图的反馈顶点集是一组顶点，其移除后使图没有环。下面的图成为有向无环图。
例子：
Input:
Enter the number of vertices:
4
Enter the number of edges:
5
Enter the graph:
1 2
2 3
3 4
4 1
1 3
Output:
The Graph is:
1-> 2-> 3
2-> 3
3-> 4
4-> 1
The set of edges in FeedBack arc set: 2 - 3
4 - 1
Input:
Enter the number of vertices:
5
Enter the number of edges:
5
Enter the graph:
1 2
2 4
5 3
5 1
4 3.
Output:
The Graph is:
1-> 2
2-> 4
4-> 3
5-> 3-> 1
The set of edges in FeedBack arc set: None 方法：
- 我们将声明所有需要的变量，如计数、边、开始、结束和顶点
- 现在我们将调用图形函数：我们将获取并将值存储在相邻的列表中，该列表将被声明为类的变量。
- 然后保持while条件，我们将在图中获取构造函数的所有起点和终点的输入。
- 现在调用 set edge函数：我们检查相邻列表是否为空，如果不是，我们将在其中存储它的值。
- 然后我们调用 printGraph()函数——这个方法基本上会打印图形，其中我们迭代循环并打印元素，并将其存储在列表中
- 然后我们调用类的对象并调用检查函数——每个迭代器检查我们是否只取了一次值 如果该值重复，我们将其删除
- 然后我们设置反馈顶点并调用函数- 我们现在将检查我们是否已经访问了所有节点，如果我们已经访问了它，我们将对其进行计数，如果我们没有我们将它保持等于 1。现在使用所有这些我们会找到可以删除的节点。
代码：
Java
// Java Program to Find a Good Feedback Vertex Set in a
// Graph
import java.util.HashMap;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
// Let us declare a class
class Edge
{
// We have declared a Map with Integer as its parameters
// Named adjacentList
private Map > adjacentList;
// Now lets us declare a function called "Graph"
public Edge(int vertices)
{
// Now taking the new List as a HashMap
adjacentList
= new HashMap >();
// Iterating i from 1 till vertices
for (int i = 1; i <= vertices; i++) {
// Adding them to a new LinkedList
adjacentList.put(i, new LinkedList());
}
}
// We are now declaring a class edge
// It has two parameters start and end
public void set_Edge(int end, int start)
{
// We will write the condition for checking
// If the the vertices are empty
if (end > adjacentList.size()
|| start > adjacentList.size())
System.out.println("There are no vertices");
// Now if the input isn't zero
// We will add them to a new list
List fls = adjacentList.get(start);
fls.add(end);
}
// We created a list function called get edge
// Help us to return the edges of a Graph
public List get_Edge(int end)
{
// Returning the edges back
return adjacentList.get(end);
}
// Now let us check
public Edge check()
{
// Now let us keep the count as 0
Integer count = 0;
// Let us iterator for easy function
Iterator iterator
= this.adjacentList.keySet().iterator();
// Let us take a size variable of adjacent List
Integer size = this.adjacentList.size() - 1;
// Iterating it till the end of the loop
while (iterator.hasNext()) {
// Now taking the variable which is an iterator
Integer i = iterator.next();
// Declaring a new list adjlist
List adjList
= this.adjacentList.get(i);
// checking for equal size we would return the
// same
if (count == size) {
return this;
}
// Now keeping the condition adjList==0
if (adjList.size() == 0) {
// Every time we run the if
// we increase the count
count++;
// Now taking an iterator Right
Iterator iteratorR
= this.adjacentList.keySet().iterator();
// Again iterating completely over the new
// Iterator
while (iteratorR.hasNext()) {
// Having the new R , help us to iterate
// the new Iterator
Integer R = iteratorR.next();
// New List is taken
List lit
= this.adjacentList.get(R);
// This if condition will help not to
// have
// Any duplicate values inside the new
// List
if (lit.contains(i)) {
// If we have one we would remove it
lit.remove(i);
}
}
// The below line would help us to remove
// the values
// Of the adjacent List as we move on to
// make the vertices
// The other values are simultaneously
// removed.
this.adjacentList.remove(i);
iterator
= this.adjacentList.keySet().iterator();
}
}
return this;
}
// This function helps us to print a graph
public void printGraph()
{
System.out.println("The Graph is:");
// Now let us taken an iterator and try to print it
// This iterator contains the values of the new
// graph
Iterator iterator
= this.adjacentList.keySet().iterator();
// Now iterating the values
while (iterator.hasNext())
{
// taking the variable i to be the next Iterator
Integer i = iterator.next();
// Taking a list which will help us have the
// side edges.
List edgeList = this.get_Edge(i);
// Now checking the edge list if it is not zero
if (edgeList.size() != 0)
{
// print them out
System.out.print(i);
// now iterating it till edgelist
for (int j = 0; j < edgeList.size(); j++)
{
// Now printing the graph in its pattern
System.out.print("-> "
+ edgeList.get(j));
}
System.out.println();
}
}
}
// Closing the function
// Now finding the FeedbackArc set
public boolean getFeedbackArcSet(int vertices)
{
// Taking boolean flag false
boolean flag = false;
// Now taking visited array
// This array length is vertices+1
int[] visited = new int[vertices + 1];
// This iterator has values of adjacent list
Iterator iterator
= this.adjacentList.keySet().iterator();
// Now let us see the feedback arc
System.out.print(
"The set of edges in FeedBack arc set: ");
// Now it has iterator which is next
while (iterator.hasNext())
{
// Now taking i which will be iterating next
Integer i = iterator.next();
// Now taking a list of values adjacent list
List list = this.adjacentList.get(i);
// Visited array to be after i
visited[i] = 1;
// Now taking if the list size not equal to 0
if (list.size() != 0)
{
// We iterate till list sie
for (int j = 0; j < list.size(); j++)
{
// If we have visited the list
// e will flag it to be true
if (visited[list.get(j)] == 1)
{
flag = true;
// Now taking the output of feedback
// arc
System.out.println(i + " - "
+ list.get(j));
}
else
{
// Now if we dint visit
// We will be iterating it to 1
visited[list.get(j)] = 1;
}
}
}
}
// Return the flag
return flag;
}
}
// Now let us declare the class GFG
class GFG {
public static void main(String[] args)
{
// Now let us declare and initialize all the
// variables
int vertices = 4, e = 5, count = 1;
int[] start = { 1, 2, 3, 4, 1 };
int[] end = { 2, 3, 4, 1, 3 };
// Now let us see the object of the class
Edge ist;
// Now let us try the exception.
try
{
// printing both the values
System.out.println("Number of vertices: "
+ vertices);
System.out.println("Number of edges: " + e);
// Now calling the function
ist = new Edge(vertices);
// calling the function by iterating the loop
for (int i = 0; i < e; i++)
{
// Now calling the function set_edge
ist.set_Edge(end[i], start[i]);
}
// Now we are calling the print Graph Function
ist.printGraph();
// Now we will call the object of class
// and then we called the function check
Edge modified = ist.check();
// If we dont get the flag to be true
// We can print the output to be None or empty
if (modified.getFeedbackArcSet(vertices)
== false)
{
System.out.println("None");
}
}
// Try for catch
// We print empty nodes
catch (Exception E)
{
System.out.println("Empty Nodes");
}
}
} 输出
Number of vertices: 4
Number of edges: 5
The Graph is:
1-> 2-> 3
2-> 3
3-> 4
4-> 1
The set of edges in FeedBack arc set: 2 - 3
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