?? 完美數(shù).mht
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Subject: =?gb2312?B?zerDwJS1?=
Date: Wed, 13 Sep 2006 01:15:23 +0800
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<HTML><HEAD><TITLE>=A7=B9=AC=FC=BC=C6</TITLE>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Dbig5"><LINK=20
href=3D"http://www.java3z.com/cwbwebhome/article/article3/AlgorithmGossip=
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<H3><A=20
href=3D"http://caterpillar.onlyfun.net/Gossip/index.html">http://caterpil=
lar.onlyfun.net/Gossip/index.html</A></H3>
<H1><A=20
href=3D"http://www.java3z.com/cwbwebhome/article/article3/AlgorithmGossip=
/AlgorithmGossip.htm">Algorithm=20
Gossip: =A7=B9=AC=FC=BC=C6</A></H1>
<H2>=BB=A1=A9=FA</H2>=A6p=AAG=A6=B3=A4@=BC=C6n=A1A=A8=E4=AFu=A6]=BC=C6=A1=
]Proper =
factor=A1^=AA=BA=C1`=A9M=B5=A5=A9=F3n=A1A=ABh=BA=D9=A4=A7=AC=B0=A7=B9=AC=FC=
=BC=C6=A1]Perfect=20
Number=A1^=A1A=A8=D2=A6p=A5H=A4U=B4X=AD=D3=BC=C6=B3=A3=ACO=A7=B9=AC=FC=BC=
=C6=A1G<BR>
<DIV style=3D"FONT-WEIGHT: bold; MARGIN-LEFT: 40px"><SPAN=20
style=3D"FONT-FAMILY: Courier New,Courier,monospace">6 =3D 1 + 2 + =
3</SPAN><BR=20
style=3D"FONT-FAMILY: Courier New,Courier,monospace"><SPAN=20
style=3D"FONT-FAMILY: Courier New,Courier,monospace">28 =3D 1 + 2 + 4 + =
7 +=20
14</SPAN><BR style=3D"FONT-FAMILY: Courier New,Courier,monospace"><SPAN=20
style=3D"FONT-FAMILY: Courier New,Courier,monospace">496 =3D 1 + 2 + 4 + =
8 + 16 + 31=20
+ 62 + 124 +=20
248</SPAN><BR></DIV><BR>=B5{=A6=A1=B0=F2=A5=BB=A4W=A4=A3=C3=F8=A1A=B2=C4=A4=
@=B2=B4=AC=DD=A8=EC=AE=C9=B7|=B7Q=A8=EC=A8=CF=A5=CE=B0j=B0=E9=A8D=A5X=A9=D2=
=A6=B3=AFu=A6]=BC=C6=A1A=A6A=B6i=A4@=A8B=A8D=A6]=BC=C6=A9M=A1A=A4=A3=B9L=AD=
Yn=AD=C8=AB=DC=A4j=A1A=ABh=A6=B9=AAk=B7|=AA=E1=B6O=B3\=A6h=AE=C9=B6=A1=A6=
b=B0j=B0=E9=B4=FA=B8=D5=A4W=A1A=A4Q=A4=C0=A8S=A6=B3=AE=C4=B2v=A1A=A8=D2=A6=
p=A8D=A4p=A9=F310000=AA=BA=A9=D2=A6=B3=A7=B9=AC=FC=BC=C6=A1C<BR>
<H2>=B8=D1=AAk</H2>=A6p=A6=F3=A8D=A4p=A9=F310000=AA=BA=A9=D2=A6=B3=A7=B9=AC=
=FC=BC=C6=A1H=A8=C3=B1N=B5{=A6=A1=BCg=AA=BA=A6=B3=AE=C4=B2v=A1H=B0=F2=A5=BB=
=A4W=A6=B3=A4T=AD=D3=A8B=C6J=A1G<BR>
<OL>
<LI>=A8D=A5X=A4@=A9w=BC=C6=A5=D8=AA=BA=BD=E8=BC=C6=AA=ED=20
=
<LI>=A7Q=A5=CE=BD=E8=BC=C6=AA=ED=A8D=AB=FC=A9w=BC=C6=AA=BA=A6]=A6=A1=A4=C0=
=B8=D1=20
=
<LI>=A7Q=A5=CE=A6]=A6=A1=A4=C0=B8=D1=A8D=A9=D2=A6=B3=AFu=A6]=BC=C6=A9M=A1=
A=A8=C3=C0=CB=ACd=ACO=A7_=AC=B0=A7=B9=AC=FC=BC=C6 </LI></OL><BR><A=20
href=3D"http://www.java3z.com/cwbwebhome/article/article3/AlgorithmGossip=
/EratosthenesPrime.htm">=A8B=C6J=A4@</A>=20
=BBP <A=20
href=3D"http://www.java3z.com/cwbwebhome/article/article3/AlgorithmGossip=
/GCDPNumber.htm">=A8B=C6J=A4G</A>=20
=A6b=A4=A7=ABe=B0Q=BD=D7=B9L=A4F=A1A=B0=DD=C3D=A6b=A8B=C6J=A4T=A1A=A6p=A6=
=F3=A8D=AFu=A6]=BC=C6=A9M=A1H=A4=E8=AAk=AB=DC=C2=B2=B3=E6=A1A=ADn=A5=FD=AA=
=BE=B9D=B1N=A9=D2=A6=B3=AFu=A6]=BC=C6=A9M=A5[=A4W=B8=D3=BC=C6=A5=BB=A8=AD=
=A1A=B7|=B5=A5=A9=F3=B8=D3=BC=C6=AA=BA=A8=E2=AD=BF=A1A=A8=D2=A6p=A1G<BR>
<DIV style=3D"MARGIN-LEFT: 40px"><SPAN=20
style=3D"FONT-WEIGHT: bold; FONT-FAMILY: Courier =
New,Courier,monospace">2 * 28 =3D 1=20
+ 2 + 4 + 7 + 14 + =
28</SPAN><BR></DIV><BR>=B5=A5=A6=A1=AB=E1=AD=B1=A5i=A5H=A4=C6=AC=B0=A1G<B=
R>
<DIV style=3D"MARGIN-LEFT: 40px"><SPAN=20
style=3D"FONT-WEIGHT: bold; FONT-FAMILY: Courier =
New,Courier,monospace">2 * 28 =3D=20
(2</SPAN><SUP=20
style=3D"FONT-WEIGHT: bold; FONT-FAMILY: Courier =
New,Courier,monospace">0</SUP><SPAN=20
style=3D"FONT-WEIGHT: bold; FONT-FAMILY: Courier New,Courier,monospace"> =
+=20
2</SPAN><SUP=20
style=3D"FONT-WEIGHT: bold; FONT-FAMILY: Courier =
New,Courier,monospace">1</SUP><SPAN=20
style=3D"FONT-WEIGHT: bold; FONT-FAMILY: Courier New,Courier,monospace"> =
+=20
2</SPAN><SUP=20
style=3D"FONT-WEIGHT: bold; FONT-FAMILY: Courier =
New,Courier,monospace">2</SUP><SPAN=20
style=3D"FONT-WEIGHT: bold; FONT-FAMILY: Courier =
New,Courier,monospace">) *=20
(7</SPAN><SUP=20
style=3D"FONT-WEIGHT: bold; FONT-FAMILY: Courier =
New,Courier,monospace">0</SUP><SPAN=20
style=3D"FONT-WEIGHT: bold; FONT-FAMILY: Courier New,Courier,monospace"> =
+=20
7</SPAN><SUP=20
style=3D"FONT-WEIGHT: bold; FONT-FAMILY: Courier =
New,Courier,monospace">1</SUP><SPAN=20
style=3D"FONT-WEIGHT: bold; FONT-FAMILY: Courier =
New,Courier,monospace">)</SPAN><BR></DIV><BR>=A9=D2=A5H=A5u=ADn=A8D=A5X=A6=
]=A6=A1=A4=C0=B8=D1=A1A=B4N=A5i=A5H=A7Q=A5=CE=B0j=B0=E9=A8D=B1o=B5=A5=A6=A1=
=AB=E1=AD=B1=AA=BA=AD=C8=A1A=B1N=B8=D3=AD=C8=B0=A3=A5H2=B4N=ACO=AFu=A6]=BC=
=C6=A9M=A4F=A1F=B5=A5=A6=A1=AB=E1=AD=B1=B2=C4=A4@=B2=B4=AC=DD=AE=C9=A5i=AF=
=E0=B7Q=A8=EC=A8=CF=A5=CE=B5=A5=A4=F1=AF=C5=BC=C6=A4=BD=A6=A1=A8=D3=B8=D1=
=A1A=A4=A3=B9L=B7|=A8=CF=A5=CE=A8=EC=A6=B8=A4=E8=B9B=BA=E2=A1A=A5i=A5H=A6=
b=B0j=B0=E9=A8=AB=B3X=A6]=A6=A1=A4=C0=B8=D1=B0}=A6C=AE=C9=A1A=A6P=AE=C9=AD=
p=BA=E2=A5X=B5=A5=A6=A1=AB=E1=AD=B1=AA=BA=AD=C8=A1A=B3o=A6b=A4U=AD=B1=AA=BA=
=B9=EA=A7@=A4=A4=A5i=A5H=AC=DD=A8=EC=A1C=20
<BR><BR>
<H2>=B9=EA=A7@</H2>
<UL>
<LI>C </LI></UL><PRE>#include <stdio.h> <BR>#include =
<stdlib.h> <BR><BR>#define N 1000 <BR>#define P 10000 <BR><BR>int =
prime(int*); // =A8D=BD=E8=BC=C6=AA=ED <BR>int factor(int*, int, int*); =
// =A8Dfactor <BR>int fsum(int*, int); // sum ot proper factor =
<BR><BR>int main(void) { <BR> int ptable[N+1] =3D {0}; // =
=C0x=A6s=BD=E8=BC=C6=AA=ED <BR> int fact[N+1] =3D {0}; // =
=C0x=A6s=A6]=A6=A1=A4=C0=B8=D1=B5=B2=AAG <BR> int count1, count2, i; =
<BR><BR> count1 =3D prime(ptable); <BR><BR> for(i =3D 0; i <=3D =
P; i++) { <BR> count2 =3D factor(ptable, i, fact); <BR> =
if(i =3D=3D fsum(fact, count2)) <BR> printf("Perfect Number: =
%d\n", i); <BR> } <BR> <BR> printf("\n"); <BR><BR> return 0; =
<BR>} <BR><BR>int prime(int* pNum) { <BR> int i, j; <BR> int =
prime[N+1]; <BR><BR> for(i =3D 2; i <=3D N; i++) <BR> =
prime[i] =3D 1; <BR><BR> for(i =3D 2; i*i <=3D N; i++) { <BR> =
if(prime[i] =3D=3D 1) { <BR> for(j =3D 2*i; j <=3D N; =
j++) { <BR> if(j % i =3D=3D 0) <BR> =
prime[j] =3D 0; <BR> } <BR> } <BR> } <BR><BR> =
for(i =3D 2, j =3D 0; i < N; i++) { <BR> if(prime[i] =3D=3D 1) =
<BR> pNum[j++] =3D i; <BR> } <BR><BR> return j; <BR>} =
<BR><BR>int factor(int* table, int num, int* frecord) { <BR> int i, =
k; <BR><BR> for(i =3D 0, k =3D 0; table[i] * table[i] <=3D num;) { =
<BR> if(num % table[i] =3D=3D 0) { <BR> frecord[k] =3D =
table[i]; <BR> k++; <BR> num /=3D table[i]; <BR> =
} <BR> else <BR> i++; <BR> } <BR><BR> =
frecord[k] =3D num; <BR><BR> return k+1; <BR>} <BR><BR>int fsum(int* =
farr, int c) { <BR> int i, r, s, q; <BR><BR> i =3D 0; <BR> r =
=3D 1; <BR> s =3D 1; <BR> q =3D 1; <BR><BR> while(i < c) { =
<BR> do { <BR> r *=3D farr[i]; <BR> q +=3D =
r; <BR> i++; <BR> } while(i < c-1 && =
farr[i-1] =3D=3D farr[i]); <BR> s *=3D q; <BR> r =3D 1; =
<BR> q =3D 1; <BR> } <BR><BR> return s / 2; <BR>} =
<BR></PRE><BR>
<UL>
<LI>Java </LI></UL><PRE>import java.util.ArrayList;<BR><BR>public =
class PerfectNumber {<BR> public static int[] lessThan(int number) =
{<BR> int[] primes =3D Prime.findPrimes(number);<BR><BR> =
ArrayList list =3D new ArrayList();<BR> <BR> for(int i =3D =
1; i <=3D number; i++) { <BR> int[] factors =3D =
factor(primes, i); <BR> if(i =3D=3D fsum(factors)) <BR> =
list.add(new Integer(i));<BR> } <BR><BR> int[] p =
=3D new int[list.size()];<BR> Object[] objs =3D list.toArray(); =
<BR> for(int i =3D 0; i < p.length; i++) {<BR> p[i] =
=3D ((Integer) objs[i]).intValue();<BR> }<BR> <BR> =
return p;<BR> }<BR> <BR> private static int[] factor(int[] =
primes, int number) { <BR> int[] frecord =3D new int[number];<BR> =
int k =3D 0;<BR> <BR> for(int i =3D 0; =
Math.pow(primes[i], 2) <=3D number;) { <BR> if(number % =
primes[i] =3D=3D 0) { <BR> frecord[k] =3D primes[i]; <BR> =
k++; <BR> number /=3D primes[i]; <BR> =
} <BR> else <BR> i++; <BR> } =
<BR><BR> frecord[k] =3D number; <BR><BR> return frecord; =
<BR> } <BR><BR> private static int fsum(int[] farr) { <BR> =
int i, r, s, q; <BR><BR> i =3D 0; <BR> r =3D 1; <BR> =
s =3D 1; <BR> q =3D 1; <BR><BR> while(i < farr.length) =
{ <BR> do { <BR> r *=3D farr[i]; <BR> =
q +=3D r; <BR> i++; <BR> } while(i < =
farr.length - 1 &&<BR> farr[i-1] =3D=3D =
farr[i]); <BR> s *=3D q; <BR> r =3D 1; <BR> =
q =3D 1; <BR> } <BR><BR> return s / 2; <BR> }<BR> =
<BR> public static void main(String[] args) {<BR> int[] pn =
=3D PerfectNumber.lessThan(1000);<BR> <BR> for(int i =3D 0; i =
< pn.length; i++) {<BR> System.out.print(pn[i] + " ");<BR> =
}<BR> <BR> System.out.println();<BR> =
}<BR>}</PRE><BR><BR></BODY></HTML>
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