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--- courses:cs211:winter2018:journals:bairdc:chapter4 [2018/03/12 23:37] – bairdc
+++ courses:cs211:winter2018:journals:bairdc:chapter4 [2018/03/13 03:55] (current) – [4.8 – Huffman Codes and Data Compression] bairdc
@@ Line 93: / Line 93: @@
 ===== 4.8 – Huffman Codes and Data Compression =====
+The goal of Huffman Codes is lossless data compression. The original top-down approach created by Shannon and Fano isn't guaranteed to always produce an optimal code. So, Huffman came up with a bottom-up approach that did. The idea in this is to have the most frequently used characters to have the shortest codes in order to optimize the overall compression. Furthermore, you don't want to have one character to be the prefix of another character, or you will get multiple ways to interpret data. To do this, we must minimize the average number of bits per letter ABL(y) = Sigma x in S fx|y(x)|.
+Using a Priority Queue, we can get Huffman's algorithm to run in O(klogk):
+<code>
+if S has two letters:
+  Encode one letter as 0 and the other letter as 1
+else:
+  Let y* and z* be the two lowest-frequency letters
+  Form a new alphabet S’ by deleted y* and z* and replacing
+    them with a new letter w of freq fy* + fz* Recursively construct a prefix code y’ for S’ with tree T’
+  Define a prefix code for S as follows:
+    Start with T’
+    Take the leaf labeled w and add two children below it
+      labeled y* and z*
+</code>
+I'd give this section a 10/10 on readability and interestingness. I was very interested in the topic, and it was explained well.