偶然看到一个Prim算法的非常好的动画演示，贴上链接【bilibili】https://www.bilibili.com/video/av47042691?from=search&seid=12957229882655641618
注意，图的最小生成树不一定只有一种
update：
之前的版本是结合我自己和up主的思路写的。今年复习，发现很难理解啊，于是严格按照up主的视频流程实现了一次
public class MinimumSpanningTree {
int[][] map;
public MinimumSpanningTree(int[][] map) {
this.map = map;
}
/**
* @param startNodeIndex 根节点下标
* @return 普里姆算法生成树，数组表示
*/ public int[] prim(int startNodeIndex) {
int[][] map = this.copyMap(this.map);
boolean[] selected = new boolean[map.length];
int[] minDist = new int[map.length];
int[] parent = new int[map.length];
// 初始化
for (int i = 0; i < selected.length; i++) {
selected[i] = false;
minDist[i] = Integer.MAX_VALUE;
parent[i] = -1;
} selected[startNodeIndex] = true;
parent[startNodeIndex] = Integer.MAX_VALUE;
/**
* 1. Update 更新所有与当前选中的顶点集相连的 minDist、parent * 2. Scan 扫描得 update 更新的顶点中（未选中的顶点），minDist 最小的定点 * 3. Add 将 Scan 中扫描到的点的 selected 更新 */ while (!this.isFinished(selected)) {
this.update(map, selected, minDist, parent);
int nodeIndex = this.scan(selected, minDist);
this.add(selected, nodeIndex);
}
return parent;
}
private void update(int[][] map, boolean[] selected, int[] minDist, int[] parent) {
for (int i = 0; i < selected.length; i++) {
// 遍历所有顶点
if (!selected[i]) {
// 找出未选入的节点下标i
int weight = Integer.MAX_VALUE;
for (int j = 0; j < selected.length; j++) {
if (selected[j]) {
// 找出已选入的节点下标j
if (map[i][j] < weight) {
// 如果当前选中的i、j边权，小于之前选中的
weight = map[i][j]; // 得到i、j边权
minDist[i] = weight; // 赋值
parent[i] = j;
} } } } } }
private int scan(boolean[] selected, int[] minDist) {
int minWeight = Integer.MAX_VALUE;
int index = -1;
for (int i = 0; i < minDist.length; i++) {
if (!selected[i] && minDist[i] < minWeight) {
index = i;
minWeight = minDist[i];
} } return index;
}
private void add(boolean[] selected, int nodeIndex) {
selected[nodeIndex] = true;
}
/**
* 判断是否所有顶点都被选中 * * @param selected
* @return
*/
private boolean isFinished(boolean[] selected) {
for (int i = 0; i < selected.length; i++) {
if (!selected[i]) {
return false;
} }
return true;
}
/**
* 复制新的地图 * * @param map 原地图
* @return 复制版地图
*/ private int[][] copyMap(int[][] map) {
int[][] newMap = new int[map.length][map[0].length];
System.arraycopy(map, 0, newMap, 0, map.length);
return newMap;
}
private void logBooleanArray(boolean[] arr) {
for (boolean value : arr) {
System.out.print(value + " ");
} System.out.println(" ");
}
private void logIntArray(int[] arr) {
for (int value : arr) {
System.out.print(value + " ");
} System.out.println(" ");
}
public static void main(String[] args) {
int max = Integer.MAX_VALUE;
int[][] map = {
{max, 4, max, max, max, max, max, 8},
{4, max, 8, max, max, max, max, 11, max},
{max, 8, max, 7, max, 4, max, max, 2},
{max, max, 7, max, 9, 14, max, max, max},
{max, max, max, 9, max, 10, max, max, max},
{max, max, 4, 14, 10, max, 2, max, max},
{max, max, max, max, max, 2, max, 1, 6},
{8, 11, max, max, max, max, 1, max, 7},
{max, max, 2, max, max, max, 6, 7, max}
};
MinimumSpanningTree minimumSpanningTree = new MinimumSpanningTree(map);
int[] res = minimumSpanningTree.prim(0);
for (int i = 0; i < res.length; i++) {
System.out.println(i + " ~ " + res[i]);
}
}}