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Suppose the execution time function for an algorithm is:
f(x) = 3 + 8x + x2
Determine the order of f(x).
S7P5A51 (Physical - Change).
Pj Problem of Interest is of type change (physical - change). Problems of time are change problems.
An algorithm is the totality of the steps necessary to solve a given problem. In the context of machine computing, an algorithm consists of the instructions a machine uses to solve a given problem. The execution time of an algorithm measures the time it takes to execute an algorithm for a given set of data.
The execution time function f(N) for an algorithm is of order g(N) if there exists a positive number K and an integer Q such that:
f(N) ≤ K[g(N)] for all N ≥ Q ---------------(1)
So, if f(x) = 3 + 8x + x2
Then for x ≥ 8, f(x) = 3 + 8x + x2 ≤ x2 + x2 + x2 = 3x2.
So, f(x) ≤ 3x2 for all x ≥ 8 satifies equation (1)
So, the given execution time function is of order x2.
The following are common orders of execution time function for an algorithm:
constant k (constant execution time)
log2N (logarithmic execution time)
N (linear execution time)
N2 (quadratic execution time)
N3 (cubic execution time)
XN (exponential execution time)
Constant execution time being the best and exponential execution time being the worst.
The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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