Algorithms to find the number of Hamiltonian paths in a graph

Question

I\'m trying to solve a slightly modified version of the Hamiltonian Path problem. It is modified in that the start and end points are given to us and instead of determining

Answer 1

It can be solved using DP with bitmasking for values of n upto 20 or a few more i guess. Create a 2d dp table. dp[i][j] represents the answer of case that you are on ith vertex and j stores the information about visited vertices.Here's a C++ code.

Macros used:

#define    oncnt    __builtin_popcount
typedef    vector   vi;

Outside Main:

vi ad[21];
 int n,m;

 int dp[20][(1<<19)+1];

int sol(int i,int mask)
{
    //cout<

Inside Main:

cin>>n>>m;

for(int i=0;i<=n-1;i++)
 {
    for(int j=0;j<=(1<<(n-1));j++)
    dp[i][j]=-1;
 }


int a,b;
for(int i=1;i<=m;i++)
{
    cin>>a>>b;
    a--;
    b--;
    ad[a].pb(b);
}


 cout<