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--- courses:cs211:winter2018:journals:bairdc:chapter4 [2018/03/06 02:44] – bairdc
+++ courses:cs211:winter2018:journals:bairdc:chapter4 [2018/03/13 03:55] (current) – [4.8 – Huffman Codes and Data Compression] bairdc
@@ Line 88: / Line 88: @@
 ===== 4.7 – Clustering =====
+Clustering happens when you're trying to classify a collection of objects into distinct groups. One way to divide them up into clusters is to calculate the distances between the distinct groups. However, there are infinitely many clusterings in a set; the issue is finding the ones with the max spacing. This procedure is the same as Kruskal's minimum spanning tree algorithm, except we stop the procedure when we obtain //k// connected components. This is the same as deleting the k-1 most expensive edges from the minimum spanning tree and returning the resulting components.
+Overall this section was very interesting and very readable to me: 10/10.
+===== 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.