GATE DA 2026 Set 1 — Question 39
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Programming, Data Structures & Algorithms → Functions, File & Error Handling → Recursion
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Question
A recursive function in Python is given.Now, consider the following function call:
def mystery(n):
if n <= 0:
return 1
else:
return mystery(n-1) + mystery(n-2)
mystery(4)Assume that a typical runtime stack is used to manage function calls. Each function call is pushed onto the stack and removed only after it finishes execution.Which of the following options denotes the total number of function calls (i.e., the total number of stack activations), including the initial call, to compute mystery(4)?Correct answer
(C) 15
Solution
Let be the number of function calls for input .
The recurrence relation for the number of calls is:
for (1 for the current call, plus calls from subproblems).
Base cases: For , the function returns immediately, so .Calculating step-by-step:
The recurrence relation for the number of calls is:
for (1 for the current call, plus calls from subproblems).
Base cases: For , the function returns immediately, so .Calculating step-by-step:
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