optimal n minus 1 symbol Huffman code tree which is optimal by induction so this here it's a final part approve it's saying no matter what tree you build you'll always pay a prize of P of X plus P of Y when you need to split on x and y you can't just get away with apparent Z that's unavoidable the Hoffman code tree will have them appear that way together so the Hoffman code tree is incurring the minimum possible cost for being a n symbol tree prison minus one symbol tree it's having that minimal cost to when