交通大學(xué)資訊工程學(xué)系

ProgramminginJavaMoreexamples,…蔡文能交通大學(xué)資訊工程學(xué)系tsaiwn@.twAgendaComputingfactorialLoopmethodRecursivemethodOtherRecursiveexamplesComputingprimesSievemethodSortinganarraySelectionSortInsertionSortBubbleSortQuickSortMergeSortList,ArrayList,GenerictypeComputingFactorialThefactorialofanintegeristheproductofthatnumberandallofthepositiveintegerssmallerthanit. - 0!=1 - 1!=1... - 5!=5*4*3*2*1=120- 6!=6*5*4*3*2*1=720... - 50!=

30414093201713378043612608166064768844377641568960512000000000000BigDecimal,BigIntegerFactorial--Iteration publicclassFactorial{ publicstaticlongfactorial(intn){ longfact=1; for(inti=2;i<=n;i++) //forLoop fact*=i; //shorthandforfact=fact*i; returnfact; } } publicclassComputingFactorial{ publicstaticvoidmain(Stringarg[]){ longa=Factorial.factorial(Integer.parseInt(arg[0])); System.out.println("Factorialof"+arg[0]+"="+a); }}InseparatefilesRecursion遞迴概念很久很久以前,這裡有一座山,山裡有一座廟,廟裡有個(gè)老和尚和小和尚,小和尚要老和尚說故事給他聽。老和尚就說:『很久很久以前,這裡有一座山,山裡友一座廟,廟裡有個(gè)老和尚和小和尚,小和尚要老和尚說故事給他聽。.....莊子與惠子游於濠梁之上。莊子曰：「鯈於出游從容，是魚之樂也?！够葑釉?『子非魚焉知魚之樂?』莊子曰:『子非我焉知我不知魚之樂?』惠子曰:『子非我焉知我不知你不知魚之樂?』莊子曰:『子非我焉知我不知你不知我知魚之樂?』惠子曰:『子非我焉知我不知你不知我不知你不知魚之樂?』莊子曰:『子非我焉知...!@#$%^&*?...Factorial–Recursion,inJava

/** *Thisclassshowsarecursivemethodtocomputefactorials.Thismethod *callsitselfrepeatedlybasedontheformula:n!=n*(n-1)! **/ publicclassFactorial2{ publicstaticlongfactorial(intn){ if(n==1)return1;

elsereturnn*factorial(n-1); } }

NFactorial(Recursive版)longfactorial(intn){if(n<0)return-factorial(-n);if(n==1||n==0)return1;returnn*factorial(n-1);}/*告訴我n-1階乘,我就給你n階乘*/#include<stdio.h>intmain(){printf("5!=%ld\n",factorial(5));}N階乘就是N乘以N-1階乘C語言版本歐幾里得的最大公約數(shù)輾轉(zhuǎn)相除法(recursive概念!)GCD(m,n)=GCD(n,m%n) 但如果n是0則答案為mlonggcd(longm,longn){if(n==0)returnm;returngcd(n,m%n);}如何寫成non-recursiveversion?最大公約數(shù)non-recursive版longgcd(longm,longn){intr;/*remainder*/while(n!=0){r=m%n;m=n;n=r;}returnm;}Recursive也可以很有趣(1/3)FibonacciSeries:(費(fèi)氏數(shù)列)一開始有一對(duì)兔子小兔子隔一個(gè)月可以長大為成兔每對(duì)成兔每隔一個(gè)月可生出一對(duì)兔子假設(shè)兔子永遠(yuǎn)不死,問第n個(gè)月時(shí)有幾對(duì)兔子？1,1,2,3,5,8,13,21,34,55,89,144,.fib(n)01234567891011=n

Recursive也可以很有趣(2/3)longfib(intn){if(n<0)return0;if(n==1||n==0)return1;returnfib(n-1)+fib(n-2);}/*給我n我就告訴你第n個(gè)月時(shí)有幾對(duì)兔子*//*第n個(gè)月兔子數(shù)=第n-1個(gè)月兔子+第n-2個(gè)月兔子*//*但是,最開始兩個(gè)月例外!*/Recursive也可以很有趣(3/3)FibonacciSeries(費(fèi)氏數(shù)列):1,1,2,3,5,8,13,21,34,55,89,144,…34/55=55/89=89/144=0.618黃金分割比:)神奇的費(fèi)氏數(shù)列:任何事物接近這些數(shù)字會(huì)有變化

請(qǐng)看..可怕的

巧合:!?三重魔力...民國34年臺(tái)灣光復(fù),民國89年變天

國民黨從日本手上搶回臺(tái)灣執(zhí)政剛好

55年!問題與思考(Recursion)寫出non-recursive版的Fibonaccifunction?考慮小兔子隔兩個(gè)月可以長大為成兔?考慮成兔的懷孕期是兩個(gè)月?其他Recursive問題Recursive版的binarysearchQuicksortHanoitowerproblem…Factorial–cacheansinaTable publicclassFactorial3{ //createanarraytocachevalues0!Through20! staticlong[]table=newlong[21]; static{ans[0]=1;}//factorialof0is1 staticintlast=0; publicstaticlongfactorial(intn){ if(n<=last)returnans[n];longtmp=ans[last];intk=last;while(k<n){tmp=(k+1)*tmp;/*(k+1)!*/if(last<20){++last;ans[last]=tmp;}++k; }/*while*/returntmp; }} Cache唸作cashComputingPrimes(1/3)Findingthelargestprimenumbersmallerthanaspecifiedinteger:

Inputintegerm,findp

msuchthatpisaprimeandifthereisprimep’>pthenp’mustbelargerthanm.Findingallprimenumbersthatsmallerthanaspecifiedinteger?

1243576891214151618201011131719ComputingPrimes(2/3)Algorithm mainidea:findprimesbyeliminatingmultiplesoftheformkj,wherejisaprimesmallerthansquare-root(m)andkisanintegersuchthatkj

m.......prime2ijsquare-root(m)

234.........234234222iiijjjComputingPrimes(3/3)Findingallprimenumbersthatsmallerthanaspecifiedinteger?

1234567891011121314151617181920Example:FindPrimes(1/2)Importjava.lang.*;publicclassSieve{ publicstaticvoidmain(String[]args){ intmax=100;//Assignadefaultvalue try{max=Integer.parseInt(arg[0]);} catch(Exceptione){}//Silentlyignoreexceptions.//Createanarraythatspecifieswhethereachnumberisprimeornot. Boolean[]isprime=newboolean[max+1];//Assumethatallnumbersareprimes,untilprovenotherwise. for(inti=0;<=max;i++)isprime[i]=true;//Weknowthatthat0and1arenotprime.Makeanoteofit. isprime[0]=isprime[1]=false;Example:FindPrimes(2/2)//Tocomputeallprimeslessthanmax,weneedtoruleoutmultiplesofall//integerslessthanthesquarerootofmax. intn=(int)Math.ceil(Math.sqrt(max)); for(inti=0;i<=n;i++){ if(isprime[i]){intk=2; for(intj=k*i;j<=max;j=(k++)*i) isprime[j]=false;} } intlargest; for(largest=max;!sprime[largest];largest--);//emptyloopbody System.out.println("Thelargestprimelessthanorequalto"+max+"is" +largest);}} SortingNumbersSorting:

Inputnnumbers,sortthemsuchthatthenumbersareorderedincreasingly. 39165482107 12345678910

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