(a) Find an asymptotic upper bound for the recurrence T(n) T(n-a)+T(a)+n where a >= 1 is...

 

Transcribed Image Text:

(a) Find an asymptotic upper bound for the recurrence T(n) T(n-a)+T(a)+n where a >= 1 is constant, by using recursion iteration to generate a guess. For base case we assume that T(n) & e(1) for n a, i.e. that T(1), T(2), T(a) are all constants. (b) Complete the substitution method by proving that the guess generated above is indeed an asymptotic upper bound for the recurrence T(n) T(n-a)+T(a) + n (a) Find an asymptotic upper bound for the recurrence T(n) T(n-a)+T(a)+n where a >= 1 is constant, by using recursion iteration to generate a guess. For base case we assume that T(n) & e(1) for n a, i.e. that T(1), T(2), T(a) are all constants. (b) Complete the substitution method by proving that the guess generated above is indeed an asymptotic upper bound for the recurrence T(n) T(n-a)+T(a) + n