Recursive Thinking Define the solution to a problem in terms of a - - PowerPoint PPT Presentation
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The Weil Zeta Function for Curves Vy Nguyen 3:45, Cleveland L1 Elicitation of Gestures for Image Editing Andreea Bancila 4:15, Cleveland L1
Define the solution to a problem in terms of a solution to one or more “smaller” subproblems Define a base case, a subproblem that can be solved directly.
Solution to recursive case Smaller subproblem Base case
private int factorial (int n) { assert n >= 0; if (n == 0) { return 1; } return n * factorial(n-1); }
http:/ /xkcd.com/244/
Define a data structure as a piece of data followed by a smaller data structure of the same type Define a base case, a trivial piece of data with nothing following it.
Lots of short lines! Call one group of connected lines a “scribble”
A line segment, followed by A shorter Scribble Base case: an “empty” scribble
<<interface>> Scribble Empty Scribble Recursive Scribble
public class RecursiveScribble implements Scribble { / / This line private Line2D line; private Color color; / / The lines that follow it private Scribble rest; / / Methods ... }
public class EmptyScribble implements Scribble { / / No instance variables!! / / Methods ... }
selectedScribble
EmptyScribble
RecursiveScribble
in RecursiveScribble: public void setColor (Color newColor) { / / Change the color of this line color = newColor; / / Recursively change the rest of the scribble rest.setColor (newColor); } in EmptyScribble: public void setColor (Color newColor) { / / Nothing to do! }
selectedScribble
color = newColor;
selectedScribble
rest.setColor (newColor);
selectedScribble
rest.setColor (newColor);
selectedScribble
rest.setColor (newColor);
selectedScribble
setColor in EmptyScribble does nothing!
Smaller substructure => 3 More pieces of broccoli Base case => Flower Little data => Stem
End of the world in 585 billion years! http:/ / en.wikipedia.org/wiki/Tower_of_Hanoi
http:/ / www.thinkgeek.com/ images/products/zoom/ b2ae_recursion.jpg
Start End
What are the subproblems? What is the base case?
Take 1 step, then search from that step to the end. Reached the end
public boolean findMazePath() { return findMazePath(0, 0); } public boolean findMazePath (int x, int y) { if (no new neighbors to visit) { return false; } if ( (x, y) is at the goal) { return true; } else if (findMazePath (x-1, y) || findMazePath (x+1, y) || …) { return true; } else { return false; } }
Start End
Recursing
Start End
Dead end - backtrack
Start End
Recurse in a different direction
Place 8 queens on a chessboard such that no queen can capture any other queen.