Big O Notation Solved Examples

Big O Notation Solved Examples

(a) f(n) = 100n³- 7n³+ 14n²

Solution:

f(n)=93n³+14n²

^{after removing all constants and lower order terms}

=O(n³⁾

(b)      f(n) = 100n³- 100n³+ 7n²

Solution:    

f(n)=100n³- 100n³+7n²

f(n)=7n²

^{after removing all constants and lower order terms}

=O(n²)

(c) f(n) = log(7n²)

Solution:

f(n)=log(7n²)

^{after removing all constants and lower order terms}

=log(n)

(d)      f(n) = 5 log log n + 4 log² (n)

Solution:

f(n)=5loglogn+4log²(n)

^{after removing all constants and lower order terms}

=O(log²n)

(e) f(n) = .001n + 100 · 2ⁿ

Solution:

f(n)=.001n+100·2ⁿ

^{after removing all constants and lower order terms}

=O(2ⁿ)

(f)  f(n) = n³(1 + 6n + 2014n²)

Solution:

f(n)=n³+6n⁴+2014n⁵

^{after removing all constants and lower order terms}

=O(n⁵)

(g) f(n) = (log n)(n + n²)

Solution:

f(n)=nlogn+n²logn

^{after removing lower order terms}

=O(n²log n)