class Solution(object):
    def calcEquation(self, equations, values, queries):
        """
        :type equations: List[List[str]]
        :type values: List[float]
        :type queries: List[List[str]]
        :rtype: List[float]
        """
        #Floyed-Warshall, find all shortest path in a graph
        #dynamic programming 
        #default d[i][j]=inf, if d[i][k]+d[k][j]<d[i][j], replace d[i][j] with smaller value
        #loop till all d[i][j] is smallest possible, or in the case of this problem, when all reachable point has been given value, none reachable points are left blank. 
        d=collections.defaultdict(dict)
        for (numerator,denominator),value in zip(equations,values): 
            d[numerator][numerator]=d[denominator][denominator]=1.0
            d[numerator][denominator]=value
            d[denominator][numerator]=1.0/value
        #find all possible permutations of all the notes in the graph
        for k,i,j in itertools.permutations(d,3):
            if k in d[i] and j in d[k]:
                d[i][j]=d[i][k]*d[k][j]
        return [d[numerator].get(denominator,-1) for (numerator,denominator) in queries]