CODEWITHSUNDEEP
mathtime-complexitybig-o
whatevahhh
whatevahhh

Reputation: 47

Order functions by growth

I'm trying to order some functions by their growth rate. All logarithms have 2 as their base. These are the functions:

2n+(n log n)
3logn
(n∑i=1i)2
4^n/n^4
n^(7/8)
2n
10logn
n (log n)!
√log5n
n^(log n)

I tried plotting them but I'm still very confused as to what the correct order is. Any idea as to how I have to order them? I also tried calculating their big-o limits but some won't return 0 or infinity.

Upvotes: 0

Views: 206

Answers (1)

erfan30
erfan30

Reputation: 105

  1. 2*n+(n log n)==> o(n log n)
  2. 3*log n ==> o(log n)
  3. 1+2+3+...=[n(n+1)]/2 ==> o(n^2)
  4. (4^n)/(n^4) ==> o((4^n)/(n^4))
  5. n^(7/8) ==> o(n^(7/8))
  6. 2*n ==> o(n)
  7. 10*log n==> o(log n)
  8. n*(log n)!==> o(n*(log n)!)
  9. sqrt(log 5*n) ==> o(sqrt(n))
  10. n^(log n) ==> o(n^(log n))

Hence:

2=7<9<5<6<3<8<10<4

Upvotes: 0

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