Consider the following C function.
C
int fun ( int n){
int x = 1, k;
if (n == 1)
return x;
for (k = 1; k < n; ++k)
x = x + fun(k) * fun(n – k);
return x;
} |
The return value of fun(5) is __________.
(A)
0
(B)
26
(C)
51
(D)
71
Answer: (C)
Explanation:
fun(5) = 1 + fun(1) * fun(4) + fun(2) * fun(3) + fun(3) * fun(2) + fun(4) * fun(1) = 1 + 2*[fun(1)*fun(4) + fun(2)*fun(3)] Substituting fun(1) = 1 = 1 + 2*[fun(4) + fun(2)*fun(3)] Calculating fun(2), fun(3) and fun(4) fun(2) = 1 + fun(1)*fun(1) = 1 + 1*1 = 2 fun(3) = 1 + 2*fun(1)*fun(2) = 1 + 2*1*2 = 5 fun(4) = 1 + 2*fun(1)*fun(3) + fun(2)*fun(2) = 1 + 2*1*5 + 2*2 = 15 Substituting values of fun(2), fun(3) and fun(4) fun(5) = 1 + 2*[15 + 2*5] = 51
Hence Option(C) is the correct answer.
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