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. We have a computer that can execute a billion (10') steps per second. For any value of n, we have five algorithms we want

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. We have a computer that can execute a billion (10') steps per second. For any value of n, we have five algorithms we want to run. Algorithm A takes n ln n steps, where In n is the natural (base-e) logarithm of n. Algorithm B takes n' steps, C takes n", D takes 2n, and E takes n! (the factorial of n). Make a table with a column for each of the five algorithms, and a row for each of the following values of n: 5, 50, 100, 500, and 1000. In the entry for each row and column, put the time that the algorithm would take for that n, in terms of seconds, days, or years (whichever is most informative). If the answer is "more than 10 years", you can just say "too long

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