lab 10

lab10/lab10

+#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.
+
+
+