Solution to A particular algorithm increases in time as the number of operations, n, increases. Suppose the … - Sikademy
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Archangel Macsika

A particular algorithm increases in time as the number of operations, n, increases. Suppose the time complexity of this algorithm is given by: f(n) =4n3+5n2 * log(n). Show that f(n) is O(g(n)) for g(n) = n3.

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f(x)=O(g(x)) if there exists a positive real number M and a real number x0 such that

|f(x)|\le Cg(x) for all x\ge x_0


So, we have:

f(n) =4n3+5n2 * log(n) < 5g(x)=5n^3 for x\ge 2

where C=5,x_0=2

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