1. What makes a good language Does the task you want Keeps you from making mistakes Supports debugging when you need it Has a strong tool kit

2. Big number bug On June 4, 1996 an unmanned Ariane 5 rocket launched by the European Space Agency exploded just forty seconds after its lift-off from Kourou, French Guiana. The rocket was on its first voyage, after a decade of development costing $7 billion. The destroyed rocket and its cargo were valued at $500 million. A board of inquiry investigated the causes of the explosion and in two weeks issued a report. It turned out that the cause of the failure was a software error in the inertial reference system. Specifically, a 64 bit floating point number relating to the horizontal velocity of the rocket with respect to the platform was converted to a 16 bit signed integer. The number was larger than 32,768, the largest integer that could be stored in a 16 bit signed integer, and so the conversion failed.

3. Pentium II bug Software bug encoded in hardware Division algorithm uses a lookup table of 1066 entries Only 1061 of the entries are downloaded to the PLA (programmed logic array from which the data are used) Intel had to recall all versions of the chip

4. Syntax “typo” bugs NASA Mariner 1, Venus probe (1992) Intended to be the first US spacecraft to visit another planet, it was destroyed by a range officer on 22 July 1962 when it behaved erratically four minutes after launch. –Essentially a period instead of a comma in a FORTRAN DO-Loop

5. Control flow bug AT&T long distance service fails for nine hours (Wrong BREAK statement in C code) January 15, 1990: 70 million of 138 million long distance customers in the US lost long distance service. Cost to ATT was between $ 75 Million and $100 Million (plus the loss of good will).

6. E-mail buffer overflow (1998) Several E-mail systems suffer from a "buffer overflow error", when extremely long e-mail addresses are received. The internal buffers receiving the addresses do not check for length and allow their buffers to overflow causing the applications to crash. Hostile hackers use this fault to trick the computer into running a malicious program in its place. Data structure management bug

7. Summary Programming is difficult –Have to thoroughly understand the task –Have to anticipate all possibilities –Code is written at a fairly primitive level –Impossible to anticipate what users might do Programming languages allow the user to use tools to build code But everything still has bugs The cost of a bug can be very large There is no Moore’s Law for software.

8. The big picture We built a computer We talked about languages and compilers to make programming the computer easier Next we talk about algorithms, which are implemented by programs

9. Algorithms Recipes for doing computations The underpinnings of programming –Think out your algorithm –Show that it works –Determine it’s efficiency –Write it as a program

10. What is an algorithm Algorithm is a recipe Has –Inputs –Rules –Evaluation Criteria –Output

11. When Do We Use Algorithms When we have a problem to solve Examples of problems –Baking cookies –Putting things in alphabetical order –Searching the Web

12. Chocolate chip cookies

13. Input –flour (2 ¼ c) –baking soda (1t) –salt (1t) –butter (1c) –granulated sugar (3/4 c) –brown sugar(3/4c) –vanilla(1t) –eggs (2) –chocolate chip morsels (2c) –chopped nuts (1c) Output –5 dozen cookies

14. Chocolate chip cookies: Steps Combine flour, baking soda, and salt in small bowl. Beat butter, granulated sugar, brown sugar and vanilla in large bowl Add eggs one at a time Beating after adding each egg Gradually beat in flour mixture Stir in morsels and nuts Drop by rounded tablespoons onto ungreased baking sheets Bake 9-11 minutes Let stand for 2 minutes

15. Chocolate chip cookie algorithm Primitives –Inputs Flour, baking soda, salt, butter, brown sugar, granulated sugar, vanilla, egg, morsels, nuts Alternatively, chocolate chip cookie mix Alternatively, wheat, sugar cane, … –Operators Combine, Beat, Gradually beat, Stir, Drop, Bake, Let stand

16. Chocolate chip cookie algorithm Execution –First 2 steps can be done in parallel? Parbegin (Combine(),Beat()) Parend –Machine dependencies Ovens vary (Bake 9-11 minutes) Ingredients vary and so need to be handled differently

17. Chocolate chip cookie algorithm Algorithm testing –Proof of the pudding is in the eating –How do we mechanize this?

18. Chocolate chip cookie algorithm Comparing different algorithms –Quality of results –User time –Machine (oven) time

19. Putting things in alphabetical order Data set sizes –Course list for COS 11110-15 students –PU directory assistance10,000 people –Manhattan phone book1 million people –Social Security database1 billion records –Long distance call billing records 100 billion/year Different methods for different tasks –Fast for large –Simple for small

20. A simple method for sorting Find smallest value -- put it first in list Find second smallest value -- put it second … Find next smallest value – put it next … When no more values, you’re done

21. How it works 57 190 219 34

22. How it works Find smallest value -- put it first in list 57 190 219 34 190 219 57

23. How it works Find second smallest value -- put it second 57 190 219 34 190 219 57 34 57 219 190

24. How it works Finish the sorting 57 190 219 34 190 219 57 34 57 219 190 34 57 190 219

25. A simple method for sorting To sort array x = {x[1],x[2], …, x[n]} For I = 1 to n For J = I+1 to n If (x[I] > x[J]) Then swap their values next

26. Another sorting algorithm Sorting by Merging Key idea  It’s easy to merge 2 sorted lists

27. Merging 2 sorted lists 190 219 463 155 255 355

28. Merging 2 sorted lists 190 219 463 155 255 355 Start at the top of each list

29. Merging 2 sorted lists 190 219 463 155 255 355 190 is bigger than 155

30. Merging 2 sorted lists 190 219 463 155 255 355 155 Record 155 and move the arrow

31. Merging 2 sorted lists 190 219 463 155 255 355 155 190 190 is less than 255

32. Merging 2 sorted lists 190 219 463 155 255 355 155 190 219 219 is less than 255

33. Merging 2 sorted lists 190 219 463 155 255 355 155 190 219 255 255 is less than 463

34. Merging 2 sorted lists 190 219 463 155 255 355 155 190 219 255 355 463 Finished when at the end of each list

35. Sorting by Merging Key idea  It’s easy to merge 2 sorted lists Sort larger lists by –Sorting smaller lists –Merging the results How do we sort smaller lists?

36. Sort then merge 157 227 345 134 157 227 345 134 Subdivide

37. Sort then merge 157 227 345 134 157 227 345 134 157 227 134 345 Subdivide Sort pieces By merging

38. Sort then merge 157 227 345 134 157 227 345 134 157 227 134 345 134 157 227 345 Subdivide Sort piecesMerge

39. SortMerge algorithm Function SortMerge(x,1,n) -- sort list of n elements x If n = 1 then Return -- nothing to sort End if Mid = (1+ n)/2-- midpoint of list SortMerge(x,1, Mid )-- sort first half of list SortMerge(x, Mid +1, n)-- sort second half of list Merge(x,1, Mid, Mid +1, n)-- merge sorted halves End Function

40. Does it work? Have to be careful about stopping There are always a lot of things going on Sort(n) Sort(n/2) Merge Sort(n/4) Merge Sort(n/2) Merge Sort(n/8) Merge Sort(n/4) Merge Sort(n/2) Merge

41. Divide and conquer Use recursion –reduce solving for problem of size n to solving two problems of size n/2 –then combine the solutions S(n) = 2 S(n/2) + M(n/2,n/2) Solving a sorting problem of size n requires solving 2 sorting problems of size n/2 and doing a merge of 2 sets of size n/2

42. Comparing running times NInsertion (ms) SortMerge(ms) 1001 0 2002 0 100058 1 10,0005841 11 100,000626943 162 1,000,00070626916 3421

43. Comparing running times NInsertion (ms) SortMerge(ms) 1001 0 2002 0 100058 1 10,0005841 11 100,000626943 162 1,000,00070626916 3421 Reducing 20 hours to 3 seconds

44. Searching Once a list is in alphabetical order, how do you find things in it? For example, is COS 111 on the list of courses that satisfy the (EC) Epistemology and Cognition requirement?

45. EC courses PHI 201 PHI 204 PHI 301 PHI 304 PHI 312 PHI 321 PHI 333 PHI 338 PSY 255 PSY 306 PSY 307 PSY 316 AAS 391 ANT 201 COS 302 FRS 135 FRS 137 GER 306 HUM 365 LIN 213 LIN 302 LIN 306 LIN 315 PHI 200

46. Searching for COS 111 Compare to the middle AAS 391 ANT 201 COS 302 FRS 135 FRS 137 GER 306 HUM 365 LIN 213 LIN 302 LIN 306 LIN 315 PHI 200 PHI 201 PHI 204 PHI 301 PHI 304 PHI 312 PHI 321 PHI 333 PHI 338 PSY 255 PSY 306 PSY 307 PSY 316 COS 111

47. Searching Compare to the middle If smaller search first half If larger search second half AAS 391 ANT 201 COS 302 FRS 135 FRS 137 GER 306 HUM 365 LIN 213 LIN 302 LIN 306 LIN 315 PHI 200 PHI 201 PHI 204 PHI 301 PHI 304 PHI 312 PHI 321 PHI 333 PHI 338 PSY 255 PSY 306 PSY 307 PSY 316 COS 111

48. Repeat Compare to the middle If smaller search first half If larger search second half AAS 391 ANT 201 COS 302 FRS 135 FRS 137 GER 306 HUM 365 LIN 213 LIN 302 LIN 306 LIN 315 PHI 200 COS 111

49. Building indices PHI 201 PHI 204 PHI 301 PHI 304 PHI 312 PHI 321 PHI 333 PHI 338 PSY 255 PSY 306 PSY 307 PSY 316 AAS 391 ANT 201 COS 302 FRS 135 FRS 137 GER 306 HUM 365 LIN 213 LIN 302 LIN 306 LIN 315 PHI 200 AAS ANT COS FRS GER HUM LIN PHI PSY

50. Search indices then data PHI 201 PHI 204 PHI 301 PHI 304 PHI 312 PHI 321 PHI 333 PHI 338 PSY 255 PSY 306 PSY 307 PSY 316 AAS 391 ANT 201 COS 302 FRS 135 FRS 137 GER 306 HUM 365 LIN 213 LIN 302 LIN 306 LIN 315 PHI 200 AAS ANT COS FRS GER HUM LIN PHI PSY COS 111