1-first you make 2D array has all shortest path between dirty tiles in addition to start position of robot by using BFS.

2-make dp[][] contain the element you stand on it and mask of elements refer to which dirty tiles became clean and which still dirty.

int num_of_dirty_tiles;

int solve(int stand,int mask){

if(mask==(1<<num_of_dirty_tile)-1) // mean that all dirty tiles changed to clean riles.

  return 0;

 if(dp[stand][mask]!=-1)
   return dp[stand][mask];

int a=MAX;

for(int i=0;i<num_of_dirty_tiles;i++){

   if((1<<i&mask==0))// it mean that the tile i still dirty

     a=Min(a,solve(i,mask|(1<<i))+shortPath[stand][i]);//it take the min 
     between paths from standing tile to any dirty tile .



 }

return dp[stand][mask]=a;

}

}

I hope to understand something from this algorithm .