Consider a file with the following character frequencies: 

A:5 B:7 C:10 D:3 E:5. 

(a) Find the Huffman tree needed to construct the Huffman code for this set. 

(b) What is the Huffman code for each of the characters in the example above? 

c) Design an efficient algorithm that constructs the Huffman tree in O(N), given a sorted set of frequencies for the N characters.