# Huffman - Upperbound Depth Given an alphabet with probabilities

Given an alphabet $$\Sigma = \{C_1, ..., C_k\}$$ where the probability of the letter $$C_k$$ is given by $$Pr(C_k)$$.

The probabilities satisfy $$Pr(C_1)> ... >P(C_k)$$ (i.e all probabilities are distinct).

Can we find an upper bound for the depth of $$C_1$$ in a Huffman Tree?