Suppose we have a 1X computer that can execute n statements in time t Assume that an algorithm which is O(f(n)) requires the execution of a number of statements proportional to f(n) For example, if A1 (n2), then assume that for a problem of size n, the algorithm will execute c n2 statements (where c is a constant) For simplicity, you can assume c 1 a If we run algorithm A2 O(n2) with problem size n on the 1X computer, how long will it take to run in terms of t b If we run algorithm A3 O(nlgn) with problem size n on the 1X computer, how long will it take to run in terms of t c Suppose an algorithm A4 runs on the 1X computer in time t When we add 1 more element of data, the same algorithm runs in time 2t Find the complexity (Big O) of A4 d If we want A2 to finish in time t with problem size n, determine how many times faster then our current 1X computer we need to purchase e How long will it take our 1X computer to run 1,000,000 statements

Question: Suppose we have a 1X computer that can execute n statements in time t. Assume that an algorithm which is O(f(n)) requires the execution of

Suppose we have a 1X computer that can execute n statements in time t. Assume that an algorithm which is O(f(n)) requires the execution of a number of statements proportional to f(n).
For example, if A1 ε (n2), then assume that for a problem of size n, the algorithm will execute c*n2 statements (where c is a constant). For simplicity, you can assume c = 1.

a. If we run algorithm A2 ε O(n2) with problem size = n on the 1X computer, how long will it take to run in terms of t?

b. If we run algorithm A3 ε O(nlgn) with problem size = n on the 1X computer, how long will it take to run in terms of t?

c. Suppose an algorithm A4 runs on the 1X computer in time t. When we add 1 more element of data, the same algorithm runs in time 2t. Find the complexity (Big O) of A4.

d. If we want A2 to finish in time t with problem size = n, determine how many times faster then our current 1X computer we need to purchase.

e. How long will it take our 1X computer to run 1,000,000 statements?

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