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Alex Rivera
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In CLRS ( Introduction to Algorithms by Cormen, Leiserson, Rivest, and Stein), for a function f ( n ) = an 2 + bn + c they said Suppose we take the constants c 1 = a /4, c 2 = 7 a /4, and n 0 = 2·max(| b |/ a , √(| c |/ a )). Then 0 ≤ c 1 n 2 ≤ an 2 + bn + c ≤ c 2 n 2 for all n ≥ n 0 . Therefore f ( n ) is Θ( n 2 ). But they didn't specify how values of these constants came ? I tried to prove it but couldn't. Please tell me how these constants came ?
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