To help you better understand why the definition of Big-O is concerned only with the behavior of functions for large values of n, choose two functions with different growth rates in which the faster growing function is lower at small values of n, but eventually becomes larger. Write a short program that periodically compares the values of the two functions and illustrates the point at which the faster growing function overtakes the slower growing one. s an example, consider the following two functions: f(n) = 500n2 + 15n + 1000 g(n) = 2n3 Shown below is a table of the values of both functions for small values of n. n f(n) g(n) 10 51150 2000 20 201300 16000 30 451450 54000 40 801600 128000 50 1251750 250000 60 1801900 432000 70 2452050 686000 80 3202200 1024000 90 4052350 1458000 100 5002500 2000000 110 6052650 2662000 120 7202800 3456000 130 8452950 4394000 140 9803100 5488000 150 11253250 6750000 160 12803400 8192000 170 14453550 9826000 180 16203700 11664000 190 18053850 13718000 200 20004000 16000000 210 22054150 18522000 220 24204300 21296000 230 26454450 24334000 240 28804600 27648000 250 31254750 31250000 260 33804900 35152000 Once n reaches 260 g overtakes f.
To help you better understand why the definition of Big-O is concerned only with the behavior of functions for large values of n, choose two functions with different growth rates in which the faster growing function is lower at small values of n, but eventually becomes larger. Write a short program that periodically compares the values of the two functions and illustrates the point at which the faster growing function overtakes the slower growing one.
s an example, consider the following two functions:
- f(n) = 500n2 + 15n + 1000
- g(n) = 2n3
Shown below is a table of the values of both functions for small values of n.
n f(n) g(n)
10 51150 2000
20 201300 16000
30 451450 54000
40 801600 128000
50 1251750 250000
60 1801900 432000
70 2452050 686000
80 3202200 1024000
90 4052350 1458000
100 5002500 2000000
110 6052650 2662000
120 7202800 3456000
130 8452950 4394000
140 9803100 5488000
150 11253250 6750000
160 12803400 8192000
170 14453550 9826000
180 16203700 11664000
190 18053850 13718000
200 20004000 16000000
210 22054150 18522000
220 24204300 21296000
230 26454450 24334000
240 28804600 27648000
250 31254750 31250000
260 33804900 35152000
Once n reaches 260 g overtakes f.
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