Aspire Faculty ID #18919 · Topic: UGC NET Computer Science Nov 2020 (Paper II) · Just now
UGC NET Computer Science Nov 2020 (Paper II)

Consider the following pseudo-code fragment, where $a$ and $b$ are integer variables that have been initialized:

Pre-conditions: $(a>1\land a<b)$

Assume that overflow never occurs.

int $x=0$; int $p=1$;

while $(p<b)$ {
$p=p*a$;
$x=x+1$;
}

When the while loop terminates, what will be the value of $x$ in terms of $a$ and $b$?

Solution

Initially,

$p=1=a^0$

After $1$ iteration:

$p=a^1$

After $2$ iterations:

$p=a^2$

After $x$ iterations:

$p=a^x$

Loop stops when:

$p\ge b$

So,

$a^x\ge b$

Minimum such value of $x$ is:

$x=\lceil \log_a b\rceil$
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