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Programming with Recursion. Recursion : when a method calls itself Classic example: the factorial function: n! = 1 · 2 · 3 · ··· · (n - 1) · n Recursive definition: As a Java method: // recursive factorial function public static int recursiveFactorial ( int n) {

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programming with recursion
Programming with Recursion

Programming with Recursion

the recursion pattern
Recursion: when a method calls itself

Classic example: the factorial function:

n! = 1· 2· 3· ··· · (n-1)· n

Recursive definition:

As a Java method:

// recursive factorial function

public static intrecursiveFactorial(intn) {

if (n == 0) return 1; // basis case

else return n * recursiveFactorial(n- 1); // recursive case

}

The Recursion Pattern

Programming with Recursion

content of a recursive method
Content of a Recursive Method
  • Base case(s)
    • Values of the input variables for which we perform no recursive calls are called base cases (there should be at least one base case).
    • Every possible chain of recursive calls must eventually reach a base case.
  • Recursive calls
    • Calls to the current method.
    • Each recursive call should be defined so that it makes progress towards a base case.

Programming with Recursion

visualizing recursion

return

4

*

6

=

24

final answer

call

recursiveFactorial

(

4

)

return

3

*

2

=

6

call

recursiveFactorial

(

3

)

return

2

*

1

=

2

call

recursiveFactorial

(

2

)

return

1

*

1

=

1

call

recursiveFactorial

(

1

)

return

1

call

recursiveFactorial

(

0

)

Visualizing Recursion
  • Example
  • Recursion trace
    • A box for each recursive call
    • An arrow from each caller to callee
    • An arrow from each callee to caller showing return value

Programming with Recursion

example english ruler
Example: English Ruler
  • Print the ticks and numbers like an English ruler:

Programming with Recursion

using recursion

Slide by Matt Stallmann included with permission.

Using Recursion
  • drawTicks(length)
      • Input: length of a ‘tick’
      • Output: ruler with tick of the given length in the middle and smaller rulers on either side

drawTicks(length)

if( length > 0 ) then

drawTicks( length - 1 )

draw tick of the given length

drawTicks( length - 1 )

Programming with Recursion

recursive drawing method

drawTicks

(

3

)

Output

drawTicks

(

2

)

drawTicks

(

1

)

drawTicks

(

0

)

drawOneTick

(

1

)

drawTicks

(

0

)

drawOneTick

(

2

)

drawTicks

(

1

)

drawTicks

(

0

)

drawOneTick

(

1

)

drawTicks

(

0

)

drawOneTick

(

3

)

drawTicks

(

2

)

(

previous pattern repeats

)

Recursive Drawing Method
  • The drawing method is based on the following recursive definition
  • An interval with a central tick length L>1 consists of:
    • An interval with a central tick length L-1
    • An single tick of length L
    • An interval with a central tick length L-1

Programming with Recursion

java implementation 1
Java Implementation (1)

// draw ruler

public static void drawRuler(intnInches, intmajorLength) {

drawOneTick(majorLength, 0); // draw tick 0 and its label

for (inti = 1; i <= nInches; i++) {

drawTicks(majorLength- 1); // draw ticks for this inch

drawOneTick(majorLength, i); // draw tick i and its label

}

}

// draw ticks of given length

public static void drawTicks(inttickLength) {

if (tickLength > 0) { // stop when length drops to 0

drawTicks(tickLength- 1); // recursively draw left ticks

drawOneTick(tickLength); // draw center tick

drawTicks(tickLength- 1); // recursively draw right ticks

}

}

Programming with Recursion

java implementation 2
Java Implementation (2)

// draw a tick with no label

public static void drawOneTick(inttickLength) { drawOneTick(tickLength, - 1);

}

// draw one tick

public static void drawOneTick(inttickLength, inttickLabel) {

for (inti = 0; i < tickLength; i++)

System.out.print("-");

if (tickLabel >= 0) System.out.print(" " + tickLabel);

System.out.print("\n");

}

Programming with Recursion

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