bzoj 1876 高精

 

　　首先我们知道，对于两个数a,b，他们的gcd情况有如下形式的讨论

　　当a为奇数，b为偶数的时候gcd(a,b)=gcd(a div 2,b)

　　当b为奇数，a为偶数的时候gcd(a,b)=gcd(a,b div 2)

　　当a为偶数，b为偶数的时候gcd(a,b)=2*gcd(a div 2,b div 2)

　　当a为奇数，b为奇数的时候，根据欧几里德定律，有gcd(a,b)=gcd(a-b,b) (a>b)时

　　那么这道题就变成了不断地缩小a,b的范围了。直接高精就行了。当然数据为1,10^1000的时候会tle，题目比较良心没有这样的数据。

 

高精写渣了。

/**************************************************************
    Problem: 1876
    User: BLADEVIL
    Language: Pascal
    Result: Time_Limit_Exceed
****************************************************************/
 
//By BLADEVIL
var
    s1, s2                      :ansistring;
    f1, f2                      :boolean;
    ans                         :ansistring;
    a, b, c                     :array[0..100000] of longint;
    i                           :longint;
    doit                        :longint;
      
function max(s1,s2:ansistring):boolean;
begin
    if length(s1)>length(s2) then exit(true);
    if (length(s1)=length(s2)) and (s1>s2) then exit(true);
    exit(false);
end;
      
function divid(s:ansistring):ansistring;
var
    i                           :longint;
    len                         :longint;
    ss                          :ansistring;
begin
    fillchar(a,sizeof(a),0);
    len:=length(s);
    for i:=1 to len do a[(len-i) div 7+1]:=a[(len-i) div 7+1]*10+ord(s[i])-48;
    len:=(len+6) div 7;
    for i:=len downto 2 do
        if a[i] mod 2=0 then
            a[i]:=a[i] div 2 else
            begin
                a[i]:=a[i] div 2;
                a[i-1]:=a[i-1]+10000000;
            end;
    a[1]:=a[1] div 2;
    divid:='';
    for i:=len downto 1 do
    begin
        str(a[i],ss);
        if a[i]<1000000 then divid:=divid+'0';
        if a[i]<100000 then divid:=divid+'0';
        if a[i]<10000 then divid:=divid+'0';
        if a[i]<1000 then divid:=divid+'0';
        if a[i]<100 then divid:=divid+'0';
        if a[i]<10 then divid:=divid+'0';
        divid:=divid+ss;
    end;
    while (divid[1]='0') and (length(divid)>1) do delete(divid,1,1);
end;
  
function jian(s1,s2:ansistring):ansistring;
var
    len1, len2                  :longint;
    ss                          :ansistring;
    i                           :longint;
begin
    fillchar(a,sizeof(a),0);
    fillchar(b,sizeof(b),0);
    fillchar(c,sizeof(c),0);
    len1:=length(s1);
    for i:=1 to len1 do a[(len1-i) div 7+1]:=a[(len1-i) div 7+1]*10+ord(s1[i])-48;
    len2:=length(s2);
    for i:=1 to len2 do b[(len2-i) div 7+1]:=b[(len2-i) div 7+1]*10+ord(s2[i])-48;
    len1:=(len1+6) div 7;
    len2:=(len2+6) div 7;
    for i:=1 to len1 do
    begin
        c[i]:=c[i]+a[i]-b[i];
        if c[i]<0 then
        begin
            c[i]:=c[i]+10000000;
            c[i+1]:=c[i+1]-1;
        end;
    end;
    jian:='';
    for i:=len1 downto 1 do
    begin
        str(c[i],ss);
        if c[i]<1000000 then jian:=jian+'0';
        if c[i]<100000 then jian:=jian+'0';
        if c[i]<10000 then jian:=jian+'0';
        if c[i]<1000 then jian:=jian+'0';
        if c[i]<100 then jian:=jian+'0';
        if c[i]<10 then jian:=jian+'0';
        jian:=jian+ss;
    end;
    while (jian[1]='0') and (length(jian)>1) do delete(jian,1,1);
end;
  
function mul(s:ansistring):ansistring;
var
    len                         :longint;
    i                           :longint;
    ss                          :ansistring;
begin
    len:=length(s);
    fillchar(a,sizeof(a),0);
    for i:=1 to len do a[(len-i) div 7+1]:=a[(len-i) div 7+1]*10+ord(s[i])-48;
    len:=(len+6) div 7;
    for i:=1 to len do a[i]:=a[i]*2;
    for i:=1 to len do
    begin
        a[i+1]:=a[i+1]+a[i] div 10000000;
        a[i]:=a[i] mod 10000000;
    end;
    inc(len);
    mul:='';
    for i:=len downto 1 do
    begin
        str(a[i],ss);
        if a[i]<1000000 then mul:=mul+'0';
        if a[i]<100000 then mul:=mul+'0';
        if a[i]<10000 then mul:=mul+'0';
        if a[i]<1000 then mul:=mul+'0';
        if a[i]<100 then mul:=mul+'0';
        if a[i]<10 then mul:=mul+'0';
        mul:=mul+ss;
    end;
    while (mul[1]='0') and (length(mul)>1) do delete(mul,1,1);
end;
      
begin
    readln(s1);
    while (s1[1]='0') and (length(s1)>1) do delete(s1,1,1);
    readln(s2);
    while (s2[1]='0') and (length(s2)>1) do delete(s2,1,1);
    doit:=0;
    while s1<>s2 do
    begin
        if ord(s1[length(s1)]) mod 2=0 then f1:=true else f1:=false;
        if ord(s2[length(s2)]) mod 2=0 then f2:=true else f2:=false;
        if f1 and f2 then
        begin
            s1:=divid(s1);
            s2:=divid(s2);
            inc(doit);
        end else
        begin
            if f1 then s1:=divid(s1);
            if f2 then s2:=divid(s2);
            if (not f1) and (not f2) then
                if max(s1,s2) then s1:=jian(s1,s2) else s2:=jian(s2,s1);
        end;
    end;
    ans:=s1;
    for i:=1 to doit do ans:=mul(ans);
    writeln(ans);
end.