最大团问题-分支界限法

1. 遍历所有点构造二叉树；

2. 广度遍历树，遍历过程中判断当前结点的点数据时，是否构成完全子图，如果不能则只将右结点加入队列，每次选取队列中完全子图最大的结点作为活结点，无子结点时到达叶子结点，记录为一个完全子图，优先队列法中第一个完全子图即为最优解。

package test;import java.util.*;/*** Created by saishangmingzhu on 2018/12/10.* 最大团问题*/
public class MaximumCliqueProblem {//图private int[][] pointIndex=new int[][]{{1,1,0,1,1},{1,1,1,0,1},{0,1,1,0,1},{1,0,0,1,1},{1,1,1,1,1}};public static void main(String[] arg){new MaximumCliqueProblem().branchAndBoundMethod();}/*** 分支界限法-优先队列式* 优先队列式求解时，到达第一个没有子结点的活结点时，即为最优解*/public void branchAndBoundMethod() {List<Point> pointList=new ArrayList<>();pointList.add(new Point("1",0));pointList.add(new Point("2",1));pointList.add(new Point("3",2));pointList.add(new Point("4",3));pointList.add(new Point("5",4));//【1】构建树Node root=new Node();createTree(pointList, root,0);//【2】广度遍历List<Node> currentLiveNodeList=new ArrayList<>();currentLiveNodeList.add(root);while (true) {//排序Node parent = currentLiveNodeList.get(0);if (parent.leftNode==null){//表示到了叶子结点，进行记录//点不算子图，所以要去除点集为1的叶子break;}List<Point> leftPointList = parent.leftNode.hasPointList;if (judge(leftPointList) != 0) {currentLiveNodeList.add(parent.leftNode);}//因为右结点是空，所以不需要判断//List<Point> rightPointList=parent.rightNode.hasPointList;currentLiveNodeList.add(parent.rightNode);currentLiveNodeList.remove(parent);Collections.sort(currentLiveNodeList, new Comparator<Node>() {@Overridepublic int compare(Node o1, Node o2) {return o2.hasPointList.size()-o1.hasPointList.size();}});}System.out.println("最大团");for (Point point:currentLiveNodeList.get(0).hasPointList){System.out.print(point.name+",");}}/*** 判断现有节点是否是完全子图 -1 表示不是* @param pointList* @return*/private int judge(List<Point> pointList){for (int i=0;i<pointList.size();i++){Point pointi=pointList.get(i);int indexi=pointi.index;for (int j=i+1;j<pointList.size();j++){Point pointj=pointList.get(j);int indexj=pointj.index;//使用[indexi][indexj]是为了说明问题，可以直接使用[i][j]if (pointIndex[indexi][indexj]!=1){return 0;}}}return 1;}private void createTree(List<Point> pointList, Node parent,int i) {if (i>=pointList.size()){return;}Node leftNode=new Node();leftNode.hasPointList.addAll(parent.hasPointList);leftNode.hasPointList.add(pointList.get(i));i++;createTree(pointList,leftNode,i);parent.leftNode=leftNode;Node rightNode=new Node();rightNode.hasPointList.addAll(parent.hasPointList);createTree(pointList,rightNode,i);parent.rightNode=rightNode;}class Point{private String name;private int index;public Point(String name,int index) {this.name = name;this.index = index;}}class Node{private Node leftNode;private Node rightNode;private List<Point> hasPointList=new ArrayList<>();}
}