HW01-sln

# HW01-sln - CSE310 HW01 Grading Keys A Please note that you...

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CSE310 HW01 Grading Keys Please note that you have to typeset your assignment using either L A T E X or Microsoft Word. Hand-written assignment will not be graded. You need to submit a hardcopy before the lecture on the due date. You also need to submit an electronic version at the digital drop box. For the electronic version, you should name your ﬁle using the format HWxy-LastName-FirstName. 1. (10 pts) Let f ( n ) = n 3 and g ( n ) = 100 × n × log 2 n . Find the smallest integer N 1 such that f ( N ) g ( N ) but f ( N + 1) > g ( N + 1). Show the values of N , f ( N ), g ( N ), f ( N + 1) and g ( N + 1). Solution: N = 20, f ( N ) = 8000, g ( N ) = 8643 . 86, f ( N + 1) = 9261, g ( N + 1) = 9223 . 87. Grading Keys: 6 pts for N ; 1 pt for each of the other values. 2. (10 pts) For each function f ( n ) (the row index in the following table) and time t (the column index in the following table), determine the largest size n of a problem that can be solved in time t , assuming that the algorithm takes

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