Suppose we have an optimal prefix code on a set c={0,-1} of characters and we wish to transmit this code using as few bits as possible. show how to represent any optimal prefix code on c using only 2n -1 + n[lgn]. (hint: use 2n -1 bits to specify the structure of the tree, as discovered by a walk of the tree.)

Your task this week is to write a very simple spam classifier in python. it will classify messages as either spam (unwanted) or ham (wanted). the program will have a set of spam_words, words that are known to appear in spam messages. that set is included in the template file spam.pypreview the document. you will also define a spam threshold which reflects the allowed percentage of spam words in the message. you'll compute a 'spam indicator', which is the ratio of spam words to the total number of unique words in the message. if the spam indicator exceeds the spam threshold, the message is classified as spam. otherwise it is classified as ham. we'll assume that the spam threshold is a constant and has a value of 0.10. your program will prompt the user for a message and then will print the corresponding spam indicator with two decimal digits and the corresponding classification (spam or ham). the program will be case insensitive. the spam words are detected whether they are in lower case or upper case or mixed case. each word, spam or not, is counted once (even if it appears multiple times in the message.) the program will remove punctuation from the message before identifying the words and computing the spam indicator. for example '! ' must be identified as the spam word 'now'.

Your computer running windows 10 is doing some very strange things with the operating system. you are fairly certain it is not a hardware issue. you need to try to get further insight into what is going on within the operating system. which tool would be best suited for this?

Aisha has finished working on a word processing document that contains 15 pages. she has added some special elements in the first three pages, page 9 and 10, and page 15 from the document. she wants to print only these pages to see how they look. which option is the correct way to represent (in the print dialog box) the pages that aisha wants to print