问题
I have a table that shows the probability of an event happening. I'm fine with part 1, but part 2 is not clicking with me. I'm trying to get my head around how the binary numbers are derived in part 2?
I understand 0 is assigned to the largest probability and we work back from there, but how do we work out what the next set of binary numbers is? And what do the circles around the numbers mean/2 shades of grey differentiate?
It's just not clicking. Maybe someone can explain it in a way that will make me understand?
回答1:
To build huffman codes, one approach is to build a binary tree, using a priority queue, in which the data to be assigned codes are inserted, sorted by frequency.
To start with, you have a queue with only leaf nodes, representing each of your data.
At each step you take the two lowest priority nodes from the queue, make a new node with a frequency equal to the sum of the two removed nodes, and then attach those two nodes as the left and right children. This new node is reinserted into the queue, according to it's frequency.
You repeat this until you only have one node in the queue, which will be the root.
Now you can traverse the tree from the root to any leaf node, and the path you take (whether you go left or right) at each level gives you either a 0 or a 1, and the length of the path (how far down the tree the node is) gives you the length of the code.
In practice you can just build this code as you build the tree, but appending 0 or 1 to the code at each node, according to whether the sub-tree it is part of is being added to the left or the right of some new parent.
In your diagram, the numbers in the circles are indicating the sum of the frequency of the two nodes which have been combined at each stage of building the tree.
You should also see that the two being combined have been assigned different bits (one a 0, the other a 1).
A diagram may help. Apologies for my hand-writing:
来源：https://stackoverflow.com/questions/14432503/how-is-this-huffman-table-created