数字之美

这是一个实现多种特征数筛选的perl脚本，有点意思。?

主要功能如下：

1.给定一个整数范围，筛选其中的素数；

2.分析给定的数字是否为素数；

3.筛选给定数范围内的梅森素数；

4.获取两个或多个数的最大公约数和最小公倍数；

5.获取给定范围的孪生素数；

6.求排列公式值；

7.求组合公式值；

8.获得二项式系数，展示杨辉三角；

9......

#! /usr/bin/perl -w

=head1 name
	obtain_some_special_integer.pl	

=head1 Description
	1.get the prime numbers from the given range;
	2.check the given number whether it is a prime number or not;
	3.get the special range mersenne prime numbers;
	4.get max common divisor and min multiple between the given two numbers or more;
	5.get the twin prime numbers from the given range;
	6.get the max number of permutations;
	7.get the max number of combinations;
	8.get the binomial coefficients;
	9.to be expected......

=head1	Version
	Original from: li Xiangfeng,xflee0608@163.com
	Version: 2.4,Date: 2014-3-8

=head1 usage
	perl obtain_some_special_integer.pl [options]
	-p,--prime    	   <int>	The range from which you want to obtain prime numbers,must be a pair arguments;
	-c,--check        <int>  	Input a number you want to check whether it is a prime number or not;
	-m,--mersenne     <int>	The range you want to grep mersenne prime numbesr,range from 2 to the number you give;
	-d,--div          <int>	Input the two number,you will get theirs max common divisor number and min multiple number.you must be a pair arguments;
	-t,--twin         <int>    	The range from which you want to obtain twin prime numbers,must be a pair arguments;
	-per,--permutation <int>	Get the max number of permutations;
	-com,--combination <int>        Get the max number of combinations;
	-n,--binomial     <int>	Get the binomial coefficients;
	-h,--help			Print help info;
	-v,--version           	Print script info.

=head1 Example
	perl obtain_some_special_integer.pl -p  1 -p 100      #grep prime numbers from 1 to 100;
	perl obtain_some_special_integer.pl -c  986           #check 986's attribute;
	perl obtain_some_special_integer.pl -m 600000         #grep mersenne prime numbers from 2 to 600000; 
	perl obtain_some_special_integer.pl -d 24 -d 36       #get max common divisor number and min multiple number of 24 and 36;
	perl obtain_some_special_integer.pl -t  1 -t 100      #grep twin prime numbers from 1 to 100;
	perl obtain_some_special_integer.pl -per  5 -per 3    #get the max number of permutations when you fetch 3 samples from 5;
	perl obtain_some_special_integer.pl -com  5 -com 3    #get the max number of combinations when you fetch 3 samples from 5;
	perl obtain_some_special_integer.pl -n  10            #get the binomial coefficients when index n equal 5;
=cut


my $heredoc =<<USAGE;
		Original from: li Xiangfeng,xflee0608@163.com.
		Version: 2.4,Date: 2014-3-8.
USAGE

use strict;
use Getopt::Long;

my (@num,$n,$mersenne,@div,@twin,@per,@com,$bino,$help,$version);
GetOptions(
	"prime|p:i"=>@num,"check|c:i"=>$n,"mersenne|m:i"=>$mersenne,"div|d:i"=>@div,"twin|t:i"=>@twin,"permutation|per:i"=>@per,"combination|com:i"=>@com,"binomial|n:i"=>$bino,"help|?" =>$help,"version|v"=>$version,);
die `pod2text $0` if($help);
die `pod2text $0` unless(@num||$n||$mersenne||@div||@twin||@per||@com||$bino||$version);
die "$heredoc" if($version);
	
##grep prime number list##
my $num_count=@num;
if($num_count==2){
	my @result_grep=&prime(@num);
	if($num[0]<$num[1]){
		print $_,"n" foreach @result_grep;
	}else{print $_,"n" foreach sort{$b<=>$a}@result_grep;}
}elsif($num_count==1){
	die "please input the correct argument:n e.g.: -p  1 -p 100n";
}

##check the given number whether it is a prime number or not##	
if($n){
	my @set=&check($n);
	print "$n is a prime number!n" if(scalar@set==2);
	print "$n is a not composite number,and also not a prime number!n" if(scalar@set==1);
	if(scalar@set>2){
		my $j=1;
		print"$n is a composite number!n$n can be exactly divided by these numbers as follows:n";
		foreach(@set){
                        printf "%12s",$_;
                        print "n" if($j%3==0);
                        $j++;
                }
                print "n" if($j%3!=1);
		my $num=$n;
		my $quotient;
		my @grep=grep{scalar&check($_)==2}@set;
		my $product=1;
		$product*=$_ foreach @grep;
		my $check_will=$num/$product;
		my @out=@grep;
		unless($check_will==1){
			my @prime_set=&prime(2,$check_will);
			for(my $i=0;;$i++){
				if(scalar&check($check_will)==2){
					push @out,$check_will;
					last;
				}
				last if(!@prime_set);
        			my $div=$prime_set[0];
        			if($check_will % $div==0){
                			push @out,$div;
					$quotient=$check_will/$div;
                			if(scalar&check($quotient)==2){
                        			push @out,$quotient;
                        			last;
                			}
                			$check_will=$quotient;
        			}else{shift @prime_set}
			}
		}
		my $result;
		print "n";
		$result.="$_*" foreach sort{$a<=>$b}@out;
		chop$result;
		print "$n=$resultn";
	
	}
}

##grep mersenne prime number##
if($mersenne){
	my @prime_set=&prime(2,$mersenne);
	my %ha=map{$_=>1}@prime_set;
	for(my $i=2;;$i++){
		my $num=2**$i-1;
		print "$num is the mersenne prime;n$num=2**$i-1;n" if(exists $ha{$num} && exists $ha{$i});
		last if($num>=$prime_set[-1]);
	}
}

##get max common divisor and min multiple##
my $div_count=@div;
if($div_count==2){
	my $result_div=&max_common_divisor_min_multiple(@div);
}elsif($div_count>=3){
	my $result_div=&max_common_divisor_min_multiple_more(@div);
}elsif($div_count==1){	die "please input the correct argument:n e.g.: -d 24 -d 36n";}
		
##grep twin prime number list##
my $twin_count=@twin;
if($twin_count==2){
	my @prime_grep=&prime(@twin);
	my @prime_twin;
	for(my $i=1;$i<@prime_grep;$i++){
		my $out=$prime_grep[$i]-$prime_grep[$i-1];
		if($out==2){
			push @prime_twin,$prime_grep[$i],$prime_grep[$i-1];
			print "($prime_grep[$i-1],$prime_grep[$i])n";
		}
	}

}elsif($twin_count==1 || $twin_count>=3){  die "please input the correct argument:n e.g.: -t  1 -t 100n";}

##get max permutation number##
if(scalar@per==2){
	my ($n,$m)=@per;
	if($n>=$m){
		my $result_per=&fac($n)/&fac($m);
		print "The result of P($n,$m) is :$result_pern";
	}else{die "please make sure the correct input!"}
}elsif(scalar@per==1){  die "please input the correct argument:n e.g.:-per  5 -per 3n";} 

##get max permutation number##
if(scalar@com==2){
	my ($n,$m)=@com;
	if($n>=$m){
		my $result_com=&fac($n)/(&fac($m)*(&fac($n-$m)));
		print "The result of C($n,$m) is :$result_comn";
	}else{die "please make sure the correct input!"}
}elsif(scalar@com==1){  die "please input the correct argument:n e.g.:-com  5 -com 3n";}

##get binomial coefficient##
if($bino){
	for(my $i=0;$i<$bino;$i++){
		my $out=&fac($bino-1)/(&fac($i)*(&fac($bino-$i-1)));
		print "$out," if($i<$bino-1);
		print "$outn" if($i==$bino-1);
	}
	for(my $i=1;$i<=$bino;$i++){
		print " " x (3*($bino-$i));
		for(my $j=0;$j<$i;$j++){
			my $out=&fac($i-1)/(&fac($j)*(&fac($i-$j-1)));
			printf "%5s  ",$out;
		}
		print "n";
	}
}

##sub##
sub prime{
	my ($start,$end)=sort{$a<=>$b}@_;
	my @set;
	for(my $i=$start;$i<=$end;$i++){
        	push @set,$i if($i==2);
        	push @set,$i if($i==3);
        	next if($i%6!=1 && $i%6!=5);
        	my $flag=1;
        	for(my $j=3;$j<=$i/2;$j+=2){
                	if($i%$j==0){
                        	$flag=0;
                        	last;
                	}
        	}
        	push @set,$i if($flag && $i>1);
	}
	return @set;
}

##sub##
sub check{
	my $num=shift@_;
	my @p;
	for(my $i=1;$i<=$num;$i++){
        	if($num % $i==0){
                	push @p,$i;
        	}
	}
	return @p;
}

##sub##
sub max_common_divisor_min_multiple{
	my ($num1,$num2)=@_;
	my (@p,@q);
	for(my $i=1;$i<=$num1;$i++){
        	if($num1 % $i==0){
                	push @p,$i;
        	}
	}
	for(my $j=1;$j<=$num2;$j++){
        	if($num2 % $j==0){
                	push @q,$j;
        	}
	}
	my %hash;
	my @inter=grep{$hash{$_}++>0}@p,@q;
	@inter=sort{$b<=>$a}@inter;
	print "$inter[0] is $num1 and $num2 's max commom divisorn";
	print $num1*$num2/$inter[0]," is $num1 and $num2 's min commom multiplen";	
}

##sub##
sub max_common_divisor_min_multiple_more{
	my @p=@_;
	my $flag=0;
	my $out=0;
	foreach(my $i=0;;$i++){
        	my %ha;
        	my @q=grep{$ha{$_}++<1}@p;
        	if(scalar@q==1){
                	$out=$q[0];
                	print "$outn";
                	last;
        	}
        	@q=sort{$a<=>$b}@q;
        	my $num=shift@q;
        	if($num==1){
                	$flag=1;
                	last;
        	}
        	my @k;
        	foreach(@q){
                	push @k,($_-$num);
        	}
        	push @k,$num;
        	@p=@k;
	}
	if($flag){
        	print "max division is 1n";
	}else{print "max division is $outn"}	
}

##sub##
sub fac{
	my ($a)=@_;
        my $out=1;
        for(my $i=1;$i<=$a;$i++){
                $out*=$i;
        }
        return $out;
}

my @timelst=times;
print "n##########n";
print "Elapsed time:n";
print "User:$timelst[0] seconds.n";
print "System:$timelst[1] seconds.n";
print "##########n";
__END__