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Section 7.4 Summary & Reading Questions
Recursion solves problems by defining a
base case and a
recursive step ; each call reduces the problem size until the base case is reached.
Java methods must declare visibility, static/instance context, return type, and parameter types; e.g.,
public static int factorial(int n).
The recursive logic in Java mirrors Python conceptually, but Java uses curly braces
{} and explicit types instead of indentation and dynamic typing.
The helper method pattern hides implementation details (like array indices) from callers, providing clean public interfaces while managing recursive state privately.
Deep or unbounded recursion can exhaust the call stack: Python raises
RecursionError; Java throws
StackOverflowError.
Neither Java nor Python guarantees tail call optimization, so programmers should use iterative solutions for algorithms that would require very deep recursion.
Recursive methods in Java must specify return types explicitly, unlike Python’s dynamic typing, which affects how you handle error cases and return values.
Reading Questions Reading Questions
1.
Which method signature and behavior best match a typical Java recursive factorial implementation?
public static int factorial(int n) that returns
0 when
n <= 0 and otherwise returns
n * factorial(n - 1).
No. While this handles negative numbers, the base case is incorrect - factorial of 0 should be 1, not 0.
public void factorial(int n) that prints each partial product and stops when
n reaches zero.
No. Printing results is fine for testing, but a proper factorial method should return the computed value.
public static int factorial(int n) that returns
1 when
n <= 1 and otherwise returns
n * factorial(n - 1).
Correct. This matches the standard recursive factorial definition in Java.
public static long factorial(int n) that returns
1 when
n == 0 and otherwise returns
n * factorial(n - 1).
No. While this logic is close, it doesn’t handle the case when n = 1, and using long as return type when int parameter is used creates inconsistency.
2.
Why use a private helper method (e.g.,
sumHelper(int[] arr, int index)) behind a public method (e.g.,
sumArray(int[] arr)) in recursive array processing?
Because it allows Java to automatically optimize the recursion for faster execution.
No. Java does not automatically optimize recursion just because you use a helper method.
To keep the public API simple while encapsulating extra recursion state (such as the current index) inside a private method.
Correct. This keeps the interface clean while hiding internal details from the caller.
Because public methods cannot take more than one parameter in recursive calls.
No. Public methods can take multiple parameters; this is about interface clarity, not parameter limits.
To eliminate the need for a base case by handling termination in the helper method automatically.
No. The helper method still needs an explicit base case to stop recursion.
3.
Which statement about recursion limits and errors is accurate?
When the call stack is exhausted, Python raises a
RecursionError whereas Java throws a
StackOverflowError, and neither language applies automatic tail call optimization.
Correct. This difference in exception types and the lack of built-in tail call optimization is a key distinction between the two languages.
Java automatically applies tail call optimization to recursive methods marked as
final, preventing most stack overflows.
No. Java does not perform automatic tail call optimization, regardless of whether methods are marked as final.
Declaring a recursive method as
static in Java reduces memory usage per call, allowing more recursive calls before a stack overflow occurs.
No. The static modifier changes method context (class vs. instance) but does not meaningfully affect per-call stack memory usage.
The JVM can detect simple recursive patterns and automatically convert them to iterative loops to prevent stack overflow.
No. The JVM does not automatically convert recursive methods to iterative ones. This optimization must be done manually by the programmer.
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