Question

Use Big-O Notation to characterize the computational cost of algorithm A1 and A2. The complexity of A1 is 10000 * n, with n being the number elements processed in A1. The complexity of A2 is 100 * n, with n elements in A2. State in Big-O notation the cost of f1, with f1(x) = log2(2x) – 14x + 3 sqrt(x) + 12x^2 - 150 this is also a theoretical question just answer no code.

Answer 1

A1 is 10000 * n

=> 0 ≤ 10000*n ≤ 10001n ∀ n≥0

=> A1 is O(n)

A2 is 100 * n

=> 0 ≤ 100*n ≤ 101n ∀ n≥0

=> A2 is O(n)

f1(x) = log2(2x) – 14x + 3 sqrt(x) + 12x^2 - 150

=> 0 ≤ log2(2x) – 14x + 3 sqrt(x) + 12x^2 - 150 ≤ x^2 + 14x^2 + 3 x^2 + 12x^2 + 150x^2 ∀ x≥5

=> 0 ≤ log2(2x) – 14x + 3 sqrt(x) + 12x^2 - 150 ≤ 180x^2 ∀ x≥5

=>log2(2x) – 14x + 3 sqrt(x) + 12x^2 - 150 is O(x^2)

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