霍夫曼编码基于贪婪方法或动态编程

Question

我们可以通过动态编程来解决霍夫曼编码问题，有没有算法

Answer 1

Huffman Coding works by creating a binary tree of nodes. These can be stored in a regular array, the size of which depends on the number of symbols, n. Huffman Coding can be implemented in O(n logn) time by using the Greedy Algorithm approach. Huffman Coding is not suitable for a Dynamic Programming solution as the problem does not contain overlapping sub problems.

Answer 2

As per my knowledge about algorithms, I beleive huffman coding is based on Greedy approach. As we do in Activity selection problem. Task scheduling and knapsack problem are another examples of it.

Answer 3

[ Update ]: I think the solution I mentioned below generates an optimal prefix code, but not necessarily same as Huffman code. Huffman code, by definition, is generated by taking the greedy approach. While it is optimal, it is not the only solution. (For example, once the Huffman tree is generated, you could interchange the leaves in the same level to give them different codes while still being optimal)

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I think this can be solved using Dynamic Programming, although it won't be that efficient. The approach here is very similar to finding the Optimal Binary Search Tree, since as you go one level down you add one more bit to the leaves.

Here is the link for the code to calculate the minimum number of total bits. Of course this is exponential, but if you use DP it can be solved in O(n^2) time. I haven't tried generating the encoding, but should be possible I believe.