1/2 (n-1)!             n>2

#include<stdio.h>
#include<conio.h>
#define ALL -1
#define MAXCITIES 10
 
enum BOOL{FALSE,TRUE};
lنودهای  پیمایش شده  اینجا علامتگذاری میشوند//long*visited;
long*min_circuit;//min inner circuit for given node as start node at position indexed 0
long*ham_circuit;//optimal circuit with length stored at position indexed 0
long min_circuit_length;//min circuit lenth for given start node
 
int n;//city count
long matrix[MAXCITIES][MAXCITIES];//nondirectional nXn symmetric matrix
//to store path distances as sourceXdestination
long INFI;// INFINITY value to be defined by user
 
// function resets minimum circuit for a given start node
//with setting its id at index 0 and setting furthr node ids to -1
void reset_min_circuit(int s_v_id)
{
                min_circuit[0]=s_v_id;
                for(int i=1;i<n;i++)               min_circuit[i]=-1;
}
 
// marks given node id with given flag
// if id==ALL it marks all nodes with given flag
void set_visited(int v_id,BOOL flag)
{
                if(v_id==ALL)        for(int i=0;i<n;i++)               visited[i]=flag;
                else                         visited[v_id]=flag;
}
 
// function sets hamiltonion circuit for a given path length
void SET_HAM_CKT(long pl)
{
                ham_circuit[0]=pl;
                for(int i=0;i<n;i++)       ham_circuit[i+1]=min_circuit[i];
                ham_circuit[n+1]=min_circuit[0];
}
 
//function sets a valid circuit by finiding min inner path for a given
//combination start vertex and next vertex to start vertex such that
// the 2nd vertex of circuits is always s_n_v and start and dest node is
//always s_v for all possible values of s_n_v, and then returns the
// valid circuit length for this combination
 
long get_valid_circuit(int s_v,int s_n_v)
{
                int next_v,min,v_count=1;
                long path_length=0;
                min_circuit[0]=s_v;
                min_circuit[1]=s_n_v;
                set_visited(s_n_v,TRUE);
                path_length+=matrix[s_v][s_n_v];
                for(int V=s_n_v;v_count<n-1;v_count++)
                {              min=INFI;
                                                for(int i=0;i<n;i++)
                                                                if(            matrix[V][i]<INFI && !visited[i]
                                                                                && matrix[V][i]<=min
                                                                  )
                                                                                min=matrix[V][next_v=i];
                                set_visited(next_v,TRUE);
                                V=min_circuit[v_count+1]=next_v;
                                path_length+=min;
                }
                path_length+=matrix[min_circuit[n-1]][s_v];
                return(path_length);
}
 
void main()
{
                clrscr();
                printf("Make sure that infinity value < sum of all path distances\nSet Infinity at (signed long):";
                scanf("%ld",&INFI);
                int pathcount,i,j,source,dest;
                long dist=0;
                long new_circuit_length=INFI;
                printf("Enter no. of cities(MAX:%d):",MAXCITIES);
                scanf("%d",&n);
                printf("Enter path count:";
                scanf("%d",&pathcount);
 
                printf("Enter paths:< source_id destination_id distance >\n ids varying from 0 to %d\n",n-1);
                //init all matrix distances to infinity
                for(i=0;i<n;i++)
                                for(j=0;j<n;j++)
                                                matrix[i][j]=INFI;
 
                //populate the matrix
                for(i=0;i<pathcount;i++)
                {
                                printf("[path %d]:",i);
                                scanf("%d %d %ld",&source,&dest,&dist);
                                if(source!=dest)
                                     matrix[source][dest]=matrix[dest][source]=dist;
                }
 
                visited=new long[n];
                min_circuit=new long[n];
                ham_circuit=new long[n+2];
                min_circuit_length=INFI;
                // algorithm
                //for each vertex, S_V as a staring node
                for(int S_V_id=0;S_V_id<n;S_V_id++)
                {       //for each and non start vertex as i
                                for(i=0;i<n;i++)
                                {       //set all to unvisited
                                                set_visited(ALL,FALSE);
                                                // set staring vertex as visited
                                                set_visited(S_V_id,TRUE);
                                                //reset/init minimum circuit
                                                reset_min_circuit(S_V_id);
                                                // obtain circuit for combination of S_V and i
                                                new_circuit_length=get_valid_circuit(S_V_id,i);
                                                // if newer length is less than the previously
                                                //calculated min then set it as min and set the
                                                //current circuit in hamiltonion circuit
                                                if(new_circuit_length<=min_circuit_length)
                                                                SET_HAM_CKT(min_circuit_length=new_circuit_length);
                                }
                }
// if any circuit found
if(min_circuit_length<INFI)
{
                printf("\n\nMinimum circuit length is: %ld\nCircuit is:\n",min_circuit_length);
                for(i=1;i<n+2;i++)               printf("<%ld> ",ham_circuit[i]);
}
else         printf(&q