next up previous
Next: Designing Algorithms Up: l1 Previous: Analysis

Order of Growth

The ORDER of a running-time function $\Theta$ is the fastest growing term, discarding constant factors.



Insertion Sort:



XYZ-Sort:


Size n
Complexity 10 20 30 40 50 60
$n$ .00001 s .00002 s .00003 s .00004 s .00005 s .00006 s
$n^2$ .0001 s .0004 s .0009 s .0016 s .0025 s .0036 s
$n^3$ .001 s .008 s .027 s .064 s .125 s .216 s
$n^5$ .1 s 3.2 s 24.3 s 1.7 min 5.2 min 13.0 min
$2^n$ .001 s 1.0 s 17.9 min 12.7 days 35.7 years 366 centuries
$3^n$ .059 s 58 min 6.5 years 3855 centuries \(2x10^8\) centuries \(1.3 x 10^{13}\) centuries


next up previous
Next: Designing Algorithms Up: l1 Previous: Analysis