Funnily familiar

Computer Science Level 2

The output of hilarious can be approximated as n a \sqrt{ na } , where n n is a positive integer . What is a a ? 

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def hilarious(n):
    j = 1
    i = 0
    s = 0
    while i < n:
        i += j
        s += 1
        j += 1
    return s


The answer is 2.

Thaddeus Abiy by Thaddeus Abiy , 25, Ethiopia

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2 solutions

Kunal Gupta
Aug 26, 2016

By the Code, we see that i i increases as the n t h nth triangular number i.e. n ( n + 1 ) 2 \frac{n(n+1)}{2} .
Hence, we need to find approximately the number of times the while loop will run that'll give the output i.e. 's'.
i.e to find a k k such that: k ( k + 1 ) 2 = n \dfrac{k(k+1)}{2}=n Solving this Quadratic Eqn. will give: k = − 0.5 + 0.25 + 2 n k=-0.5+\sqrt{0.25+2n} ≈ 2 n \approx \sqrt{2n} giving a = 2 a=2

6 Helpful 0 Interesting 0 Brilliant 0 Confused
Vlad Vasilescu
Jul 8, 2018

By extending the range for i and r the result tends to 2 \boxed{2}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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