Entropy. The Shannon entropy measures the information content of an input string and plays a cornerstone role in information theory and data compression. Given a string of n characters, let fc be the frequency of occurrence of character c. The quantity Pc = fc/n an estimate of the probability that c would be in the string if it were a random string, and the entropy is defined to be the sum of the quantity –pc log2 pc, over all characters that appear in the string. The entropy is said to measure the information content of a string: if each character appears the same number times, the entropy is at its minimum value among strings of a given length. Write a program that takes the name of a file as a command-line argument and prints the entropy of the text in that file. Run your program on a web page that you read regularly, a recent paper that you wrote, and the fruit fly genome found on the website.
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