Hamiltonian 주기는 Hamiltonian Path의 마지막 정점에서 첫 번째 정점까지의 모서리(그래프에서)가 있는 것과 같은 Hamiltonian Path입니다. 무방향 그래프에서 그래프의 각 꼭짓점을 정확히 한 번만 방문하는 경로입니다.
기능 및 목적
Begin 1. function isSafe() is used to check for whether it is adjacent to the previously added vertex and already not added. 2. function hamiltonianCycle() solves the hamiltonian problem. 3. function hamCycle() uses hamiltonianCycle() to solve the hamiltonian problem. It returns false if there is no Hamiltonian Cycle possible, otherwise return true and prints the path. End
예시
#include <iostream>
#include <cstdio>
#include <cstdlib>
#define N 5
using namespace std;
void displaytheSolution(int path[]);
bool isSafe(int n, bool g[N][N], int path[], int pos)
{
if (g [path[pos-1]][n] == 0)
return false;
for (int i = 0; i < pos; i++)
if (path[i] == n)
return false;
return true;
}
bool hamiltonianCycle(bool g[N][N], int path[], int pos)
{
//If all vertices are included in Hamiltonian Cycle
if (pos == N)
{
if (g[ path[pos-1] ][ path[0] ] == 1)
return true;
else
return false;
}
for (int n = 1; n < N; n++)
{
if (isSafe(n, g, path, pos)) //Check if this vertex can be added to Hamiltonian Cycle
{
path[pos] = n;
//recur to construct rest of the path
if (hamiltonianCycle (g, path, pos+1) == true)
return true;
path[pos] = -1; //remove vertex if it doesn’t lead to the solution
}
}
return false;
}
bool hamCycle(bool g[N][N])
{
int *path = new int[N];
for (int i = 0; i < N; i++)
path[i] = -1;
//put vertex 0 as the first vertex in the path. If there is a Hamiltonian Cycle, then the path can be started from any point
//of the cycle as the graph is undirected
path[0] = 0;
if (hamiltonianCycle(g, path, 1) == false)
{
cout<<"\nCycle does not exist"<<endl;
return false;
}
displaytheSolution(path);
return true;
}
void displaytheSolution(int p[])
{
cout<<"Cycle Exists:";
cout<<" Following is one Hamiltonian Cycle \n"<<endl;
for (int i = 0; i < N; i++)
cout<<p[i]<<" ";
cout<< p[0]<<endl;
}
int main()
{
bool g[N][N] = {{0, 1, 0, 1, 1},
{0, 0, 1, 1, 0},
{0, 1, 0, 1, 1},
{1, 1, 1, 0, 1},
{0, 1, 1, 0, 0},
};
hamCycle(g);
return 0;
} 출력
Cycle Exists: Following is one Hamiltonian Cycle 0 4 1 2 3 0