Editing Shannon–Fano coding (section)

===Huffman coding===

{{Main|Huffman coding}}

A few years later, [[David A. Huffman]] (1952)<ref>{{Cite journal | last1 = Huffman | first1 = D. |author-link1=David A. Huffman| title = A Method for the Construction of Minimum-Redundancy Codes | doi = 10.1109/JRPROC.1952.273898 | journal = [[Proceedings of the IRE]]| volume = 40 | issue = 9 | pages = 1098–1101 | year = 1952 | url = http://compression.ru/download/articles/huff/huffman_1952_minimum-redundancy-codes.pdf}}</ref> gave a different algorithm that always produces an optimal tree for any given symbol probabilities. While Fano's Shannon–Fano tree is created by dividing from the root to the leaves, the Huffman algorithm works in the opposite direction, merging from the leaves to the root. 
# Create a leaf node for each symbol and add it to a [[priority queue]], using its frequency of occurrence as the priority.
# While there is more than one node in the queue:
## Remove the two nodes of lowest probability or frequency from the queue
## Prepend 0 and 1 respectively to any code already assigned to these nodes
## Create a new internal node with these two nodes as children and with probability equal to the sum of the two nodes' probabilities.
## Add the new node to the queue.
# The remaining node is the root node and the tree is complete.