经典的贪心策略 Prim算法，Kruskal算法求最小生成树，dijkstra求最短路径
最小生成树算法 用到的并查集 在之前博客写，图都是下面的，最小生成树无向就行了
/**
* 文件名：GraphTest2.java
* 时间：2max14年11月17日下午6:2max:1max
* 作者：修维康
*/
package chapter9;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.Scanner;
import chapter8.DisjSets;//并查集
/**
* 类名：Edeg 说明：边
*/
class Edge {
public int v1;
public int v2;
public int dist;
public Edge(int v1, int v2, int dist) {
this.v1 = v1;
this.v2 = v2;
this.dist = dist;// 权值
}
}
class DistComparator implements Comparator<Edge> {
@Override
public int compare(Edge o1, Edge o2) {
// TODO Auto-generated method stub
if (o1.dist > o2.dist)
return 1;
else if (o1.dist < o2.dist)
return -1;
return 0;
}
}
public class GraphTest2 {
public static final int max = Integer.MAX_VALUE;
/**
* 方法名：dijkstra 说明：迪杰斯克拉算法，V代表源 g存储图的信息，dist[i]代表到v到i的权,prev[i]代表 顶点i的前一个顶点
*/
public static void Dijkstra(int v, int n, int[][] g, int[] dist, int[] prev) {
boolean[] s = new boolean[n + 1];
for (int i = 1; i <= n; i++) {
dist[i] = g[v][i];
s[i] = false;
if (dist[i] == max)
prev[i] = 0;
else
prev[i] = v;
}
s[v] = true;
dist[v] = 0;
// 从V-S中找到权值最小的边
for (int i = 1; i < n; i++) {
int temp = max;
int u = v;
for (int j = 1; j <= n; j++)
if (!s[j] && temp > dist[j]) {
temp = dist[j];
u = j;
}
s[u] = true;
// 更新
for (int j = 1; j <= n; j++) {
if (!s[j] && g[u][j] < max) {
int newDist = dist[u] + g[u][j];
if (newDist < dist[j]) {
dist[j] = newDist;
prev[j] = u;
}
}
}
}
}
/**
* 方法名：printPath 说明：打印最短路径
*/
public static void printPath(int[] prev, int v) {
System.out.print(v + " ");
while (prev[v] != 0) {
System.out.print(prev[v] + " ");
v = prev[v];
}
}
/**
* 方法名：Prim 说明：最小生成树 Prim算法 lowcost[i]为顶点i到S集合中任意一点 最小的权值 closest[i]为
* S中与i顶点相连权值最小的顶点
*/
public static void Prim(int[][] g, int n) {
boolean[] s = new boolean[n + 1];
int[] lowcost = new int[n + 1];
int[] closest = new int[n + 1];
s[1] = true;
lowcost[1] = 0;
for (int i = 2; i <= n; i++) {
lowcost[i] = g[1][i];
closest[i] = 1;
s[i] = false;
}
// 从V-S中找到与S中的顶点相连 且权值最小的点
for (int i = 1; i < n; i++) {
int min = max;
int j = 1;
for (int k = 2; k <= n; k++) {
if (!s[k] && lowcost[k] < min) {
min = lowcost[k];
j = k;
}
}
s[j] = true;
System.out.println(j + " " + closest[j]);
// 重新更新 lowcost lowcost[i]为顶点i到S集合中任意一点 最小的权值
for (int k = 2; k <= n; k++) {
if (!s[k] && g[j][k] < lowcost[k]) {
lowcost[k] = g[j][k];
closest[k] = j;
}
}
}
}
/**
* 方法名：Kruskal 说明：最小生成树 Kruskal算法
*/
public static void Kruskal(PriorityQueue<Edge> p, int n) {
DisjSets ds = new DisjSets(n + 1);// 并查集
Edge e;
int edgesAccepted = 0;
while (edgesAccepted < n - 1) {
e = p.poll();
int uset = ds.find(e.v1);
int vset = ds.find(e.v2);
if (uset != vset) {
edgesAccepted++;
System.out.println(e.v1 + " " + e.v2);
ds.union1(uset, vset);
}
}
}
/**
* 方法名：main 说明：测试
*/
public static void main(String[] args) {
// TODO Auto-generated method stub
int[][] g = new int[][] { { max, max, max, max, max, max, max, max },
{ max, max, 2, max, 1, max, max, max },
{ max, max, max, max, 3, 10, max, max },
{ max, 4, max, max, max, max, 5, max },
{ max, max, max, 2, max, 2, 18, 4 },
{ max, max, max, max, max, max, max, 6 },
{ max, max, max, max, max, max, max, max },
{ max, max, max, max, max, max, 1, max } };
// Graph graph = new Graph(g);
int[] dist = new int[8];
int[] prev = new int[8];
Scanner in = new Scanner(System.in);
System.out.println("请输入顶点号：");
int v = in.nextInt();
Dijkstra(v, 7, g, dist, prev);
System.out.println("请输入目的顶点：");
int n = in.nextInt();
System.out.println("顶点" + v + "到顶点" + n + "的权值为" + dist[n]);
printPath(prev, n);
int[][] g2 = new int[][] { { max, max, max, max, max, max, max, max },
{ max, max, 2, 4, 1, max, max, max },
{ max, 2, max, max, 3, 10, max, max },
{ max, 4, max, max, 2, max, 5, max },
{ max, 1, 3, 2, max, 7, 8, 4 },
{ max, max, 10, max, 7, max, max, 6 },
{ max, max, max, 5, 8, max, max, 1 },
{ max, max, max, max, 4, 6, 1, max } };
Prim(g2, 7);
PriorityQueue<Edge> p = new PriorityQueue<Edge>(12,
new DistComparator());
p.add(new Edge(1, 2, 2));
p.add(new Edge(1, 4, 1));
p.add(new Edge(2, 4, 3));
p.add(new Edge(1, 3, 4));
p.add(new Edge(3, 4, 2));
p.add(new Edge(4, 5, 7));
p.add(new Edge(2, 5, 10));
p.add(new Edge(3, 6, 5));
p.add(new Edge(4, 6, 8));
p.add(new Edge(6, 7, 1));
p.add(new Edge(4, 7, 4));
p.add(new Edge(5, 7, 6));
System.out.println("Kruskal算法：");
Kruskal(p, 7);
}
}
原文地址：http://blog.csdn.net/xiuweikang/article/details/41249601
