Asymptotic analysis

Question

what is the time complexities of the following code snippets.

 

1.

k=1;i=1;
while(k<=n)
{
    i++;
    k=k+i;
}

 

 

2.

for(i=1;i<=n;++i)
{
    for(j=1;j<n;j=j*2)
    c=c+1;
}

 

 

 

3.
m=pow(2,n)
for(i=1;i<=n;i++)
{
    for(j=1;j<=m;j=j*2)
    c=c+1;
}

Comments

1. $O(n) $bcoz k still grows linealry even though i added.

2. $O(nlogn) $

3.$O(nlogm) = O(n^2)$

Correct? Can someone else verify?

---

@Kunal Kadian i think for 1. it should be $O(\sqrt n)$

since for $i=p, k= \frac{p(p+1)}{2}$, and i (=p)  represents no. of times looping is done. So $p=O(\sqrt n)$

---

1) O(sqrt(n))

2) O(nlogn)

3) O(n^2)