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看到论坛里好多讨论大数阶乘的话题的,我也来凑个热闹,贴一个自己前段时间刚写的。
文件内的注释已经很清楚了,懒得再用中文写一遍了,请大家看英文注释吧。
文件已包含测试代码,main函数计算了1000!。
测试结果:
- [ykuang@qdcvs 0_UnSorted]$ a.out
- indexEnd: 641
- ======================== 1000! =======================
- 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
- ======================== end ===========================
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放上计算10000!(恩,不是1000!, 是10000!)的运行时间, 供大家参考:
- [ykuang@qdcvs 0_UnSorted]$ time a.out
- indexEnd: 8914
- ======================== 10000! =======================
- 2846259680917054518906413212119868890148....
- /*结果太大,论坛发帖限制,这里省略,但运行时间是硬梆梆的!*/
- ======================== end ===========================
- real 0m2.196s
- user 0m1.730s
- sys 0m0.000s
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/* LargeNumFactorial.cpp
* #g++ LargeNumFactorial.cpp
* #a.out
*/
- #include <iostream>
- #include <string>
- #include <sstream>
- #include "LargeNumMultiply.h"
- using namespace std;
- /*
- * The factorial of big number: e.g. 20000!
- *
- * Parameter:
- * N - The big number;
- * factorial - The result of factorial.
- * indexEnd - The valid max index of factResult array.
- * baseSize - How many bits of factResult[i] should be saved.
- * e.g. If N = 8, baseSize = 2,
- * then factResult[0] = 20
- * factResult[1] = 3, should be taken as 03 because baseSize if 2
- * factResult[2] = 4, should be taken as 04, but since indexEnd is 2, only 4 is good.
- * result = 40302
- *
- * If N = 8, baseSize = 3,
- * then factResult[0] = 320,
- * factResult[1] = 40, should be taken as 040, but since indexEnd is 1, only 40 is good.
- *
- * If N = 8, baseSize = 4,
- * then factResult[0] = 320, should be taken as 0320 because baseSize if 4.
- * factResult[1] = 4, should be taken as 0004, but since indexEnd is 1, only 4 is good.
- *
- * Note:
- * Make sure N is <= MAX_FACT.
- * Because every multiply result is stored at an unsigned int var, so we need to make sure
- * the every step of mutiply result should be less than UINT_MAX.
- * */
- int Factorial (unsigned int N, unsigned int *factResult, int *indexEnd, unsigned int baseSize)
- {
- if (N > MAX_FACT)
- {
- cout << "N should not be larger than: " <<MAX_FACT <<endl;
- return 0;
- }
- int valIndex = 0;
- factResult[0] = 1;
- unsigned int baseValue = 1;
- for( unsigned int k = 0; k < baseSize; k++ )
- baseValue *= 10;
- /* If baseValue * N is larger than UINT_MAX, we will overflow at factResult[j] *= i;*/
- if ( baseValue > (UINT_MAX/N))
- {
- cout <<"baseSize: "<< baseSize<<" is too large, will make factResult[i] * N larger than UINT_MAX." <<endl;
- cout <<"Please choose smaller baseSize"<<endl;
- return 0;
- }
-
- for( unsigned int i = 1; i <= N; i++ )
- {
- unsigned int add = 0;
- // Every time we multiply i, we should multily every section of factResult.
- // valIndex stands for the lagest index of elem that is valid in factResult;
- for( int j = 0; j <= valIndex ; j++ )
- {
- // Multiply of result section j.
- factResult[j] *= i;
- // Add the 'add' from lower section.
- factResult[j] += add;
- // Caculate 'add' of section j.
- add = factResult[j]/baseValue;
- // Caculate value of section j.
- factResult[j] %= baseValue;
- }
- if( add > 0 )
- // if 'add' is not 0, then store 'add' to higher section.
- factResult[++valIndex] = add;
- }
- // Store the valid index of array factResult;
- *indexEnd = valIndex;
- return 1;
- }
- string IntToStr (unsigned int value, unsigned int baseSize )
- {
- ostringstream o;
- string s="";
- if( o<<value )
- s = o.str();
- else return "";
- int j;
- int l = baseSize - s.length();
- for( j = 0; j < l; j++ )
- s = "0" + s;
- return s;
- }
- int main()
- {
- unsigned int factResult[100000];
- int indexEnd;
- int baseSize = 4;
- Factorial (1000, factResult, &indexEnd, baseSize);
- cout <<"indexEnd: "<< indexEnd << endl;
- cout <<"======================== start ======================="<<endl;
- /*
- * 8! = 40320, if baseSize is 2, then factResult:
- * factResult[0] = 4
- * factResult[1] = 3
- * factResult[2] = 20
- * Result: 40320, not 040320
- * */
- cout << factResult[indexEnd];
- for (int i = indexEnd-1; i >= 0; i-- )
- cout << IntToStr (factResult[i], baseSize);
- cout<<"\n======================== end ==========================="<<endl;
- }
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/*LargeNumMultiply.h*/
- #ifndef __MYUTILSTUFF_H
- #define __MYUTILSTUFF_H
- #include <climits>
- #include <cmath>
- #include <iostream>
- using namespace std;
- const unsigned int MAX_FACT = (unsigned int)sqrt((double)UINT_MAX);
- int Factorial (unsigned int N, unsigned int *factResult, int *indexEnd , unsigned int baseSize = 5 );
- string IntToStr (unsigned int value, unsigned int baseSize);
- void BigNumMutiply (unsigned int N1, unsigned int N2, unsigned int *factResult, unsigned int n);
- #endif
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[ 本帖最后由 softsongs 于 2007-4-29 21:14 编辑 ] |
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