How to prove that for a full binary tree $T$ there's a series of frequencies such that Huffman alg. will produce $T$?
The proof is by induction. The case $n = 1$ is clear. For $n &gt; 1$, choose two leaves at maximal depths, and merge them. Huffman's algorithm could have chosen these two leaves at the first step and merged them. Now apply the inductive hypothesis to complete the proof. 

Note that Huffman's algorithm, as described in your textbook, is non-deterministic in the sense that at any step there could be many valid choices. Any actual implementation of the algorithm will use a tie-breaking rule to arbitrarily choose which two leaves of minimal probability to merge at any given step.