1 / 25

Recursion in Java

Recursion in Java. The answer to life’s greatest mysteries are on the last slide. Recursion. Recursion is a technique widely used in programming In fact some programming languages have no loops, only recursion Recursion is a key element to advanced studies such as computational intelligence

dfraser
Download Presentation

Recursion in Java

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Recursion in Java The answer to life’s greatest mysteries are on the last slide

  2. Recursion • Recursion is a technique widely used in programming • In fact some programming languages have no loops, only recursion • Recursion is a key element to advanced studies such as computational intelligence • Beginning programmers usually groan at recursion… real programmers love it!

  3. Recursion in Java • A method is recursive if it calls itself. • There are two key things in recursion • Base step: ends the recursion • Recursive step: breaks down the problem to smaller sub problems • Before you code anything, you need to find those two steps… otherwise you may not understand the problem properly

  4. Example • Here is a simple recursive java function for called countdown: public void countDown( int value ) { if( value == 0 ) System.out.println( “Blast Off!!!” );//base case, no recursion else { System.out.println( value ); countDown( value – 1);//recursive call of small problem } } LETS TRACE countDown( 5 ) BY HAND

  5. Why Recursion? • Fact: All recursion can be re written as a non recursive form with a loop • Some algorithms are exceedingly complex as a loop, yet very elegant in a recursive form. • Easier to understand  less “bugs” = better programs • Let’s take a look at Paint for a minute…

  6. The Flood Fill Algorithm • The recursion is tricky to follow, but look at how simple the code is! public void floodFill( int x, int y, Colour clicked, Colour change ) { if( outOfBounds(x,y) || getColour(x,y) == change || getColour(x,y) != clicked ) return;//nothing to do – base case setColour(x,y,change);//colour is the same as was clicked, change it //Recursive call on neighbours floodFill( x + 1, y, clicked, colour ); floodFill( x, y + 1, clicked, colour ); floodFill( x - 1, y, clicked, colour ); floodFill( x, y - 1, clicked, colour ); }

  7. Getting the hang of it? • Let’s try a couple together • Base step • Recursive step • Sum of n numbers • Ex. 1 + 2 + 3 + 4 + 5 = 15 • Factorials • 0! = 1 • 3! = 3 x 2 x 1 = 3 x 2! • 100! = 100x99x98x..x3x2x1 = 100 x 99!

  8. Still Need Practice? • Here are two other famous recursive examples: • Fibonacci numbers • 1st number is 1, 2nd number is 1 • Every number after 2 is the sum of the previous two: 1,1,2,3,5,8,13,… • Euclid’s GCF (from ~300BC) • http://en.wikipedia.org/wiki/Euclidean_algorithm • Take the larger of the two and divide it by the smaller • If the remainder is zero, return the smaller number • Otherwise take the GCF of smaller and remainder • Example let’s try 60 and 105

  9. Pascal’s Triangle

  10. Pascal’s Triangle Cont’ • What’s the recursive pattern in Pascal’s triangle? • Hint: Number each row and column • What is/are the base case(s)? • What is the recursive case?

  11. Performance: Loops vs. Recursion • Why not always use recursion if it makes our code easier to understand? • The key reason is performance • Recursion can quickly overflow the computer’s memory • Each method call has its own “stack” in memory when it is called (holds variables, loops, etc.) • When you make a recursive call, another copy of the method is stored in memory to preserve the state when it returns. • With loops, the variables are reused • Last I had heard, Sun’s java compiler will translate tail recursion into a loop for you • Tail recursion means the recursive call is the last piece of code in the method (nothing is computed after it returns)

  12. Recursion in Memory • Consider a call to factorial( 3 ): • factorial(3)  3 * factorial(2)  2 * factorial(1)  1 * factorial(0) 1 Recursion ends, return to last caller: 1 * 1 = 1  2 * 1 = 2  3 * 2 = 6

  13. Recursion in Memory • With a loop it would look like this: public int factorial( int n ) { int fac = 1; for( int counter = 2; counter <= n; counter++ ) fac *= counter; return fac; } A call to factorial( 3 ) is now just: 1 * 2 * 3 = 6

  14. The H-Fractal • I’ll code a fractal with you so you can see just how powerful recursion is for problem solving • It would probably take me all day to code this with a loop • I can do it with recursion in about 5 minutes

  15. Exercises • Create a recursive method to calculate the sum of squares: • For example, sumSquares( 3 ) • Is 1 + 4 + 9 = 14

  16. Exercises • Create a recursive method to calculate positive integer exponents • Ex. • findExponent( 3, 2 ) • Returns 9

  17. Exercises • Create a recursive method to determine if the values in an array are increasing • You need an extra parameter telling you which index to start testing from • isIncr( int[] data, int start ) • isIncr( {1,3,5,9},0 ) returns true • isIncr( {3,1,2,4},0 ) returns false

  18. Exercises • Create a recursive method to sum the values in an array: • sum( int[] data, int start ) • sum( {4,2,5}, 0 ) • Returns 11

  19. Exercises • Create a recursive method called reverse that reverses the elements in an array • Reverse( int[] data ) • Reverse( {1,3,5,2,7 } ) • {7,2,5,3,1}

  20. Exercises – Reverse Cont’ • Sometimes when we are using recursion, we will write a helper method to hold more parameters. • In the previous example to reverse an array you should write a helper method called: • ReverseHelper( int[] data, int start, int end ) • When you call Reverse( int[] data ) use the helper method as follows (it does all the work) • ReverseHelper( data, 0, data.length)

  21. Exercises • Create a recursive method to determine whether or not a word is a palindrome or not. • A palindrome is a word spelled the same forwards and backwards • For example Ogopogo • public boolean isPalidrome(String word)

  22. Exercises • To convert an integer to base 2 (binary) here is an algorithm: • public String toBinary( int n ) • If the number is zero, return 0 • Otherwise, • Compute the quotient and remainder when dividing by 2 • The binary value of the number given is the binary value of the quotient followed by the remainder

  23. Binary Numbers • Ex. Binary value of 13: Calculation Quotient Remainder 13/2 6 1 6/2 3 0 3/2 1 1 1/2 0 1 0 return 0 13 = 01101 in binary

  24. Bonus Graphics - Fractals • Three fractals which can be created using recursion are: • Sierpinski’s Gasket • Koch’s Snowflake • Dragon Fractal • Create a recursive graphics program to display any of these fractals at a given level • Demo will be done in class for each fractal and how they can be obtained

  25. Life’s Greatest Mysteries Revealed! • The answer to life’s greatest mysteries are on the first slide

More Related