Suppose we are given a file F that is composed of n different words, with frequencies f1, f2, ..., f n. respectively. Assuming that for the ith word, the cost per bit of its encoding is c > 0 with 1sisn. Thus, if we find a prefix-free code where the ith word has codeword of length l;, then the total cost of the encoding of file F is i=1 Devise an O(n log n)-time algorithm for finding a prefix-free encoding of the n words in file F such that the total cost of the encoding is minimised. Show the correctness of your proposed algorithm. Analyse the time complexity of your proposed algorithm Show transcribed image text