Recursion and Modular Programming

What Recursion and Modular Programming covers

Recursion and Modular Programming is examined in Component 1, Programming and System Development. It covers recursion and the base case, how recursive calls use the stack, recursive algorithms: factorial and Fibonacci, recursion compared with iteration, integer division with DIV and MOD, standard functions and standard modules and user defined subprograms and modular design.

The 7 subtopics

Each one has its own page.

• Recursion and the base caseBase case, two essential parts of any recursive definition and what is meant by the depth of recursion.Open →
• How recursive calls use the stackCall stack used for during recursion and stack frame.Open →
• Recursive algorithms: factorial and FibonacciFibonacci sequence recursively and why the towers of Hanoi puzzle is naturally recursive.Open →
• Recursion compared with iterationWhat tail recursion means, iterative version of the factorial algorithm and why recursion can make a program harder to debug.Open →
• Integer division with DIV and MODThe whole-number quotient and the remainder, worked with real figures, and the jobs they do — extracting digits, converting units, and testing divisibility.Open →
• Standard functions and standard modulesStandard function, two standard mathematical functions found in most languages and standard module or library.Open →
• User defined subprograms and modular designUser defined subprogram, modular programming and interface of a module.Open →

What you need to know

Answer each one before you reveal it.

Take Recursion and Modular Programming further

The same content, four other ways.

Commonly confused

Pairs that lose marks when they are blurred together.

• Recursion vs Iteration

  Recursion: repeating by calling itself and building a new stack frame each time. Iteration: repeating with a loop and reusing one set of variables.

• Base case vs Recursive case

  Base case: returning without calling again. Recursive case: calling itself on a smaller problem.

• DIV vs MOD

  DIV: giving the whole number of times the divisor fits. MOD: giving what is left over.

Questions from this topic

Each one with the model answer underneath.

1. 1

   What is recursion?

   Model answer

   Recursion is a technique in which a subprogram calls itself to solve a smaller version of the same problem. Each call works on a simpler case than the one before.

2. 2

   What is a base case, and why must a recursive subprogram have one?

   Model answer

   A base case is a condition that returns an answer without any further call. Without a base case the recursion never stops and the program crashes.

3. 3

   State the two essential parts of any recursive definition.

   Model answer

   A recursive definition needs a base case that stops the recursion. A recursive case then calls the subprogram on a smaller problem.

4. 4

   What happens if the recursive case never moves towards the base case?

   Model answer

   The subprogram calls itself for ever and the call stack fills. The program halts with a stack overflow error.

5. 5

   Give the recursive definition of the factorial of a positive integer n.

   Model answer

   The factorial of 0 is defined as 1. The factorial of n is n multiplied by the factorial of n − 1.

6. 6

   Why is a recursive solution often described as elegant?

   Model answer

   A recursive solution expresses the problem almost exactly as it is defined mathematically. The code is short and its intention is clear.

What is inside Levo

Six ways to work the same material.

Recursion and Modular Programming revision questions

What does Recursion and Modular Programming cover in Eduqas A-Level Computer Science?

7 subtopics: recursion and the base case, how recursive calls use the stack, recursive algorithms: factorial and fibonacci, recursion compared with iteration, integer division with div and mod, standard functions and standard modules and user defined subprograms and modular design. Each one has its own page with questions and model answers.

How is Recursion and Modular Programming organised?

By the Eduqas A500QS specification, subtopic by subtopic, so it matches the order you are taught it in.