Please provide answers i through v, they are all part of the same question. Also

Question

Please provide answers i through v, they are all part of the same question. Also give reasoning (simplification process)

e. When analyzing the speed of an algorithm we often use asymptotic runtime analysis. In asymptotic analysis we drop all but the largest term from the expression (because they become infinitely small relative to larger terms), and also drop any constant factors (because they are meaningless in a unitless runtime analysis) Simplify each of the following expressions into their asymptotic forms (in terms of n) nl: i. 5n + 30"log(n) + 500 ii. n*(n+40) iii. (n/2)*(3*n + log(n)) iv. log(n/2) + log(n*2) + 42 v. e*(log(n/2)) * log(50n):

Explanation / Answer

1.In the given expression n is greater than log n

So the time complexity is O(n).

2.the given expression is n^2+40 n

So the time complexity is O(n^2)

3.(n/2)*(3*n+log(n)) in this expression the largest term is n^2. The time complexity is O(n^2)

4.the time complexity of this expression is O(logn)

5.the time complexity of this expression is O(e^logn)

Since all these are largest terms in the given expressions.

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