You found a lost civilizations' library and you are interested in its alphabet of n strange characters. Each book has a title in this alphabet and you hope that the books are arranged in lexicographical order on the bookshelves. You would like to know whether the order of the books uniquely determines the order of the characters of the alphabet, or if there is insufficient information, or whether even such an order cannot exists (meaning that someone must have shuffled the books). Think of the input as a list of words without spaces from the alphabet "a-z", and the question is the order of the characters "a-z" in the examined alphabet. Try to find an algorithm which solves this problem in time linear in the size of the input (that is, the number of characters on input). You may assume that each character appears at least once. Don't assume that the size of the alphabet is a fixed constant (like 26); treat it as a variable n., and let L be the total number of characters on input.

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explain and prove the algorithm
You found a lost civilizations' library and you are interested in its alphabet of 7 strange characters. Each book has a title
in this alphabet and you hope that the books are arranged in lexicographical order on the bookshelves. You would like to
know whether the order of the books uniquely determines the order of the characters of the alphabet, or if there is
insufficient information, or whether even such an order cannot exists (meaning that someone must have shuffled the
books).
Think of the input as a list of words without spaces from the alphabet "a-z", and the question is the order of the characters
"a-z" in the examined alphabet. Try to find an algorithm which solves this problem in time linear in the size of the input
(that is, the number of characters on input). You may assume that each character appears at least once. Don't assume that
the size of the alphabet is a fixed constant (like 26); treat it as a variable n, and let L be the total number of characters on
input.
Transcribed Image Text:explain and prove the algorithm You found a lost civilizations' library and you are interested in its alphabet of 7 strange characters. Each book has a title in this alphabet and you hope that the books are arranged in lexicographical order on the bookshelves. You would like to know whether the order of the books uniquely determines the order of the characters of the alphabet, or if there is insufficient information, or whether even such an order cannot exists (meaning that someone must have shuffled the books). Think of the input as a list of words without spaces from the alphabet "a-z", and the question is the order of the characters "a-z" in the examined alphabet. Try to find an algorithm which solves this problem in time linear in the size of the input (that is, the number of characters on input). You may assume that each character appears at least once. Don't assume that the size of the alphabet is a fixed constant (like 26); treat it as a variable n, and let L be the total number of characters on input.
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