关键路径

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import java.util.*;

/**
 * 关键路径：路径长度最长的路径叫做关键路径。
 * 关键活动：活动ai的最早和最迟开始时间相同的活动叫做关键活动。
 * （1）输入e条弧<j,k>,建立AOE-网的存储结构
 * （2）从源点v0出发，令ve[0]=0,按拓扑有序求其余各顶点的最早发生时间ve[i](1<= i <=n-1)>。如果得到的拓扑有序序列中顶点个数小于王忠顶点数n，
 * 说明网中存在环，不能求关键路径，算法终止；否则执行步骤（3）。
 * （3）从汇点vn出发，vl[n-1] = ve[n-1],按逆拓扑有序求其余各顶点的最迟发生时间vl[i](n-2>= i >=2)
 * （4）根据各顶点的ve和vl值，求每条弧s的最早开始时间e(s)和最迟开始时间l(s),若某条弧满足条件e(s)=l(s),则为关键活动。
 */

public class TopologicalTest {
    private static final int V_COUNT = 6;
    public static void main(String[] args) {
        //初始化节点
        Topological topological1 = new Topological("C1", 0, new ArrayList<Topological>());
        Topological topological2 = new Topological("C2", 1, new ArrayList<Topological>());
        Topological topological3 = new Topological("C3", 1, new ArrayList<Topological>());
        Topological topological4 = new Topological("C4", 2, new ArrayList<Topological>());
        Topological topological5 = new Topological("C5", 1, new ArrayList<Topological>());
        Topological topological6 = new Topological("C6", 3, new ArrayList<Topological>());

        //将节点添加后驱
        List<Topological> list = topological1.getTopologicals();
        list.add(topological2);
        list.add(topological3);
        topological1.setTopologicals(list);

        list = topological2.getTopologicals();
        list.add(topological4);
        list.add(topological5);
        topological2.setTopologicals(list);

        list = topological3.getTopologicals();
        list.add(topological4);
        list.add(topological6);
        topological3.setTopologicals(list);

        list = topological4.getTopologicals();
        list.add(topological6);
        topological4.setTopologicals(list);

        list = topological5.getTopologicals();
        list.add(topological6);
        topological5.setTopologicals(list);

        //将图中的节点放入列表
        List<Topological> topologicals = new ArrayList<Topological>();
        topologicals.add(topological1);
        topologicals.add(topological2);
        topologicals.add(topological3);
        topologicals.add(topological4);
        topologicals.add(topological5);
        topologicals.add(topological6);

        //定义一个列表来存放入度为零的节点
        List<Topological> topologicalListForReturn = new ArrayList<Topological>();
        int i = 0;
        while(i++ <= V_COUNT) {
            for(Topological each : topologicals) {
                //判断一下是否已经在入度为0的列表中
                //如果是，则返回，判断下一个
                if(topologicalListForReturn.contains(each)) {
                    continue;
                }

                if(each.getIndegree() == 0) {
                    for(Topological topological : each.getTopologicals()) {
                        topological.setIndegree(topological.getIndegree() - 1);
                    }
                    topologicalListForReturn.add(each);
                    break;
                }
            }
        }

        //如果入度为0的节点数少于图总节点数，则存在环
        if(topologicalListForReturn.size() < topologicals.size()) {
            System.out.println("此图存在环");
            System.exit(0);
        }

        //输出拓扑排序序列
        for (Topological each : topologicalListForReturn) {
            System.out.print(each.getName() + " ");
        }
        System.out.println();

        //初始化二维数组
        int p[][] = {{0,3,2,0,0,0},{0,0,0,2,3,0},{0,0,0,4,0,3},{0,0,0,0,0,2},{0,0,0,0,0,1},{0,0,0,0,0,0}};



        //最早和最晚发生时间
        int[] ve = new int[V_COUNT];
        int[] vl = new int[V_COUNT];
        //初始化最早发生时间
        for(int j = 0; j < V_COUNT; j++) {
            ve[j] = 0;
        }
        //初始化最晚发生时间
        for(int j = 0; j < V_COUNT; j++) {
            vl[j] = Integer.MAX_VALUE;
        }

        //开始给每个节点的最早发生时间赋值
        for(int j = 0; j < V_COUNT; j++) {
            for(int k = j +1; k < V_COUNT; k++) {
                if(p[j][k] != 0 && ve[k] < ve[j] + p[j][k]) {
                    ve[k] = ve[j] + p[j][k];
                }
            }
        }

        //开始给每个节点的最晚发生时间赋值
        vl[V_COUNT -1] = ve[V_COUNT -1];
        for(int j = V_COUNT - 1; j > 0; j--) {
            for(int k = j - 1; k >= 0; k--) {
                if(p[k][j] != 0 && vl[k] > vl[j] - p[k][j]) {
                    vl[k] = vl[j] - p[k][j];
                }
            }
        }

        System.out.print("从c1-c6的最早开始时间为：");
        for(int j = 0; j < V_COUNT; j++) {
            System.out.print(ve[j] + " ");
        }
        System.out.println();

        System.out.print("从c1-c6的最晚开始时间为：");
        for(int j = 0; j < V_COUNT; j++) {
            System.out.print(vl[j] + " ");
        }
        System.out.println();

        //求关键路径
        System.out.print("关键路径为：");
        for(int j = 0; j < V_COUNT; j++) {
            if(ve[j] == vl[j]) {
                System.out.println(topologicals.get(j).getName() + " ");
            }
        }
    }
}
问题：这里的拓扑有序序列感觉没怎么用，估计是还没有理解透彻，这里的最早和最晚开始时间都是基于拓扑有序序列？

关键路径

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原文地址：http://www.cnblogs.com/mucheng/p/5766059.html