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ys554
Final-Project
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3d7303c6
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3d7303c6
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6 years ago
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ys554
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3d7303c6
#Yegeon Seo
#Lab 10
Q1
n T(n) f(n)=n f(n)=n2 f(n)=n3
--------------------------------------------------------------
10000 2.384 0.0002384 2.384E-08 2.384E-12
20000 5.156 0.0002578 1.289E-08 6.445E-13
30000 8.08 0.000269333 8.97778E-09 2.99259E-13
40000 11.064 0.0002766 6.915E-09 1.72875E-13
50000 14.148 0.00028296 5.6592E-09 1.13184E-13
60000 17.14 0.000285667 4.76111E-09 7.94E-14
Conclusions:
T(n) : is increasing to infinity, so T(n) = w(f(n)) and is bound below by a constant.
f(n) : is increasing to infinity, so T(n) = w(f(x)) and is a lower bound
f(n)^2 : is decreasing to a zero or non zero constant, f(n) is an upper bound and T(n) = o(f(n))
f(n)^3 : is decreasing to zero, f(n) is an upper bound and T(n) = o(f(n))
Q2
n T(n) f(n) =n f(n)=n^2 f(n)=n^3
---------------------------------------------------------------------
10000 45721062 4572.1062 4.57211E-05 0.45721062
20000 98107982 4905.3991 1.22635E-05 0.245269955
30000 153522280 5117.4093 5.68601E-06 0.137058031
40000 210173451 5254.3362 3.28396E-06 0.131358407
50000 265180908 5303.61816 2.12145E-06 0.106072363
60000 319847373 5330.78955 1.48077E-06 0.088846493
Conclusions:
T(n) : is increasing to a non-zero constant, so T(n) = w(1) and is bound below by a constant.
f(n) : is increasing to infinity, so T(n) is bound below by a line and T(n) = w(f(x)).
f(n)^2 : is decreasing to zero or a non zero constant, so T(n) = o(f(n)).
f(n)^3 : is decreasing to zero, so T(n) = o(f(n)) and f(n) is an upper bound.
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