What algorithm can I use to find the shortest path between specified node types in a graph?

Question

This is the problem:

I have n points (p1, p2, p3, .. pn), each of them can connect to any other with a determined cost x.

Each point belongs to one of a set of p

Answer 1

Here is pseudocode with dynamic programming solution:

n - length of desired path
m - number of vertices
types[n] // desired type of ith node
vertice_types[m]
d[n][m] // our DP tab initially filled with infinities

d[0][0..m] = 0
for length from 1 to n 
  for b from 0 to m
    if types[length] == vertice_types[b]
      for a from 0 to m
        if types[length-1] == vertice_types[a]
          d[length][b] = min(d[length][b], d[length-1][a] + cost(a,b))

your minimum cost path is min(d[n][0..m])

you can reduce size of d table to 2 rows, but it would obfuscate the solution