233-234

1. 233-234 chazelle@cs.princeton.edu Sedgewick & Wayne (2004); Chazelle (2005)

2. theory experimentation computation

3. theory experimentation 1950... computation

4. theory experimentation 2005... computation

5. experimentation theory 2005 computation Moore’s Law

6. No Moore’s Law there ! Inverse Moore’s Law?

7. 1. Power of algorithms

8. 1. Power of algorithms 2. Duality: data & programs 3. Recursion

9. A program in C /**/char q='"',*a="*//**/char q='%c',*a=%c%s%c*/};)b(stup;]d[b=]d-472[b)--d(elihw;)q,a,q,q,2+a,b(ftnirps;)b(stup{)(niam;731=d tni;]572[b,",b[275];int d=137;main(){puts(b);sprintf(b,a+2,q,q,a,q);while(d--)b[274-d]=b[d];puts(b);}/*c%s%c%=a*,'c%'=q rahc/**//*"=a*,'"'=q rahc/**/ (By Dan Hoey) palindrome

10. A program in C char*s="char*s=%c%s%c;void main(){ printf(s,34,s,34);}";void main(){printf(s,34,s,34);}

11. A program in php <?php $s='<?php $s=%c%s%c; printf($s,39,$s,39); ?>'; printf ($s,39,$s,39); ?>

12. A program in perl $s="$s=%c%s%c;printf$s,34,$s,34;";printf$s,34,$s,34;

13. A program in python l='l=%s;print l%%`l`';print l%`l`

14. A program in Java class S{public static void main(String[]a){String s="class S{ public static void main(String[]a){String s=;char c=34; System.out.println(s.substring(0,52)+c+s+c+s.substring(52));}}"; char c=34; System.out.println(s.substring(0,52)+c+s+c+s.substring(52));}} Output = ? class S{public static void main(String[]a){String s="class S{ public static void main(String[]a){String s=;char c=34; System.out.println(s.substring(0,52)+c+s+c+s.substring(52));}}"; char c=34; System.out.println(s.substring(0,52)+c+s+c+s.substring(52));}}

15. A Print next statement twice B Why does Schroedinger hate cats? Output = ? Why does Schroedinger hate cats? Why does Schroedinger hate cats? AB  BB

16. AA  AA Set B=A Print next statement twice Print next statement twice Output = ? Print next statement twice Print next statement twice

17. duality

19. Babbage (1820) input data output data program data Rogozhin (1996) : 24 states

20. Print next statement twice Why does Schroedinger hate cats? Print next statement twice Print next statement twice recursion

21. duality Print next statement twice Print next statement twice recursion

22. Self-reproduction = duality + recursion

23. duality gene - protein dble-stranded recursion http://www.accessexcellence.org/RC/VL/GG/dna_replicating.html

24. What is the difference between classical math and computer science ?

25. Jos Leys

27. Protein Interaction Network Jeong et al

28. Adjacency matrix

29. Adjacency lists

30. Adjacency List Implementation publicclass Graph { privateint V; private Node[] adj; privateint[] degree; privatestaticclass Node { int vertex; Node next; Node(int v, Node next) { this.vertex = v; this.next = next; } } Node next vertex

31. Adjacency List Implementation publicclass Graph { privateint V; private Node[] adj; privateint[] degree; privatestaticclass Node { int vertex; Node next; Node(int v, Node next) { this.vertex = v; this.next = next; } } public Graph(int V) { this.V = V; adj =new Node[V]; degree =newint[V]; } graph on V verticeswith no edges Node Node Node Node Node Node

32. Adjacency List Implementation publicint V() { return V; } publicvoid addEdge(int v,int w) { adj[v]=new Node(w, adj[v]); adj[w]=new Node(v, adj[w]); degree[v]++; degree[w]++; } # vertices add w to v's adjacency listadd v to w's adjacency list v x y z w

33. Adjacency List Implementation publicint V() { return V; } publicvoid addEdge(int v,int w) { adj[v]=new Node(w, adj[v]); adj[w]=new Node(v, adj[w]); degree[v]++; degree[w]++; } # vertices add w to v's adjacency listadd v to w's adjacency list v x y z w

34. Adjacency List Implementation publicint V() { return V; } publicvoid addEdge(int v,int w) { adj[v]=new Node(w, adj[v]); adj[w]=new Node(v, adj[w]); degree[v]++; degree[w]++; } # vertices add w to v's adjacency listadd v to w's adjacency list v x y z w

35. Adjacency List Implementation publicint V() { return V; } publicvoid addEdge(int v,int w) { adj[v]=new Node(w, adj[v]); adj[w]=new Node(v, adj[w]); degree[v]++; degree[w]++; } # vertices add w to v's adjacency listadd v to w's adjacency list w v x y z w

36. Adjacency List Implementation publicint V() { return V; } publicvoid addEdge(int v,int w) { adj[v]=new Node(w, adj[v]); adj[w]=new Node(v, adj[w]); degree[v]++; degree[w]++; } # vertices add w to v's adjacency listadd v to w's adjacency list w v x y z w

37. Adjacency List Implementation publicint V() { return V; } publicvoid addEdge(int v,int w) { adj[v]=new Node(w, adj[v]); adj[w]=new Node(v, adj[w]); degree[v]++; degree[w]++; } # vertices add w to v's adjacency listadd v to w's adjacency list w v x y z w

38. Adjacency List Implementation publicint V() { return V; } publicvoid addEdge(int v,int w) { adj[v]=new Node(w, adj[v]); adj[w]=new Node(v, adj[w]); degree[v]++; degree[w]++; } # vertices add w to v's adjacency listadd v to w's adjacency list v w x y z w

39. Return list of neighbors of v as an array publicint[] neighbors(int v) { int[] neighbors =newint[degree[v]]; int i =0; for(Node x = adj[v]; x !=null; x = x.next) neighbors[i++]= x.vertex; return neighbors; } x x v a b c null d i= 0 i= 1 i= 2 i= 3 d b c a adj neighbors

42. Hansel & Gretel random walk 1. Birds eat the bread crumbs DFS/BFS 2. They don’t

44. Diffusion equation

45. Random walk Diffusion equation Normal distribution 3 views of the same thing

47. Hansel & Gretel With bread crumbs one can find exit in time proportional to V+E DFS/BFS

48. Undirected Depth First Search A H I B C G Adjacency Lists A: F C B GB: AC: AD: F EE: G F DF: A E D:G: E A:H: I:I: H: D E F

49. Undirected Depth First Search A H I B C G D E F newly discovered F visit(A) (A, F) (A, C) (A, B) (A, G) Stack

50. Undirected Depth First Search A H I A alreadymarked B C G D E visit(F) (F, A) (F, E) (F, D) F visit(A) (A, F) (A, C) (A, B) (A, G) Stack