Algorithm 1: Huffman Code

Input: $\mathbb{P}=\left\{p\right(1),p(2),\dots ,p(m\left)\right\},$$G=\{1,2,\dots ,m\}$

1  If $\left|\mathbb{P}\right|=1,$$C\left(1\right):=0$

2  Otherwise, while $\left|\mathbb{P}\right|>1$

–   define

∗  $I:=argmin\left\{p\right(i)\in \mathbb{P}:i\in G\}$

∗  $J:=argmin\left\{p\right(i)\in \mathbb{P}\setminus \{p\left(k\right):k\in I\}:i\in G\}$

∗  $H:=I\cup J$

–   If $\left|H\right|=2$ set $l\left(h\right):=0\forall h\in H,$$C\left(I\right):=0$ and $C\left(J\right):=1$

–   Otherwise, if $h\in I,C\left(h\right):=0C\left(h\right)$ and if $h\in J,C\left(h\right)=1C\left(h\right).$

–   Set $I^{\prime }:=H,$${\mathbb{P}}^{\prime }:=\{p\left(k\right):k\in I^{\prime }\},$$p\left(I^{\prime }\right)={\sum }_{k\in I^{\prime }}p\left(k\right),$$G^{\prime }=\{k:k\in I^{\prime }\}$

–   Define $\mathbb{P}:=\{\mathbb{P}\setminus {\mathbb{P}}^{\prime }\}\cup \left\{p\left(I^{\prime }\right)\right\},$$G:=\{G\setminus G^{\prime }\}\cup \left\{I^{\prime }\right\}$ and return to 1.

Output: $\left\{C\right(1),C(2),\dots ,C(m\left)\right\}$