Engineering Principles in Software Engineering

1. Engineering Principles in Software Engineering five important concepts in CS that you will learn that can enhance software development

2. 1. Divide-and-conquer • a general strategy for solving problems • an aspect of Computational Thinking • break problems into smaller sub-problems, which might be easier to solve (if decoupled) • example: chess moves • if I could just capture the opponents queen, then I could.... • or break large datasets into smaller pieces

3. example: mergesort • given a list of numbers in random order • split the list into 2 halves • sort each half independently • merge the two sub-lists (interleave) ← here is a list to sort ←divide into 2 sub-lists ←sort each separately ←merge them back together 1 18 22 17 6 13 9 10 7 15 14 4 1 18 22 17 6 13 | 9 10 7 15 14 4 1 6 13 17 18 22 | 4 7 9 10 14 15 1 4 6 7 9 10 13 14 15 17 18 22

4. 2. Recursion • a form of divide-and-conquer • write functions that call themselves • example: factorial n! = 1x2x3...n = n(n-1)! def fact(n): if n<=1: return 1 // base case return n*fact(n-1) • example: mergesort • when you divide list into 2 halves, how do you sort each half – by calling mergesort, of course! call trace: fact(3) => fact(2) => fact(1) 1 <= 2*1=2<= 3*2=6 <=

5. 3. Greedy algorithms • most implementations involve making tradeoffs • we know NP-complete problems are hard and probably cannot be solved in polynomial time • use a heuristic/shortcut – might get a pretty good solution (but not optimal) in faster time • greedy methods do not guarantee an optimal solution • however, in many cases, a near-optimal solution can be good enough • it is important to know when a heuristic will NOT produce an optimal solution, and to know how sub-optimal it is (i.e. an “error bound”)

6. Examples of greedy algorithms • navigation, packet routing, shortest path in graph, robot motion planning • choose the “closest” neighbor in the direction of the destination • document comparison (e.g. diff) • start by aligning the longest matching substrings • knapsack packing • choose item with highest value/weight ratio first • scheduling • schedule the longest job first, (or the one with most constraints) ..out to be more efficient to find thelength of the longest subsequence. Then in the case where the...... .....increase the efficiency using thelength of the longest subsequence. But if the first characters differ..

7. 4. Caching • One way to improve the efficiency of many programs is to use caching – saving intermediate results in memory that will get used multiple times • why calculate the same thing multiple times? • might require designing a special data structure (e.g. a hash table) to store/retrieve these efficiently • amortization: the cost of calculating something gets divided over all the times it is used

8. calculating Fibonacci numbers • F(n) = F(n-1)+F(n-2) • base cases: F(1) = F(2) = 1 • this sequence of numbers arises in several patterns in nature, as well as the stock market • 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... • (show how calculating this slows down, and can be dramatically speeded up by caching results of previous function calls)

9. 80486 • Caching also applies to hardware design • memory hierarchy • for constants or global variables that get used frequently, put them in a register or L1 cache • analog to a “staging area” • variables used infrequently can stay in RAM • very large datasets can be swapped out to disk 1kb cache

10. B 18 22 20 A C 25 32 D 19 B E 18 22 26 20 A C 25 32 D • An important example of caching is Dynamic Programming • Suppose our goal is to compute the min. travel distance between A and E • build-up a table of smaller results for a subgraph

11. 19 B E 18 22 26 20 A C 25 32 D • extend table for larger results • add row/column for E • E connects to the network at B and C • compute dist of XE based on XB and XC d(D,E)=min[d(D,B)+19,d(D,C)+26] =min(47+19,25+26) =min(66,51)=51 d(A,E)=min[d(A,B)+19,d(A,C)+26] =min(18+19,20+26) =min(37,47)=37

12. 5. Abstraction and Reuse • Abstraction is the key to becoming a good programmer • don’t reinvent the wheel • more importantly, reuse things that have already been tested and debugged • This is the basis of Object-Oriented Programming

13. Many large software projects are built by plugging components together • write a small amount of (“glue”) code the makes things work together • example: creating a web browser out of: a) an HTML text parser b) a display engine (graphics, windows) c) URL query/retrieval network functions d) plug-ins

14. Examples of Abstraction • Making a function out of things you do repeatedly • parameterizing it so it can be applied to a wider range of inputs

15. Here is output for scores of Aggies in basketball games so far this year: histo([82,91,68,75,79,88,67,52,74,73,52,41,63,69,57,75,72,51,55,52,36,72]) 50 **** 55 ** 60 * 65 *** 70 **** 75 *** 80 * 85 * 90 * 95 Here is code for printing a histogram of basketball scores (which typically range between 50 and 100 points): def histo(Scores): i = 50 while i<100: c = 0 for s in Scores: if si and s<i+5: c += 1 print i,’*’*c i += 5

16. Here is output for scores of Aggies in football games last year: histo([52,65,42,42,45,41,41,56,57,51,10,21,52],A=0,B=70,S=10) 0 10 * 20 * 30 40 ***** 50 ***** 60 * Suppose we want to generalize this code for printing a histogram of football scores too, which span a different range. Add parameters of lower and upper bound of histogram A and B, and step size S. def histo(Scores,A,B,S): i = A while i<B: c = 0 for s in Scores: if si and s<i+S: c += 1 print i,’*’*c i += S

17. Object-oriented classes • encapsulation – define internal representation of data • interface – define methods, services • good design – make the external operations independent of the internal representation (helps decouple code) • example: a Complex number is a ‘thing’ that can be added/subtracted, multiplied (by another Complex or a scalar), conjugated, viewed as (a+bi) or (reiq)

18. class Complex { double re,im; // interval variables public: // constructor (initialization) Complex(double x,double y) { re = x; im = y; } void conjugate() { im *= -1; } double magnitude() { double z=re*re+im*im; return sqrt(z); } void print() { cout << "(" << re << "+" << im << "i)"; } }; • Here is an example of class definition of Complex Numbers in C++ A Complex object representing 1+2i has two member variables for holding the real and imaginary components. re=1.0 im=2.0

19. #include <iostream> #include <iomanip> #include <math.h> using namespace std; class Complex {...from previous slide... }; int main() { Complex p=Complex(1,2); cout << “|p|=“ << p.magnitude() << "\n"; Complex p2=p+p; // custom addition } Note how we get the magnitude of a Complex object by invoking a method on it, p.magnitude(). The calculation is done internally to the object. Output: > g++ complex.cpp –o complex -lm > complex p = (1.0+2.0i) |p| = 2.23607

20. Templates in C++ • if you can sort a list of integers, why not generalize it to sort lists with any data type that can be pairwise-compared (total order)? 1 2 3 5 6 4 9 8 7 1 2 3 4 5 6 9 8 7 1 2 3 5 6 4 9 8 7 1 3 5 2 6 4 9 8 7 void insertionSort(int a[], int n) { for (int i = 1; i <= n; i++) { int temp = a[i]; for (int j=i; j>0; j--) if(temp < a[j-1]) a[j] = a[j-1]; else break; a[j] = temp; } }

21. Templates in C++ • can use same algorithm to sort any type T, as long as element can be compare with ‘<‘ operator • works on float, characters, strings... template <class T> void insertionSort(T a[], int n) { for(int i = 1; i <= n; i++) { T temp = a[i]; for (int j=i; j>0; j--) if(temp < a[j-1]) a[j] = a[j-1]; else break; a[j] = temp; } } defined for string, characters, floats...

22. API design – Application-Programmer Interface • a coherent, complete, logical system of functions and data formats • example: OCR (optical character recognition) • you don’t want to have to implement feature-based character recognition that is font- and scale-independent yourself (probably) • interface defines input (e.g. scanned TIFF images) and output (e.g. ASCII strings) String* OCRscan(TiffImage* input_image) • are you going to indicate coordinates where word was found on the page? • is the user able to load different character sets (alphabets)?

23. Engineering Principles in Software Engineering A summary of the key ideas we talked about... 1. divide-and-conquer 2. recursion 3. greedy algorithms, tradeoffs 4. caching, dynamic programming 5. abstraction and reuse