Мой код Java: (абсолютно на основе рекурсивного метода)
алгоритм:
+ Начните с 1 точки, подключитесь к другой точке, которую он может видеть (чтобы сформировать путь).
+ удалить путь и рекурсивно найти новый путь в самой новой точке, пока все точки графа не соединятся.
+ удалить путь и вернуться к исходному графику, если не могу сформировать путь Гамильтона из новейшей точки
public class HamiltonPath {
public static void main(String[] args){
HamiltonPath obj = new HamiltonPath();
int[][]x = {{0,1,0,1,0}, //Represent the graphs in the adjacent matrix forms
{1,0,0,0,1},
{0,0,0,1,0},
{1,0,1,0,1},
{0,1,0,1,0}};
int[][]y = {{0,1,0,0,0,1},
{1,0,1,0,0,1},
{0,1,0,1,1,0},
{0,0,1,0,0,0},
{0,0,1,0,0,1},
{1,1,0,0,1,0}};
int[][]z = {{0,1,1,0,0,1},
{1,0,1,0,0,0},
{1,1,0,1,0,1},
{0,0,1,0,1,0},
{0,0,0,1,0,1},
{1,0,1,0,1,0}};
obj.allHamiltonPath(y); //list all Hamiltonian paths of graph
//obj.HamiltonPath(z,1); //list all Hamiltonian paths start at point 1
}
static int len;
static int[]path;
static int count = 0;
public void allHamiltonPath(int[][]x){ //List all possible Hamilton path in the graph
len = x.length;
path = new int[len];
int i;
for(i = 0;i<len;i++){ //Go through column(of matrix)
path[0]=i+1;
findHamiltonpath(x,0,i,0);
}
}
public void HamiltonPath(int[][]x, int start){ //List all possible Hamilton path with fixed starting point
len = x.length;
path = new int[len];
int i;
for(i = start-1;i<start;i++){ //Go through row(with given column)
path[0]=i+1;
findHamiltonpath(x,0,i,0);
}
}
private void findHamiltonpath(int[][]M,int x,int y,int l){
int i;
for(i=x;i<len;i++){ //Go through row
if(M[i][y]!=0){ //2 point connect
if(detect(path,i+1))// if detect a point that already in the path => duplicate
continue;
l++; //Increase path length due to 1 new point is connected
path[l]=i+1; //correspond to the array that start at 0, graph that start at point 1
if(l==len-1){//Except initial point already count =>success connect all point
count++;
if (count ==1)
System.out.println("Hamilton path of graph: ");
display(path);
l--;
continue;
}
M[i][y]=M[y][i]=0; //remove the path that has been get and
findHamiltonpath(M,0,i,l); //recursively start to find new path at new end point
l--; // reduce path length due to the failure to find new path
M[i][y] = M[y][i]=1; //and tranform back to the inital form of adjacent matrix(graph)
}
}path[l+1]=0; //disconnect two point correspond the failure to find the..
} //possible hamilton path at new point(ignore newest point try another one)
public void display(int[]x){
System.out.print(count+" : ");
for(int i:x){
System.out.print(i+" ");
}
System.out.println();
}
private boolean detect(int[]x,int target){ //Detect duplicate point in Halmilton path
boolean t=false;
for(int i:x){
if(i==target){
t = true;
break;
}
}
return t;
}
}