Big O Notion Help for project

hello guys i am in 3th years of studying in uni,i am toke this example as a heading of my project and need answers for it with all thanks, i am software eng

first part: O(g(n)) for this:

(n + 3 )(n + n2+ 4)
5logn+3n+1000
Logn+ 100 +1/ n2
100n2+ ½ n3 +5
(3n2 + 4)3



second part : number of operation of this

1)
if (condition)
{ cout<<”Hello”<<endl; }
else
{
for (i = 0; i < N; i++) {
cout<<”Hi”<<endl;
}
}



2)for (i = 0; i < N; i++) {
for (j = i+1; j < N; j++) {
sequence of statements
}
}



3)for (i = 0; i < 2*N; i++) {
sequence of statements
}
for (j = 0; j < M-1; j++) {
sequence of statements
}



4)
void fun(int k)
{
for (i = 0; i < N; i++) {
sequence of statements
}
}
void main(){
//declaration statements
for (i = 0; i < N; i++) {
fun(i);
}
}

Give us your answers first and then we can help you out.

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this my answer for first part:

first: n3

sec:n

third:n2

forth:n2

five:n6

Quote:

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Originally Posted by javaguys

this my answer for first part:

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Your notation is somewhat ambiguous since you don't separate multiplication and power-of clearly.

Still the Ordo complexity of an expression is determined by the fastest growing term when N approaches infinity. In my view you've got it wrong in the third and fourth example. They should be O(logN) and O(N^3) respectively.

thanks bro,i want o(n) of it, as i said above for:
1)
(n + 3 )(n + n^2+ 4)

2)5logn+3n+1000


3)Logn+ 100 +1/ n^2

4)100n^2+ ½ n^3 +5

5)(3n^2 + 4)^3

still wait answers

Quote:

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Originally Posted by javaguys

still wait answers

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I think you got it all right except for 3 and 4 (for which I gave suggestions in my previous reply).

O(logN) and O(N^3) for third and fourth this is true answer?

hmmm, what about part B bro?

Quote:

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Originally Posted by javaguys

O(logN) and O(N^3) for third and fourth this is true answer?

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Yes, I would say so. The Ordo complexity is determined by the term that grows the fastest asymptotically. And that's the term you picked in all cases except in 3 and 4. In 3 it's log(n) and in 4 it's n^3 so these will determine the complexity.

But don't take what I say at face value. After having studied software engineering for 3 years at a university you should know this better than I do.

Quote:

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hmmm, what about part B bro?

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Yes what about it? If you suggest something with a motivation I'll tell you what I think.

i know how to find number of operation, but i need to know big o of this codes in part b, i want to tell you that just first material talking about algorithms so sorry if i need just Little help