Consider the following recursive function F() in Java that takes an integer value and returns a string value:
public static String F(int N) {
if (N < = 0) return “–”;
return F(N – 3) + N + F(N – 2) + N;
}
The value of F(5) is:

Correct option is D

To compute the value of F(5), let's trace the recursive function step-by-step:
1. Base Case: When N <= 0, the function returns "-".
2. Recursive Case: The function computes:
return F(N - 3) + N + F(N - 2) + N;
This means that the function calls itself twice: once with (N - 3) and once with (N - 2), concatenating the results with the current value of N.
Step-by-Step Execution for F(5):
1. Initial Call: F(5)
return F(5 - 3) + 5 + F(5 - 2) + 5;
i.e.,
return F(2) + "5" + F(3) + "5";
2. Evaluate F(2):
F(2) = F(2 - 3) + 2 + F(2 - 2) + 2;
i.e.,
F(2) = F(-1) + "2" + F(0) + "2";
· F(-1) → "-" (Base case)
· F(0) → "-" (Base case)
Thus,
F(2) = "-" + "2" + "-" + "2" = "-2-2";
3. Evaluate F(3):
F(3) = F(3 - 3) + 3 + F(3 - 2) + 3;
i.e.,
F(3) = F(0) + "3" + F(1) + "3";
· F(0) → "-" (Base case)
· Evaluate F(1):
F(1) = F(1 - 3) + 1 + F(1 - 2) + 1;
i.e.,
F(1) = F(-2) + "1" + F(-1) + "1";
· F(-2) → "-" (Base case)
· F(-1) → "-" (Base case)
Thus,
F(1) = "-" + "1" + "-" + "1" = "-1-1";
Now substitute back into F(3):
F(3) = "-" + "3" + "-1-1" + "3" = "-3-1-13";
4. Substitute back into F(5):
F(5) = F(2) + "5" + F(3) + "5";
i.e.,
F(5) = "-2-2" + "5" + "-3-1-13" + "5";
Final concatenation:
F(5) = "-2-25-3-1-135";
Information Booster
1. Base Case in Recursion: The base case prevents infinite recursion and serves as the stopping condition for recursive calls. In this example, N <= 0 is the base case, returning "-".
2. Concatenation in Recursion: The function builds the result by recursively solving smaller sub-problems and concatenating their outputs.
3. Common Recursion Patterns:
· Tail Recursion: The recursive call is the last operation in the function.
· Divide and Conquer: The problem is divided into smaller sub-problems (as in this example).
4. Practical Use Cases: Recursive functions like this are commonly used in parsing, tree traversals, and dynamic programming problems.