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C\u3068\u304bPerl\u3067\u306f\u6392\u4ed6\u7684\u8ad6\u7406\u548c\u306f^\u306e\u6f14\u7b97\u5b50\u3092\u4f7f\u3046\u304b\u3089\u300131^7=24\u3068\u66f8\u3051\u3070\u3088\u3044\u304b\u3002
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\u304b\u3051\u7b97\u3060\u304c\u3001\u03b1n<\/sup>\u30671\uff5e31\u307e\u3067\u306e\u5024\u3092\u8868\u305b\u308b\u3088\u3046\u306b\u3057\u3066\u3001\u6307\u6570\u6cd5\u5247\u3067\u8a08\u7b97\u3057\u308d\u3068\u3002
\u03b1\u3068\u3044\u3046\u306e\u306f\u306a\u3093\u304b\u308f\u304b\u3089\u3093\u3051\u3069\u3053\u306e\u4e16\u754c\u306e\u3079\u304d\u4e57\u30671\uff5e31\u306e\u6570\u5b57\u3092\u7528\u610f\u3067\u304d\u308b\u3082\u306e\u3068\u3044\u3046\u3053\u3068\u3002
\u305d\u308c\u3067\u3001\u3069\u3046\u3082\u3053\u308c\u3092\u4f5c\u308c\u308b\u306e\u304c\u7d20\u6570\u500b\u306e\u3068\u304d\u3068\u3001\u7d20\u6570\u306e\u3079\u304d\u4e57\u500b\u306e\u3068\u304d\u3089\u3057\u3044\u3002
\u306a\u306e\u306710\u9032\u6570\u3067RS\u7b26\u53f7\u306f\u4f5c\u308c\u306a\u3044\u3068\u300211\u9032\u6570\u3068\u304b9\u9032\u6570\u306a\u3089\u3067\u304d\u308b\u307f\u305f\u3044\u3060\u3051\u3069\u3002
\u3053\u308c\u306a\u3093\u3060\u304c\u3001\u3055\u3063\u304d\u66f8\u3044\u305fWikipedia\u306e\u8a18\u4e8b\u306b\u3044\u308d\u3044\u308d\u66f8\u3044\u3066\u3042\u308b\u304c\u3001
\u307e\u305a\u03b10<\/sup>=1\u3001\u03b11<\/sup>=2\u3001\u03b12<\/sup>=4\u3001\u03b13<\/sup>=8\u3001\u03b14<\/sup>=16\u3068\u3002
\u3053\u3053\u307e\u3067\u306f\u305d\u3046\u3044\u3046\u3082\u306e\u3089\u3057\u3044\u3002\u3053\u3053\u304b\u3089\u304c\u554f\u984c\u3002
\u3053\u3053\u3067\u539f\u59cb\u591a\u9805\u5f0f\u3068\u3044\u3046\u9b54\u6cd5\u306e\u3088\u3046\u306a\u5f0f\u3092\u4f7f\u3063\u3066\u3084\u308b\u3002
\u305d\u308c\u4ee5\u4e0b\u306e\u6b21\u6570\u306e\u5f0f\u3067\u306f\u5272\u308a\u5207\u308c\u306a\u3044\u5f0f\u3068\u3044\u3046\u3084\u3064\u3067\u3001\u305d\u306e\u6027\u8cea\u304c\u3042\u308c\u3070\u3044\u3044\u3089\u3057\u3044\u3002
\u64ec\u4f3c\u30e9\u30f3\u30c0\u30e0\u30d1\u30bf\u30fc\u30f3\u767a\u751f\u56de\u8def<\/a>\u306e\u30da\u30fc\u30b8\u306e\u4e0b\u306e\u65b9\u306b\u8f09\u3063\u3066\u307e\u3059\u306d\u3002
\u307e\u3041\u3053\u308c\u306e5\u6b21\u306e\u5f0f\u3092\u6301\u3063\u3066\u304f\u308b\u3002x5<\/sup>+x2<\/sup>+1\u3063\u3066\u5f0f\u3067\u3059\u306d\u3002
\u3053\u308c\u3092\u5909\u5f62\u3057\u3066\u3001+\u3092\u3053\u306e\u4e16\u754c\u306e\u8db3\u3057\u7b97\u3067\u3042\u308b^\u306b\u7f6e\u304d\u63db\u3048\u3066\u3001x\u306b\u03b1\u3092\u4ee3\u5165\u3057\u3066\u2026
\u03b15<\/sup>=\u03b12<\/sup> ^ 1 = 5
\u3053\u308c\u4ee5\u4e0a\u3060\u304c\u3001\u3053\u308c\u3092\u4e21\u8fba\u03b1\u500d\u3057\u3066\u2026\u3068\u3084\u3063\u3066\u3044\u304f\u306e\u3067\u2026
\u03b15+n<\/sup>=\u03b12+n<\/sup> ^ \u03b1n<\/sup>
\u306e\u5f0f\u306en\u3092\u5897\u3084\u3057\u306a\u304c\u3089\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u3093\u3058\u3083\u306a\u3044\u304b\u306a\u3002\u3053\u308c\u3067\u03b10<\/sup>\u304b\u3089\u03b130<\/sup>\u306e\u5024\u3092GET!
\u3061\u306a\u307f\u306b\u03b131<\/sup>=\u03b10<\/sup>=0\u3067\u3059\u3002\u307e\u3041\u4e00\u5468\u56de\u3063\u3066\u304f\u308b\u3068\u3044\u3046\u3053\u3068\u3002
\u3057\u304b\u3057\u624b\u4f5c\u696d\u3067\u3084\u308b\u306e\u3082\u3081\u3093\u3069\u304f\u3055\u3044\u306e\u3067\u3001$a[$n]\u304c\u03b1$n<\/sup>\u306e\u5024\u306b\u306a\u308b@a\u3092Perl\u3067\u4f5c\u3063\u3066\u307f\u305f\u3002<\/p>\n@a=(1,2,4,8,16);
$a[5+$_]=$a[2+$_]^$a[$_] for(0..30-5);<\/pre>\n
@a=(1,2,4,8,16 , 5,10,20,13,26 , 17,7,14,28,29 , 31,27,19,3,6 , 12,24,21,15,30 , 25,23,11,22,9 , 18)
\u3068\u306a\u308b\u3002\u3053\u308c\u3092\u4f7f\u3048\u3070\u3053\u306e\u4e16\u754c\u306e\u304b\u3051\u7b97\u30fb\u308f\u308a\u7b97\u304c\u3067\u304d\u308b\u3002
10\u00d77\u306f\u300110\u304c\u03b16<\/sup>\u30017\u304c\u03b111<\/sup>\u306a\u306e\u3067\u3001\u6307\u6570\u6cd5\u5247\u3067\u7b54\u3048\u306f\u03b117<\/sup>=19\u3068\u3002
\u308f\u308a\u7b97\u308210\u00f77=\u03b1-5<\/sup>=\u03b126<\/sup>=23\u3068\u306a\u308b\u308f\u3051\u3002
\u5b9f\u306f\u3053\u3053\u307e\u3067\u305f\u3069\u308a\u7740\u304f\u306e\u304c\u4e00\u756a\u5927\u5909\u3060\u3063\u305f\u3002<\/p>\n
\n
$x\u3092@a\u306e\u4e2d\u306e\u4f55\u756a\u76ee\u304b\u63a2\u3059\u306e\u306f\u5b9f\u306flog\u03b1<\/sub>($x)\u306a\u306e\u3067loga\u95a2\u6570\u3068\u3057\u3066\u7528\u610f\u3002<\/p>\nsub loga{
for(0..$#a){
return $_ if($a[$_]==$_[0]);
}
return undef;
}<\/pre>\n
\u03b1$n<\/sup>\u3092$a[$n]\u3068\u66f8\u304f\u306e\u306f\u304b\u3063\u3053\u308f\u308b\u3044\u6c17\u304c\u3057\u305f\u304b\u3089apow\u95a2\u6570\u3068\u3057\u3066\u7528\u610f\u3002<\/p>\nsub apow{
return $a[ $_[0] % 31 ];
}<\/pre>\n
\u3053\u308c\u3092\u4f7f\u3048\u3070\u304b\u3051\u7b97\u30fb\u308f\u308a\u7b97\u30fb\u3079\u304d\u4e57\u3082\u7c21\u5358\u3067\u3059\u306d\u3002<\/p>\nsub mul{
my $p=0;
for(@_){
my $c=loga($_);
return 0 if(!defined $c);
$p+=$c;
}
return apow($p);
}<\/pre>\n
0\u306b\u4f55\u3092\u304b\u3051\u3066\u30820\u306a\u306e\u306f\u3053\u306e\u4e16\u754c\u3067\u3082\u5909\u308f\u308a\u307e\u305b\u3093\u3002
mul(2,3,4)\u3068\u3059\u308c\u30702\u00d73\u00d74\u3068\u3044\u3046\u3053\u3068\u306d\u3002\u307e\u3041\u3042\u3093\u307e\u308a\u610f\u5473\u306f\u306a\u3044\u3051\u3069\u3002<\/p>\nsub div{
my $p=loga($_[0]);
return 0 if(!defined $p);
return undef if(!defined $c);
$p-=$c;
return apow($p);
}<\/pre>\nsub pow{
return apow(loga($_[0])*$_[1]);
}<\/pre>\n
\u3053\u306e\u4e16\u754c\u3067\u306e\u8a08\u7b97\u306f\u3053\u308c\u3068\u6392\u4ed6\u7684\u8ad6\u7406\u548c\u3060\u3051\u3042\u308c\u3070\u5341\u5206\u3067\u3059\u3002<\/p>\n
\n
@i=(1,2,3,4,5,6)\u3092\u7b26\u53f7\u5316\u3057\u307e\u3059\u3002
\u3067\u7b26\u53f7\u5316\u306e\u7406\u5c48\u3067\u3059\u304c\u30012\u6841\u52a0\u3048\u308b\u3068\u304d\u306f\u3001
G(x)=(x ^ \u03b10<\/sup>)(x ^ \u03b11<\/sup>)
\u3068\u3044\u3046x\u306e\u5f0f\u3092\u7528\u610f\u3057\u307e\u3059\u30022\u6841\u3060\u304b\u30892\u3064\u306e\u9805\u306d\u30024\u3064\u306a\u3089\u03b1\u306e\u6307\u6570\u3092\u5897\u3084\u3057\u3066\u7528\u610f\u3059\u308b\u3060\u3051\u3002
Perl\u3067\u30b9\u30af\u30ea\u30d7\u30c8\u66f8\u3044\u3066\u5c55\u958b\u3055\u305b\u3066\u3082\u3088\u3044\u304c\u2026\u3081\u3093\u3069\u304f\u3055\u3044\u304b\u3089\u624b\u3067\u3084\u308d\u3046\u3002
G(x)=x2<\/sup> ^ (\u03b10<\/sup> ^ \u03b11<\/sup>)x ^ \u03b11<\/sup>
\u5206\u914d\u6cd5\u5247\u4f7f\u3063\u3066\u5c55\u958b\u3059\u308c\u3070\u3044\u3044\u306e\u306d\u3002
\u3067\u3001\u6574\u7406\u3059\u308b\u3068 x2<\/sup> ^ 3x ^ 2\u3068\u306a\u308b\u3002@g=(1,3,2)\u3068\u3057\u3066\u683c\u7d0d\u3057\u3066\u304a\u3053\u3046\u3002
\u53c2\u8003\u307e\u3067\u306b\u30b9\u30af\u30ea\u30d7\u30c8@g\u3092\u81ea\u52d5\u751f\u6210\u3059\u308b\u30b9\u30af\u30ea\u30d7\u30c8\u3002<\/p>\n@g=(1);
for my $i(0..2-1){
my $a=$a[$i];
unshift @g,0;
$g[$_]=($g[$_+1]\/\/0)^mul($g[$_],$a) for(0..$#g);
}<\/pre>\n
\u3053\u306e\u5f0f\u3092\u751f\u6210\u591a\u9805\u5f0f\u3068\u3044\u3046\u3089\u3057\u3044\u3002\u3053\u308c\u306f32\u500b\u306e\u30b7\u30f3\u30dc\u30eb\u3092\u4f7f\u3063\u3066\u30012\u6841\u4ed8\u52a0\u3059\u308b\u3068\u304d\u306f\u5171\u901a\u3002
\u3055\u3063\u304d\u306e@i\u306b\u4ed8\u52a0\u3059\u308b2\u6841\u3092\u52a0\u3048\u3066\u3001\u3053\u3093\u306a\u591a\u9805\u5f0f\u3092\u4f5c\u308b\u3002
C(x)=1x6<\/sup> ^ 2x7<\/sup> ^ 3x5<\/sup> ^ 4x4<\/sup> ^ 5x3<\/sup> ^ 6x2<\/sup> ^ Px ^ Q\u3068\u3044\u3046x\u306e\u5f0f\u3067\u8868\u3057\u305f\u3082\u306e\u3002
\u3053\u308c\u3092G(x)\u3067\u5272\u308a\u5207\u308c\u308b\u3088\u3046\u306b\u3059\u308c\u3070\u3088\u3044\u3068\u3002\u7d50\u5c40\u306e\u6240\u3001
1x6<\/sup> ^ 2x7<\/sup> ^ 3x5<\/sup> ^ 4x4<\/sup> ^ 5x3<\/sup> ^ 6x2<\/sup>\u3092G(x)\u3067\u5272\u3063\u305f\u3042\u307e\u308a\u304cPx ^ Q\u306b\u306a\u308b\u3068\u3002
\u3081\u3093\u3069\u304f\u3055\u3044\u3067\u3059\u306d\u30fc\u3002\u4e00\u4f53\u8ab0\u304c\u3053\u3093\u306a\u306e\u3092\u8003\u3048\u305f\u3093\u3060\u3002
\u3068\u308a\u3042\u3048\u305a\u3055\u3063\u304d\u306e\u5f0f\u3092@p=(1,2,3,4,5,6,0,0)\u3068\u8868\u3057\u3066\u3001@g\u3067\u8868\u3057\u3066G(x)\u3067\u5272\u308a\u307e\u3057\u3087\u3046\u304b\u3002<\/p>\nwhile(@p>=@g){
my $r=div(@p[$#p] , $g[0]);
$p[$_] ^= mul($g[$_],$r) for(1..$#g);
shift @p;
}<\/pre>\n
\u4f8b\u3048\u3070\u3001(2x+2)\u00f7(x+2)\u306f\u5546\u304c2\u3067\u3001\u4f59\u308a\u304c-4\u3001\u3053\u308c\u306f2x+2=2(x+2)-2\u3067\u5f0f\u304c\u8868\u3055\u308c\u308b\u3068\u8a00\u3046\u3053\u3068\u3002
\u305d\u308c\u3067\u3053\u306e\u51e6\u7406\u3067\u6b8b\u3063\u305f@p\u304c\u4f59\u308a\u3068\u3002(13,10)\u304c\u6b8b\u308b\u3002
\u3068\u3044\u3046\u308f\u3051\u3067\u3055\u3063\u304d\u306e\u5f0f\u306eP\u306b\u306f13\u304c\u3001Q\u306b\u306f10\u304c\u5f53\u3066\u306f\u307e\u308b\u3002
\u3053\u308c\u3067\u5b8c\u6210\u3002
\u3042\u3068\u306f\u521d\u3081\u306b\u66f8\u3044\u305f32\u9032\u6570\u306e\u6587\u5b57\u306b\u5f53\u3066\u306f\u3081\u308b\u3068\u3002
1,2,3,4,5,6\u306f\u6570\u5b57\u305d\u306e\u307e\u307e\u300110\u306fA\u300113\u306fD\u3067\u3059\u306d\u3002
\u6587\u5b57\u30ea\u30b9\u30c8\u3092@c\u306b\u5165\u308c\u3066\u3001$c[$n]\u3068\u3084\u3063\u3066\u53d6\u308a\u51fa\u3059\u3068\u4fbf\u5229\u3067\u3059\u3088\u306d\u3002
\u3068\u3044\u3046\u308f\u3051\u3067\u7d50\u679c\u306f123456DA\u3068\u306a\u308b\u3068\u3002\u3053\u308c\u30671\u6587\u5b57\u9593\u9055\u3048\u3066\u3082\u8a02\u6b63\u3067\u304d\u308b\u30c7\u30fc\u30bf\u3067\u304d\u3042\u304c\u308a\u3002<\/p>\n
\n
\u53d7\u3051\u53d6\u3063\u305f\u65b9\u306f\u3001\u3053\u308c\u3092\u591a\u9805\u5f0f\u306b\u3059\u308b\u3002
C(x)=1x6<\/sup> ^ 2x7<\/sup> ^ 3x5<\/sup> ^ 4x4<\/sup> ^ 5x3<\/sup> ^ 6x2<\/sup> ^ 10x ^ 13
\u305d\u308c\u3067\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u3068\u3044\u3046\u3082\u306e\u3092\u6c42\u3081\u308b\u3002
2\u500b\u6587\u5b57\u3092\u52a0\u3048\u305f\u306a\u30892\u500b\u306e\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u304c\u3067\u304d\u3066\u3001
\u305d\u308c\u306fS1<\/sub>=C(\u03b10<\/sup>)\u3001S1<\/sub>=C(\u03b11<\/sup>)\u3001\u306a\u3093\u3068\u4ee3\u5165\u3059\u308b\u3093\u3067\u3059\u306d\u3002
\u307e\u3041\u3081\u3093\u3069\u304f\u3055\u3044\u308f\u3002\u3055\u3063\u304d\u306e\u591a\u9805\u5f0f\u306f@r\u306b(1,2,3,4,5,6,10,13)\u3068\u683c\u7d0d\u3059\u308b\u3053\u3068\u306b\u3057\u3088\u3046\u3002<\/p>\n@s=();
for my $n(0..2-1){
my $s=0;
for(0..$#r){
$s^=mul($r[$_],pow($a[$n] , $#r-$_ ));
}
push @s,$s;
}<\/pre>\n
\u5b9f\u306f\u6210\u529f\u3057\u3066\u3044\u308c\u3070\u5168\u90e8\u306e\u5024\u304c0\u306b\u306a\u308b\u3002\u306a\u305c\u306a\u3089\u3070C(x)\u306fG(x)\u3067\u5272\u308a\u5207\u308c\u3066\u3001
G(x)\u306f\u5f0f\u306e\u5f62\u3092\u307f\u3066\u3082\u308f\u304b\u308b\u3088\u3046\u306b\u3001x\u306b\u03b10<\/sup> \u3068 \u03b11<\/sup>\u3092\u5165\u308c\u305f\u30890\u306b\u306a\u308b\u3002
\u3060\u304b\u3089C(x)\u306b\u305d\u308c\u3092\u5165\u308c\u3066\u30820\u3068\u306a\u308b\u3068\u3002\u306a\u3089\u306a\u3051\u308c\u3070\u9593\u9055\u3048\u3067\u3059\u3002
\u305d\u308c\u3067\u8a02\u6b63\u65b9\u6cd5\u3060\u304c\u3001Wikipedia\u306e\u8a18\u4e8b\u3092\u898b\u308b\u3068\u3051\u3063\u305f\u3044\u306a\u884c\u5217\u5f0f\u304c\u66f8\u3044\u3066\u3042\u308b\u3002
\u3051\u30691\u6587\u5b57\u3057\u304b\u8a02\u6b63\u3057\u306a\u3044\u306a\u3089\u3044\u308d\u3093\u306a\u5f0f\u304c\u7c21\u5358\u306b\u306a\u3063\u3066\u3001
1 ^ (S1<\/sub>S2<\/sub>)\u03b1n<\/sup>=0\u3092\u6e80\u305f\u3059n\u3092\u767a\u898b\u3059\u308c\u3070\u3088\u3044\u3068\u3002
\u5909\u5f62\u3057\u3066\u3001\u03b1n<\/sup>=S1<\/sub>\/S2<\/sub>\u3001
\u5bfe\u6570\u3092\u53d6\u3063\u3066\u3001n=log\u03b1<\/sub>(S1<\/sub>)-log\u03b1<\/sub>(S2<\/sub>)\u3001
$n=loga($s[0])-loga($a[2]) \u3068\u306a\u308b\u308f\u3051\u3067\u3059\u306d\u3002
\u305d\u3057\u3066\u3001x31-$n<\/sup>\u306e\u9805\u3092\u4fee\u6b63\u3059\u308b\u3002(-$n)%31\u3092\u53d6\u308b\u3068\u3044\u3044\u3068\u601d\u3044\u307e\u3059\u3002
\u4fee\u6b63\u65b9\u6cd5\u306fS1<\/sub>\u306e\u5024\u3092\u8db3\u3059\u3001\u3060\u304b\u3089\u6392\u4ed6\u7684\u8ad6\u7406\u548c\u3092\u53d6\u308b\u3060\u3051\u3002
\u4f8b\u3001@r=(1,2,3,4,5,6,10,13)\u3092@r=(1,2,3,0,5,6,10,13)\u3068\u5165\u529b\u3055\u308c\u3066\u3057\u307e\u3063\u305f\u3002
\u3059\u308b\u3068@s=(4,10)\u3068\u306a\u308b\u3002\u3053\u308c\u3088\u308a$n\u3092\u8a08\u7b97\u3059\u308b\u3068-4\u3068\u306a\u308b\u3002
\u3060\u304b\u3089x4<\/sup>\u306e\u9805\u3001\u3060\u304b\u3089$r[$#r-4]\u306e\u9805\u3067\u3059\u306d\u3002
\u73fe\u5728\u306e\u5024\u306f0\u3060\u3051\u3069\u3001\u3053\u308c\u3092$r[$#r-4] ^= $s[0]\u3068\u4fee\u6b63\u3059\u308b\u3002
\u3059\u308c\u3070@r=(1,2,3,4,5,6,10,13)\u306b\u8a02\u6b63\u3067\u304d\u305f\u3002\u3081\u3067\u305f\u3057\u3081\u3067\u305f\u3057\u3002<\/p>\n
\n
\u3053\u308c\u3092Perl\u3067\u4f5c\u3063\u3066\u3044\u308d\u3044\u308d\u3084\u3063\u3066\u307f\u308b\u3068\u306a\u304b\u306a\u304b\u697d\u3057\u3044\u3067\u3059\u3002
\u3061\u3087\u3063\u3068\u6253\u3061\u9593\u9055\u3048\u3066\u307f\u3066\u3082\u3001\u76f4\u3063\u3066\u3057\u307e\u3046\u3093\u3067\u3059\u306d\u3002
\u3053\u308c\u30672\u500b\u8a02\u6b63\u53ef\u80fd\u306b\u3057\u305f\u3044\u3093\u3067\u3059\u304c\u3001\u8a02\u6b63\u306e\u5f0f\u304c\u96e3\u3057\u3059\u304e\u308b\u306e\u3067\u2026
\u307e\u3041\u3044\u308d\u3044\u308d\u8a66\u3057\u3066\u307f\u3088\u3046\u304b\u306a\u3068\u601d\u3044\u307e\u3059\u3002
\u3046\u3063\u304b\u308a\u30df\u30b9\u3092\u4fee\u5fa9\u3067\u304d\u308c\u3070\u4f55\u304b\u3068\u4fbf\u5229\u3060\u3088\u306a\u30fc\u3068\u306f\u601d\u3044\u307e\u3059\u3051\u3069\u306d\u3002
\u3057\u304b\u3057\u3048\u3089\u3044\u3082\u306e\u304c\u3042\u308b\u3082\u3093\u3060\u3002\u3053\u3093\u306a\u306b\u3059\u3054\u3044\u3082\u306e\u304c\u4e16\u306e\u4e2d\u306b\u3042\u3063\u305f\u3068\u306f\u3002
\u96e3\u89e3\u3060\u3057\u3001\u8a08\u7b97\u3057\u306b\u304f\u3044\u3051\u3069\u3001\u3059\u3054\u3044\u5f37\u529b\u3060\u306a\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"