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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
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 $b$?
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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