「疯狂的高精度」高精度大模板
来源：互联网 发布：期刊数据库 编辑：程序博客网 时间：2024/05/17 08:07
高精度都应该很熟练了，原理什么的也就不用多说。
当你把高精度加减乘除都摞在一起，就会有很神奇的事情发生——大模板诞生：
Pascal代码：
program High_Precision;var os1,os2,os,md:ansistring; ch:char; u,v,l:integer;function High_Precision_Addition(s1,s2:ansistring):ansistring; //高精度加法 var a,b:array[1..1000000] of integer; la,lb,k:integer; i:integer; s:ansistring; begin High_Precision_Addition:=''; la:=length(s1); lb:=length(s2); fillchar(a,sizeof(a),0); fillchar(b,sizeof(b),0); for i:=1 to la do a[i]:=ord(s1[la-i+1])-48; for i:=1 to lb do b[i]:=ord(s2[lb-i+1])-48; if la>lb then k:=la else k:=lb; for i:=1 to k do begin a[i+1]:=a[i+1]+(a[i]+b[i]) div 10; a[i]:=(a[i]+b[i]) mod 10; end; if a[k+1]>0 then k:=k+1; for i:=k downto 1 do begin str(a[i],s); High_Precision_Addition:=High_Precision_Addition+s; end; end;function High_Precision_Subtraction(s1,s2:ansistring):ansistring;//高精度减法 var a,b:array[1..1000000] of integer; s,p:ansistring; la,lb,k:integer; i:integer; symbol:char; begin High_Precision_Subtraction:=''; fillchar(a,sizeof(a),0); fillchar(b,sizeof(b),0); if s1=s2 then begin writeln(0) ;halt; end; if (length(s1)<length(s2)) or ((length(s1)=length(s2)) and(s1<s2)) then begin symbol:='-'; s:=s1; s1:=s2; s2:=s; end; la:=length(s1); lb:=length(s2); for i:=1 to la do a[i]:=ord(s1[la-i+1])-48; for i:=1 to lb do b[i]:=ord(s2[lb-i+1])-48; k:=la; for i:=1 to k do begin if a[i]<b[i] then begin a[i+1]:=a[i+1]-1; a[i]:=a[i]+10; end; a[i]:=a[i]-b[i]; end; while a[k]=0 do k:=k-1; if symbol='-' then High_Precision_Subtraction:=symbol+High_Precision_Subtraction; for i:=k downto 1 do begin str(a[i],p); High_Precision_Subtraction:=High_Precision_Subtraction+p; end; end;function High_Precision_Multiplication(s1,s2:ansistring):ansistring;//高精度乘法 var la,lb,lc,x,i,j:longint; a,b,c:array [1..1000000] of longint; s:ansistring; begin la:=length(s1);lb:=length(s2); for i:=1 to la do a[la-i+1]:=ord(s1[i])-48; for i:=1 to lb do b[lb-i+1]:=ord(s2[i])-48; for i:=1 to la do begin x:=0; for j:=1 to lb do begin x:=a[i]*b[j]+x div 10+c[i+j-1]; c[i+j-1]:=x mod 10; end; c[i+j]:=x div 10; end; lc:=i+j; while (c[lc]=0)and(lc>1) do lc:=lc-1; for i:=lc downto 1 do begin str(c[i],s); High_Precision_Multiplication:=High_Precision_Multiplication+s; end; end; function High_Precision_Division(s1,s2:ansistring;temp:integer):ansistring;//高精度除法（temp:{‘0’:相除保留10位小数；‘1’:取模；‘2’:求商}） type hp=record len:integer; s:array[1..1000000] of integer; end; var x:array[1..2] of hp; y,w:hp; s:ansistring; procedure out(const p:hp); var i:integer; begin for i:=p.len downto 1 do begin str(p.s[i],s); High_Precision_Division:=High_Precision_Division+s; end; end; procedure init; var j,i:integer; begin if temp=0 then s1:=s1+'0000000000'; //提前加长保留10位小数 x[1].len:=length(s1); for i:=1 to x[1].len do x[1].s[i]:=ord(s1[x[1].len+1-i])-48; x[2].len:=length(s2); for i:=1 to x[2].len do x[2].s[i]:=ord(s2[x[2].len+1-i])-48; end; procedure subtract(a,b:hp;var c:hp); var i,len:integer; begin fillchar(c,sizeof(c),0); if a.len>b.len then len:=a.len else len:=b.len; for i:=1 to len do begin inc(c.s[i],a.s[i]-b.s[i]); if c.s[i]<0 then begin inc(c.s[i],10); dec(c.s[i+1]); end; end; while (len>1) and (c.s[len]=0) do dec(len); c.len:=len; end; function compare(const a,b:hp):integer; var len:integer; begin if a.len>b.len then len:=a.len else len:=b.len; while (len>0) and (a.s[len]=b.s[len]) do dec(len); if len=0 then compare:=0 else compare:=a.s[len]-b.s[len]; end; procedure multiply10(var a:hp); var i:integer; begin for i:=a.len downto 1 do a.s[i+1]:=a.s[i]; a.s[1]:=0; inc(a.len); while (a.len>1) and (a.s[a.len]=0) do dec(a.len); end; procedure divide(a,b:hp;var c,d:hp); var i,j,len:integer; begin fillchar(c,sizeof(c),0); len:=a.len; fillchar(d,sizeof(d),0); d.len:=1; for i:=len downto 1 do begin multiply10(d); d.s[1]:=a.s[i]; while (compare(d,b)>=0) do begin subtract(d,b,d); inc(c.s[i]); end; end; while (len>1) and (c.s[len]=0) do dec(len); c.len:=len; end; begin init; divide(x[1],x[2],y,w); if temp=0 then begin out(y); insert('.',High_Precision_Division,length(High_Precision_Division)-9); //加上小数点 end; if temp=1 then out(w); if temp=2 then out(y); end;function Quick_Power(s1,s2,modulus:ansistring):ansistring; //高精度快速幂 var t,y:ansistring; x,l:integer; begin t:='1'; y:=s1; while s2<>'0' do begin val(s2[length(s2)],x,l); if odd(x)=true then t:= High_Precision_Multiplication(High_Precision_Division(t,modulus,1) , High_Precision_Division(y,modulus,1)); //t:=(t mod modulus)*(y mod modulus) y:=High_Precision_Multiplication(High_Precision_Division(y,modulus,1) , High_Precision_Division(y,modulus,1)); //y:=(y mod modulus)^2; 这里如果模数很大，就先不再加大代码长度，在外面套一个取模了（按理应该加上的） s2:=High_Precision_Division(s2,'2',2); end; exit(High_Precision_Division(t,modulus,1)); end;begin readln(os1); readln(ch); readln(os2); case ch of //在主过程里处理运算符问题及符号问题 '+':begin {加法} if (os1[1]='-')and(os2[1]='-') then begin delete(os1,1,1); delete(os2,1,1); writeln(High_Precision_Addition(os1,os2)); halt; end; if (os1[1]='-')and(os2[1]<>'-') then begin delete(os1,1,1); writeln('-',High_Precision_Subtraction(os2,os1)); halt; end; if (os1[1]<>'-')and(os2[1]<>'-') then begin writeln(High_Precision_Addition(os1,os2)); halt; end; if (os1[1]<>'-')and(os2[1]='-') then begin delete(os2,1,1); writeln(High_Precision_Subtraction(os1,os2)); halt; end; end; '-':begin {减法} if (os1[1]='-')and(os2[1]='-') then begin delete(os1,1,1); delete(os2,1,1); writeln(High_Precision_Subtraction(os2,os1)); halt; end; if (os1[1]='-')and(os2[1]<>'-') then begin delete(os1,1,1); writeln('-',High_Precision_Addition(os1,os2)); halt; end; if (os1[1]<>'-')and(os2[1]<>'-') then begin writeln(High_Precision_Subtraction(os1,os2)); halt; end; if (os1[1]<>'-')and(os2[1]='-') then begin delete(os2,1,1); writeln(High_Precision_Addition(os1,os2)); halt; end; end; '*':begin {乘法} if (os1[1]='-')and(os2[1]='-') then begin delete(os1,1,1); delete(os2,1,1); writeln(High_Precision_Multiplication(os1,os2)); halt; end; if (os1[1]<>'-')and(os2[1]<>'-') then begin writeln(High_Precision_Multiplication(os1,os2)); halt; end; if (os1[1]='-')and(os2[1]<>'-')then begin delete(os1,1,1); writeln('-',High_Precision_Multiplication(os1,os2)); halt; end; if (os1[1]<>'-')and(os2[1]='-') then begin delete(os2,1,1); writeln('-',High_Precision_Multiplication(os1,os2)); halt; end; end; '/':begin {除法} if (os1[1]='-')and(os2[1]='-') then begin delete(os1,1,1); delete(os2,1,1); writeln(High_Precision_Division(os1,os2,0)); halt; end; if (os1[1]<>'-')and(os2[1]<>'-') then begin writeln(High_Precision_Division(os1,os2,0)); halt; end; if (os1[1]<>'-')and(os2[1]='-') then begin delete(os2,1,1); writeln('-',High_Precision_Division(os1,os2,0)); halt; end; if (os1[1]='-')and(os2[1]<>'-') then begin delete(os1,1,1); writeln('-',High_Precision_Division(os1,os2,0)); halt; end; end; '%':begin {取模} if (os1[1]='-')and(os2[1]='-') then begin delete(os1,1,1); delete(os2,1,1); writeln('-',High_Precision_Division(os1,os2,1)); halt; end; if (os1[1]='-')and(os2[1]<>'-') then begin delete(os1,1,1); writeln(High_Precision_Division(os1,os2,1)); halt; end; if (os1[1]<>'-')and(os2[1]='-') then begin delete(os2,1,1); writeln('-',High_Precision_Division(os1,os2,1)); halt; end; if (os1[1]<>'-')and(os2[1]<>'-') then begin writeln(High_Precision_Division(os1,os2,1)); halt; end; end; '^':begin {乘方} readln(md); //由于乘方会炸，这里建议再读入一个模数 val(os2[length(os2)],v,l); if (os1[1]='-')and(odd(v)=true) then begin delete(os1,1,1); if (os2[1]='-') then begin delete(os2,1,1); writeln('-',High_Precision_Division('1',Quick_Power(os1,os2,md),0)); end else writeln('-',Quick_Power(os1,os2,md)); halt; end; if (os1[1]<>'-')and(odd(v)=true) then begin if (os2[1]='-') then begin delete(os2,1,1); writeln(High_Precision_Division('1',Quick_Power(os1,os2,md),0)); end else writeln(Quick_Power(os1,os2,md)); halt; end; if (os1[1]='-')and(odd(v)=false) then begin delete(os1,1,1); if (os2[1]='-') then begin delete(os2,1,1); writeln(High_Precision_Division('1',Quick_Power(os1,os2,md),0)); end else writeln(Quick_Power(os1,os2,md)); halt; end; if (os1[1]<>'-')and(odd(v)=false) then begin if (os2[1]='-') then begin delete(os2,1,1); writeln(High_Precision_Division('1',Quick_Power(os1,os2,md),0)); end else writeln(Quick_Power(os1,os2,md)); halt; end; end; end;end. 0 0
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