Let
0,1,2,..N-1     - outer door
N ..  2*N - 1   - 1-inner room doors
2*N .. 3N - 1   - 2-inner room doors
....
i*N  i*N + 1,  .. i*N + N-1   - i-th room doors

total  (K+1)*N  doors.

W[i][j] - minimum dist from i to j-th door, where  0 <= i,j < (K+1)*N

initially  W[i][i] = 0,  W[i][j] = inifinity  for i <> j.

read,  and set W[i][j] = 1   if there exists road from i to j doors.

-----------------
N times run following steps:

1. Floyd algorithm  for 0.. (K+1)*N - 1   doors.

2.
  for  1<= t <= K ,  0 <= i, j < N  update
        W[t*N + i][ t*N + j]  = min(W[t*N + i][t*N+j], W[i][j])
  Because  (t*N + i, t*N + j)  - is identical path as outer  (i,j) path.


Edited by author 31.10.2020 16:46