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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Consider the following recursive Java function $f$ that takes two long arguments and returns a float value:
public static float f(long m, long n) {
float result = (float)m / (float)n;
if (m < 0 || n < 0) return 0.0f;
else result -= f(m * 2, n * 3);
return result;
}
Which of the following real values best approximates the value of $f(1,3)$?
public static float f(long m, long n) {
float result = (float)m / (float)n;
if (m < 0 || n < 0) return 0.0f;
else result -= f(m * 2, n * 3);
return result;
}
Which of the following real values best approximates the value of $f(1,3)$?
Solution
$f(1,3)=\frac{1}{3}-f(2,9)$
$=\frac{1}{3}-\frac{2}{9}+\frac{4}{27}-\frac{8}{81}+\cdots$
This is a geometric series with first term $\frac{1}{3}$ and common ratio $-\frac{2}{3}$.
Sum:
$\frac{\frac{1}{3}}{1-(-\frac{2}{3})}=\frac{\frac{1}{3}}{\frac{5}{3}}=\frac{1}{5}=0.2$
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