C++ Performing mapping between vectors and unique numbers and vice versa

I need to create a dictionary data structure which maps vector to unique numbers and vice versa:

For example for mapping vectors to unique numbers, I can do the following:

   vector   ---------> unique number
   (0,7,8)                   0
   (0,8,10)                  1
   (1,2,9)                   2
   (1,2,10)                  3
   (1,3,1)                   4

Then I need to map back unique numbers to vectors, e.g. given below:

   unique numbers --------> vector   
   0                        (0,7,8)    
   1                        (0,8,10)   
   2                        (1,2,9)    
   3                        (1,2,10)   
   4                        (1,3,1)    

I tried to do this mapping by creating a structure of integers and vectors -- however, this turned to be very inefficient. Is there some c++ data structure which can perform the forward and reverse mapping efficiently.