[j++] + " " + Arrays.toString(link));
		}
	}

	// prim算法
	/**
	 * @param graph 图对象
	 * @param v     表示最小生成树的起始点
	 */
	public void prim(MGraph graph, int v) {
		// visted用于标记节点是否被访问过 默认初始值都为0表示所有节点都没有被访问过
		int[] visited = new int[graph.verNum];
		// 将起始点v标记为已经访问
		visited[v] = 1;
		// 用 indexBegin 和 indexEnd 记录两个顶点的下标
		int indexBegin = -1;
		int indexEnd = -1;
		int minWeight = 1024;
		for (int k = 0; k < graph.verNum-1; k++) {// 普利姆算法结束后，一共有graph.verNum-1条边，故k∈[0,graph.verNum-2]

			// 下面双重循环的作用寻找已经访问过的节点和为访问过的节点之间权值最小的未访问节点
			for (int i = 0; i < graph.verNum; i++) {// i节点表示访问过的节点
				for (int j = 0; j < graph.verNum; j++) {// j节点表示未被访问过的节点
					if (visited[i] == 1 && visited[j] == 0 && graph.weight[i][j] < minWeight) {
						minWeight = graph.weight[i][j];
						indexBegin = i;
						indexEnd = j;
					}
				}
			} // 此时已经找到
			System.out.println("边<" + graph.data[indexBegin] + "," + graph.data[indexEnd] + "> 权值：" + minWeight);
			//将信息存入minTreeEdage
			// 将新找到的节点标记为已访问
			visited[indexEnd] = 1;
			minWeight = 1024;// 重置minWeight用于找下一个待加入子图的节点
		}
	}
}

class MGraph {
	int verNum; // 表示图的节点个数
	char[] data;// 存放节点数据
	int[][] weight; // 邻接矩阵

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