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[Function add]
1.Add DFS way to find cycle int the graph. 2. Add conclusion.
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‎Algorithm(4th_Edition)/src/ca/mcmaster/chapter/four/graph/directed/DirectedCycle.java

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package ca.mcmaster.chapter.four.graph.directed;
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import java.io.File;
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import java.io.FileInputStream;
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import java.io.FileNotFoundException;
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import java.util.Stack;
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public class DirectedCycle {
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private final boolean[] marked;
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private final int[] edgeTo;
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private Stack<Integer> cycle = null; //有向环上的所有顶点
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private final boolean[] onStack; //递归调用的栈上的所有顶点
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public DirectedCycle(Digraph g){
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onStack = new boolean[g.V()];
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marked = new boolean[g.V()];
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edgeTo = new int[g.V()];
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int size = g.V();
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for(int v = 0; v < size; v++)
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if(!marked[v]) dfs(g, v);
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}
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private void dfs(Digraph g, int v){
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//在此次的遍历中，记录当前的位置可能在环上。如果结束了没有在环上则改回false
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onStack[v] = true;
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marked[v] = true;
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for(int w : g.adj(v)){
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if(this.hasCycle()) return;
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else if(!marked[w]){ //当前结点未被访问过，一定不是闭环，递归调用
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edgeTo[w] = v;
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dfs(g, w);
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}
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else if(onStack[w]){ //在此次的遍历中，当前点已经在环上，说明已经构成了cycle.v的下一个结点构成了闭环。
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//创建stack对象，并添加元素。
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cycle = new Stack<>();
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for(int x = v; x != w; x = edgeTo[x])
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cycle.push(x);
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cycle.push(w);
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cycle.push(v);
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}
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}
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onStack[v] = false;
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}
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public boolean hasCycle(){
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return cycle != null;
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}
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public Iterable<Integer> cycle(){
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return cycle;
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}
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public static void main(String[] args) throws FileNotFoundException {
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Digraph g = new DigraphImpl(new FileInputStream(new File("src/ca/mcmaster/chapter/four/graph/tinyDG.txt")));
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DirectedCycle cycle = new DirectedCycle(g);
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StringBuilder sb = new StringBuilder();
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for(int i : cycle.cycle()){
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sb.append(i + " ");
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}
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System.out.println(sb.toString());
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}
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}

‎Algorithm(4th_Edition)/src/ca/mcmaster/chapter/four/graph/tinyDAG.txt

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13
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2 3
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0 6
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0 1
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2 0
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11 12
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9 12
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9 10
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9 11
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3 5
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8 7
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5 4
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0 5
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6 4
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6 9
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7 6

‎DataStructrue/Graph/DirectedCycle.java

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package ca.mcmaster.chapter.four.graph.directed;
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import java.io.File;
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import java.io.FileInputStream;
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import java.io.FileNotFoundException;
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import java.util.Stack;
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public class DirectedCycle {
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private final boolean[] marked;
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private final int[] edgeTo;
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private Stack<Integer> cycle = null; //有向环上的所有顶点
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private final boolean[] onStack; //递归调用的栈上的所有顶点
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public DirectedCycle(Digraph g){
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onStack = new boolean[g.V()];
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marked = new boolean[g.V()];
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edgeTo = new int[g.V()];
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int size = g.V();
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for(int v = 0; v < size; v++)
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if(!marked[v]) dfs(g, v);
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}
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private void dfs(Digraph g, int v){
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//在此次的遍历中，记录当前的位置可能在环上。如果结束了没有在环上则改回false
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onStack[v] = true;
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marked[v] = true;
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for(int w : g.adj(v)){
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if(this.hasCycle()) return;
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else if(!marked[w]){ //当前结点未被访问过，一定不是闭环，递归调用
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edgeTo[w] = v;
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dfs(g, w);
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}
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else if(onStack[w]){ //在此次的遍历中，当前点已经在环上，说明已经构成了cycle.v的下一个结点构成了闭环。
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//创建stack对象，并添加元素。
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cycle = new Stack<>();
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for(int x = v; x != w; x = edgeTo[x])
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cycle.push(x);
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cycle.push(w);
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cycle.push(v);
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}
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}
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onStack[v] = false;
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}
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public boolean hasCycle(){
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return cycle != null;
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}
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public Iterable<Integer> cycle(){
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return cycle;
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}
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public static void main(String[] args) throws FileNotFoundException {
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Digraph g = new DigraphImpl(new FileInputStream(new File("src/ca/mcmaster/chapter/four/graph/tinyDG.txt")));
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DirectedCycle cycle = new DirectedCycle(g);
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StringBuilder sb = new StringBuilder();
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for(int i : cycle.cycle()){
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sb.append(i + " ");
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}
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System.out.println(sb.toString());
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}
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}

‎DataStructrue/Graph/DirectedGraph.md

+61-2
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@@ -257,7 +257,6 @@ public class BreadFirstPathDirectedGraph implements Path {
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public boolean hasPathTo(int v) {
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return marked[v];
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}
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@Override
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public Iterable<Integer> pathTo(int v) {
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Stack<Integer> path = new Stack<>();
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}
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```
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* 测试和DFS完全一致。
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* 测试和DFS完全一致。
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### 寻找有向环
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```Java
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public class DirectedCycle {
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private final boolean[] marked;
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private final int[] edgeTo;
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private Stack<Integer> cycle = null; //有向环上的所有顶点
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private final boolean[] onStack; //递归调用的栈上的所有顶点
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public DirectedCycle(Digraph g){
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onStack = new boolean[g.V()];
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marked = new boolean[g.V()];
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edgeTo = new int[g.V()];
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int size = g.V();
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for(int v = 0; v < size; v++)
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if(!marked[v]) dfs(g, v);
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}
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private void dfs(Digraph g, int v){
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//在此次的遍历中，记录当前的位置可能在环上。如果结束了没有在环上则改回false
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onStack[v] = true;
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marked[v] = true;
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for(int w : g.adj(v)){
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if(this.hasCycle()) return;
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else if(!marked[w]){ //当前结点未被访问过，一定不是闭环，递归调用
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edgeTo[w] = v;
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dfs(g, w);
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}
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else if(onStack[w]){ //在此次的遍历中，当前点已经在环上，说明已经构成了cycle.v的下一个结点构成了闭环。
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//创建stack对象，并添加元素。
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cycle = new Stack<>();
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for(int x = v; x != w; x = edgeTo[x])
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cycle.push(x);
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cycle.push(w);
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cycle.push(v);
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}
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}
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onStack[v] = false;
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}
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public boolean hasCycle(){
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return cycle != null;
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}
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public Iterable<Integer> cycle(){
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return cycle;
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}
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}
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```
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* 测试
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```Java
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public static void main(String[] args) throws FileNotFoundException {
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Digraph g = new DigraphImpl(new FileInputStream(new File("src/ca/mcmaster/chapter/four/graph/tinyDG.txt")));
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DirectedCycle cycle = new DirectedCycle(g);
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StringBuilder sb = new StringBuilder();
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for(int i : cycle.cycle()){
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sb.append(i + " ");
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}
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System.out.println(sb.toString());
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}
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```
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> 3 4 5 3

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