Consider the following rec function.rec(int x){static int f;if (x==1)return(1);elsef+=x*rec(x-1);return(f);}Find the value returned by rec(5).a)120b)160c)210d)240Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Recursion Explanation:
The given code snippet represents a recursive function named 'rec' that takes an integer parameter 'x'. The function calculates the factorial of 'x' using recursion.

Code Explanation:
1. The code snippet declares a static integer variable 'f' within the function 'rec'. The static variable retains its value across function calls.
2. The function checks if the value of 'x' is 1. If it is, the function returns 1 (base case) as the factorial of 1 is 1.
3. If the value of 'x' is not 1, the function calculates the factorial by recursively calling itself with the parameter 'x-1' and storing the result in the variable 'f'.
4. The factorial of 'x' is then calculated as the product of 'x' and the value stored in 'f'.
5. Finally, the calculated factorial is returned.

Calculation:
To find the value returned by 'rec(5)', we trace the recursive function calls as follows:

1. rec(5)
2. 5*rec(4)
3. 5*(4*rec(3))
4. 5*(4*(3*rec(2)))
5. 5*(4*(3*(2*rec(1))))
6. 5*(4*(3*(2*1)))
7. 5*(4*(3*2))
8. 5*(4*6)
9. 5*24
10. 120

So, the value returned by 'rec(5)' is 120.

Therefore, the correct answer is option 'D' (120).

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