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个人认为此算法遍历顺序的决定条件:
1.确定第一个顶点
2.下一个顶点可到(小于正无穷)
3.取可到顶点中最小权值的一个
代码中的图
最小生成树:99
代码(参考其他文章):
public class MinSpanTree { /** 邻接矩阵*/ int[][] matrix; /** 表示正无穷*/ int MAX_WEIGHT = Integer.MAX_VALUE; /** 顶点个数*/ int size; /** * 普里姆算法实现最小生成树:先初始化拿到第一个顶点相关联的权值元素放到数组中-》找到其中权值最小的顶点下标-》再根据该下标,将该下标顶点相关联的权值加入到数组中-》循环遍历处理 */ public void prim() { /**存放当前到全部顶点最小权值的数组,如果已经遍历过的顶点权值为0,无法到达的为正无穷*/ int[] tempWeight = new int[size]; /**当前到下一个最小权值顶点的最小权值*/ int minWeight; /**当前到下一个最小权值的顶点*/ int minId; /**权值总和*/ int sum = 0; //第一个顶点时,到其他顶点的权值即为邻接矩阵的第一行 for (int i = 0; i < size; i++) { tempWeight[i] = matrix[0][i]; } System.out.println("从顶点v0开始查找"); for (int i = 1; i < size; i++) { // 每次循环找出当前到下一个最小权值的顶点极其最小权值 minWeight = MAX_WEIGHT; minId = 0; for (int j = 1; j < size; j++) { //权值为0的顶点已经遍历过,不再计入 if (tempWeight[j] > 0 && tempWeight[j] < minWeight) { minWeight = tempWeight[j]; minId = j; } } // 找到目标顶点minId,他的权值为minweight。 System.out.println("找到顶点:v" + minId + " 权值为:" + minWeight); sum += minWeight; // 算法核心所在:将目标顶点到各个顶点的权值与当前tempWeight数组中的权值做比较,如果前者比后者到某个顶点的权值更小,将前者到这个顶点的权值更新入后者。 tempWeight[minId] = 0; for (int j = 1; j < size; j++) { if (tempWeight[j] != 0 && matrix[minId][j] < tempWeight[j]) { tempWeight[j] = matrix[minId][j]; } } } System.out.println("最小权值总和为:" + sum); } private void createGraph(int index) { size = index; matrix = new int[index][index]; int[] v0 = { 0, 10, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 11, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT }; int[] v1 = { 10, 0, 18, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 16, MAX_WEIGHT, 12 }; int[] v2 = { MAX_WEIGHT, 18, 0, 22, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 8 }; int[] v3 = { MAX_WEIGHT, MAX_WEIGHT, 22, 0, 20, MAX_WEIGHT, MAX_WEIGHT, 16, 21 }; int[] v4 = { MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 20, 0, 26, MAX_WEIGHT, 7, MAX_WEIGHT }; int[] v5 = { 11, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 26, 0, 17, MAX_WEIGHT, MAX_WEIGHT }; int[] v6 = { MAX_WEIGHT, 16, MAX_WEIGHT, 24, MAX_WEIGHT, 17, 0, 19, MAX_WEIGHT }; int[] v7 = { MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 16, 7, MAX_WEIGHT, 19, 0, MAX_WEIGHT }; int[] v8 = { MAX_WEIGHT, 12, 8, 21, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 0 }; matrix[0] = v0; matrix[1] = v1; matrix[2] = v2; matrix[3] = v3; matrix[4] = v4; matrix[5] = v5; matrix[6] = v6; matrix[7] = v7; matrix[8] = v8; } public static void main(String[] args) { MinSpanTree graph = new MinSpanTree(); graph.createGraph(9); graph.prim(); }}