Discrete Mathematics

(Software Engineering)

UI

IT Page 2 UI

Software Engineeringby Yang-Sae Moon2Page 3We are now UI Software Engineeringby Yang-Sae Moon3Page 4 . : . () (1/2)Module (, ) : .... : 0 . UI Software Engineeringby Yang-Sae Moon4Page 5

(flow chart)N-S (Nassi-Schneiderman Chart) // - (pseudo code) (decision table) (decision diagram)PDL(Program Design Language)(state transition diagram)(action diagram)() (2/2) UI Software Engineeringby Yang-Sae Moon5Page 6 : , 0, , .

. : 1 N (1/4)

SeriesSum = 0for Counter = 1 to N doSeriesSum = SeriesSum + Counterwrite "The sum is", SeriesSum

SeriesSum = (1.0 + N)*(N/2.0)write "The sum is", SeriesSum

UI Software Engineeringby Yang-Sae Moon6Page 7 () (2/4) (N3 , exponential ) : Greedy Algorithm 1101001,00010,0001Constant11111log NLogarithmic1471014NLinear1101001,00010,000N log NN log N14070010,000140,000N2Quadratic110010,0001,000,000100,000,000N3Cubic11,0001,000,0001,000,000,00010122nExponential21,0241.27 x 10301.07 x 103011.99 x 103010 UI Software Engineeringby Yang-Sae Moon7Page 8 (3/4) (TSP: Traveling Salesman Problem) N (C1, C2, CN) i j dij , (shortest tour)?

: N : (N-1) = N(N-1)(N-2)(2)(1) = N!

TSP ? 1 ns (1 GHz 1 flop/1 ns)N=10: 3,628,800 ns = 0.0036288 sec.N=50: 3.02 x 1064 ns = 3.02 x 1055 seconds = 3.50 x 1050 days = 9.59 x 1047 years ? (Refer to http://www.tsp.gatech.edu//index.html)5632516211573108498994 UI Software Engineeringby Yang-Sae Moon8Page 9 (4/4) ?Machine processible specification sequential file, random access file ? UI Software Engineeringby Yang-Sae Moon9Page 10 .

BUT, , .

. (or )

UI Software Engineeringby Yang-Sae Moon10Page 11 . , C , Pascal .

, , (1/4) UI Software Engineeringby Yang-Sae Moon11Page 12 ( ) vs. (2/4) (sequence) (selection) (iteration) UI Software Engineeringby Yang-Sae Moon12Page 13 (3/4) = + +

= [1|2|3]Module ( ; ) Assume = {1, 2, 3}0