Time Complexity

Question

Please find the time complexity of the following code:-int i,s1;

i=1,s1=1;
while(s1<=n)
    {
     i++;
    s1+=s1+i;
    printf("Hope");
    }

Answer 1

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Comments

@ankitgupta.1729 thanks bro

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from

1+3+6+ 10 + k =n

k(K+1)(K+2)

____                    = n

6

 

how did this k(k+1)(k+2 )/6 come from the previous step?

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@rohan devaki

$1+3+6+10+15+….\text{till some finite number of terms}$

$1+(1+2)+(1+2+3)+(1+2+3+4)+(1+2+3+4+5)+….\text{till some finite number of terms}$

$\Sigma_{n=1}^{n=k}\;\left( \Sigma_{p=1}^{p=n}\; p\right)$

$\Sigma_{n=1}^{n=k}\;\left( \frac{n(n+1)}{2}\right)$

$\Sigma_{n=1}^{n=k}\;\left( \frac{n^2+n}{2}\right)$

$\frac{1}{2}\left(\Sigma_{n=1}^{n=k} (n^2) + \Sigma_{n=1}^{n=k} (n)\right)$

$\frac{1}{2}\left(\frac{k(k+1)(2k+1)}{6} + \frac{k(k+1)}{2}\right)$

$\frac{k(k+1)}{4}\left(\frac{2k+1}{3}+1\right)$

$\frac{k(k+1)}{4}\left(\frac{2k+4}{3}\right)$

$\frac{k(k+1)(k+2)}{6}$