GATE CS 2015 Set 2 — Question 24
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Programming & Data Structures → C Programming → Functions & Recursion
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Question
Consider the following C function.The return value of
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;
}
fun(5) is ________.Correct answer
51 to 51
Solution
Let be the value returned by
The variable is initialized to 1.
Base case: If , return . So .Recursive step:
For to , .
Since is initialized to 1, the recurrence is:Calculate values sequentially:
Return 2.
Return 5.
Return 15.
Return 51.
fun(n).The variable is initialized to 1.
Base case: If , return . So .Recursive step:
For to , .
Since is initialized to 1, the recurrence is:Calculate values sequentially:
1.
2.:
Return 2.
3.:
Return 5.
4.:
Return 15.
5.:
Return 51.
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