1. 1 Algorithms & Data Structures for games Lecture 2B Minor Games Programming

2. 2 Algorithms and Data Structures  Feedback previous lectures  Theory: Divide and Conquer Jan Verhoeven j.verhoeven@windesheim.nl

3. 3 Theory: Divide and Conquer  10.2 Divide and Conquer  10.2.2 Closest-Points Problem  10.2.3 The Selection Problem  10.2.4 Theoretical Improvements for Arithmetic Problems

4. Divide and conquer  Another common technique to design algorithms.  Divide:  Smaller problems are solved recursively  Conquer:  The solution to the original problem is then formed from the solutions of the subproblems 4

5. Examples of divide and conquer  Section 2.4.3: maximum subsequence sum problem  Chapter 4: linear-time tree traversal strategies  Chapter 7: mergesort and quicksort 5

6. 10.2.2 Closest-Points Problem 6 Find the closest pair of points. (Better than O(N 2 ) of course)

7. P partitioned into P L and P R ; shortest distances are shown 7

8. Two-lane strip, containing all points considered for d c strip. δ (delta) = min(d l,d r ) 8

9. Nice Demo  http://www.cs.mcgill.ca/~cs251/Closest Pair/ClosestPairApplet/ClosestPairApplet.html http://www.cs.mcgill.ca/~cs251/Closest Pair/ClosestPairApplet/ClosestPairApplet.html 9

10. 10.2.3 The Selection Problem  Find the k-th smallest element in a collection S of N elements.  Of particular interest is the special case of finding the median. This occurs when k = N/2.  Just read it when you are very interested or have a lot of free time 10

11. 10.2.4 Theoretical Improvements for Arithmetic Problems  Matrix Multiplication  Just read it when you are very interested or have a lot of free time 11

12. 12 Homework to study  Homework  Study Chapter 10.2 (except 10.2.3 and 10.2.4)

13. Homework (and practice preparation) 13

14. 14 Homework exercise  Exercise and preparation for practice:  Exercise 10.16 of your study book:  Write a program to implement the closest-points algorithm in a brute force approach (see study book);  Please give a graphical presentation of the input set and the points of the solution;  You’re free to choose your programming language: C++ or C#