# Answered Essay: 1. Using Θ-notation, provide asymptotically tight bounds in terms of n for the solution to each of the following recurrences. Assume eac

1. Using Θ-notation, provide asymptotically tight bounds in terms of n for the solution to each of the following recurrences. Assume each recurrence has a non-trivial base case of T(n) = Θ(1) for all n no where no is a suitably large constant. For example, if asked to solve T(n)-2T(n/2) + n, then your answer should be Θ(n log n). Give a brief explanation for each solution. Giving only the upper or lower bound (using big-oh or big-Ω notation) may be worth partial credit. (a) T(n)-8T(n/2)+13 (b) T(n) = 5T(n/3) + n (c) T(n)=T(n-1) + ㎡ (d) T(n)=T(n/2) + 2T(n/5)+n

1)2) For First One and Second one We can go for Masters thoerem since it is of Divide and Conquer type.

3) can be solved by Substitution method.So here in the above equation we can see n2is the highest power of the series. So Asymptotically it will be

T(n) = O (n 2).

4)Can be solved by Recursion tree method.

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