Recursion: Base Case and Recursive Case
A recursive function solves a problem by calling itself on a smaller or simpler instance.
Summary
A recursive function solves a problem by calling itself on a smaller or simpler instance. Correct recursion requires both a stopping condition and progress toward that condition along every recursive path.
| Component | Role |
|---|---|
| Base case | Returns a directly solvable result without another recursive call. |
| Recursive case | Calls the same function on a reduced problem and uses its result. |
For factorial on nonnegative integers, the base case is , and the recursive rule is for integers . A termination measure is a nonnegative integer quantity that strictly decreases along each recursive path until a base case is reached.
🧠 Key Concepts
- Base case
- Recursive case
- Termination measure
- Stack frame
- Stack unwinding
- Return propagation
- Stack overflow
- Factorial complexity
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Recursion: Base Case and Recursive Case
📘 Overview A recursive function solves a problem by calling itself on a smaller or simpler instance. Correct recursion requires a base case that stops further calls and a recursive case that makes progress toward it.
🧠 Key Idea Every recursive path must eventually reach a base case. The recursive case reduces the problem and uses the result of the smaller call to produce the current result.
⚔️ Core Details: - A base case returns a result without making another recursive call. - A recursive case calls the same function with an input that moves toward a base case. - For factorial on nonnegative integers, the base case is . - The recursive factorial rule is
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