一个新算法的表达式求值的函数

Delphi-一个新算法的表达式求值的函数

我经过思考，自已做了一个表达式求值的函数，与标准算法不同，这是我闭门造车而成的，目的在于求简单。
一个BUG是小数点0.999999999。。。。。未自动消除为1。时间匆忙，来不及多说，让读者看了再说吧。
另辟溪径也许有利于开拓新思路吧。我这种方法叫逐层去括号法的表达式求值。
更新日期为2007.5.14.我的邮箱是[e-mail],QQ:165442523.
程序没有用到递归，只用到循环。

unit Unit1;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, StdCtrls,StrUtils, Spin;

type
  TForm1 = class(TForm)
    Edit1: TEdit;
    Edit2: TEdit;
    Button1: TButton;
    procedure Button1Click(Sender: TObject);
   
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form1: TForm1;

implementation

{$R *.dfm}
function   nospace(s:string):string;
begin
result:= stringreplace(s,' ','',[rfReplaceAll]);
end;
function   is123(c:char):boolean;
begin
if  c  in ['0'..'9','.']
then  result:=true
else   result:=false;

end;
function isminus(s:string;i:integer):boolean ;
var
t:integer;
begin

 for t:=i-1 downto 1  do
 begin
   if s[t]=')'  then
   begin
   result:=false;
   break;
   end;
   if (s[t]='(') and (s[t+1]='-') then
   begin
    result:=true;
    break;
   end;
   if (not is123(s[t])) and ( not ((s[t]='-') and(s[t-1]='(')))  then
   begin
   result:=false;
   break;
   end;
 end;
end;

function firstJ(s:string):integer ;
var
i,L:integer;
begin
result:=0;
 L:=length(s);
 for i:=1  to L  do
 begin
   if (s[i]=')')  and (not isminus(s,i))  then
   begin
   result:=i;
   break;
   end;

 end;
end;
function firstC(s:string;firstJ:integer):integer ;
var
t:integer;
begin
 for t:=firstJ downto 1  do
 begin
   if (s[t]='(') and (s[t+1]<>'-') then
   begin
    result:=t;
    break;
   end;

 end;
end;
function firstsign(s:string):integer ;
var
i:integer;
begin
result:=0;
  for  i:=1  to length(s) do
    if  s[i]  in ['+','-','*','/']  then
    begin
    result:=i;
    exit;
    end;
end;
function firstaddsub(s:string;var sigh:char):integer ;
var
i:integer;
begin
result:=0;
  for  i:=1  to length(s) do
  begin
    if  s[i]='+'  then
    begin
    sigh:='+';
    result:=i;
    exit;
    end;
    if  (s[i]='-') and (s[i-1]<>'(')  then
    begin
    sigh:='-';
    result:=i;
    exit;
    end;
    end;
end;
function firstmultidiv(s:string;var sigh:char):integer ;
var
i:integer;
begin
result:=0;
  for  i:=1  to length(s) do
  begin
    if  s[i]='*'  then
    begin
    sigh:='*';
    result:=i;
    exit;
    end;
    if  s[i]='/'  then
    begin
    sigh:='/';
    result:=i;
    exit;
    end;
    end;
end;
function firstsignEX(s:string;sigh:char):integer ;
var
i:integer;
begin
result:=0;
  for  i:=1  to length(s) do
    if  s[i]=sigh  then
    begin
    result:=i;
    exit;
    end;
end;
function firstMinussignEX(s:string):integer ;
var
i:integer;
begin
result:=0;
  for  i:=1  to length(s) do
    if  (s[i]='-') and (s[i-1]<>'(')  then
    begin
    result:=i;
    exit;
    end;
end;
function secondsign(s:string):integer ;
var
i,j:integer;
begin
  j:=firstsign(s);

  for i:=j+1  to length(s) do
    if  s[i]  in ['+','-','*','/']  then
    begin
    result:=i;
    exit;
    end;
  result:=length(s);
end;
function secondsignEX(s:string;sigh:char):integer ;
var
i,j:integer;
begin
  j:=firstsignex(s,sigh);

  for i:=j+1  to length(s) do
    if  s[i]   in ['+','-','*','/']  then
    begin
    result:=i;
    exit;
    end;
  result:=length(s);
end;
function leftnum(s:string;i:integer):double  ;
var
t,L:integer;
begin
L:=length(s);
if s[i-1]=')'  then
begin
  for t:=i-1 downto 1 do
  if  s[t]='('  then
  begin
  result:=strtofloat(copy(s,t+1,i-2-t));
  exit;
  end;
end
else
begin
   for t:=i-1 downto 1 do
   begin
     if  not is123(s[t])  then
     begin
       result:=strtofloat(copy(s,t+1,i-1-t));
       exit;
     end;
     if  t=1  then  result:=strtofloat(leftstr(s,i-1));
   end;
end;

end;
function rightnum(s:string;i:integer):double  ;
var
t,L:integer;
begin
L:=length(s);
if s[i+1]='('  then
begin
  for t:=i+2 to L do
  if  s[t]=')'  then
  begin
  result:=strtofloat(copy(s,i+2,t-i-2));
  exit;
  end;
end
else
begin
   for t:=i+1 to L do
   begin
     if  not is123(s[t])  then
     begin
       result:=strtofloat(copy(s,i+1,t-i-1));
       exit;
     end;
     if  t=L  then  result:=strtofloat(rightstr(s,L-i));
   end;
end;
end;
/////////////////////////////////
function leftsigh(s:string;i:integer):integer  ;
var
t,L:integer;
begin
L:=length(s);
if s[i-1]=')'  then
begin
  for t:=i-1 downto 1 do
  if  s[t]='('  then
  begin
  result:=t;
  exit;
  end;
end
else
begin
   for t:=i-1 downto 1 do
   begin
     if  not is123(s[t])  then
     begin
       result:=t+1;
       exit;
     end;
     if  t=1  then  result:=1;
   end;
end;

end;
function rightsigh(s:string;i:integer):integer  ;
var
t,L:integer;
begin
L:=length(s);
if s[i+1]='('  then
begin
  for t:=i+2 to L do
  if  s[t]=')'  then
  begin
  result:=t;
  exit;
  end;
end
else
begin
   for t:=i+1 to L do
   begin
     if  not is123(s[t])  then
     begin
       result:=t-1;
       exit;
     end;
     if  t=L  then  result:=L;
   end;
end;
end;
////////////////////////////////////

function nomultidiv(s:string):string ;
var
i,L,le,ri:integer;
j,k:double ;
sigh:char;
begin
while 1=1 do
begin
s:=nospace(s);
result:=s;
L:=length(s);
i:=firstmultidiv(s,sigh);
if (i=0) or (s[i]<>sigh)  then exit;
le:=leftsigh(s,i);
j:=leftnum(s,i);
k:=rightnum(s,i);
ri:=rightsigh(s,i);
//if ii<L then
if (sigh<>'*') and (sigh<>'/')  then break;
if sigh='*' then
if j*k>=0  then
s:=leftstr(s,le-1)+floattostr(j*k)+rightstr(s,L-ri)
else
s:=leftstr(s,le-1)+'('+floattostr(j*k)+')'+rightstr(s,L-ri);
if sigh='/' then
if j/k>=0 then
s:=leftstr(s,le-1)+floattostr(j/k)+rightstr(s,L-ri)
else
s:=leftstr(s,le-1)+'('+floattostr(j/k)+')'+rightstr(s,L-ri);
end;
result:=s;
end;
function nodiv(s:string):string ;
var
i,L,le,ri:integer;
j,k:double ;
begin
s:=nospace(s);
result:=s;
L:=length(s);
i:=firstsignex(s,'/');
if (i=0) or (s[i]<>'/')  then exit;
le:=leftsigh(s,i);
j:=leftnum(s,i);
k:=rightnum(s,i);
ri:=rightsigh(s,i);
if j/k>=0 then
result:=nodiv(leftstr(s,le-1)+floattostr(j/k)+rightstr(s,L-ri))
else
result:=nodiv(leftstr(s,le-1)+'('+floattostr(j/k)+')'+rightstr(s,L-ri))

end;
function noaddsub(s:string):string ;
var
i,L,le,ri:integer;
j,k:double ;
sigh:char;
begin
while 1=1 do
begin
s:=nospace(s);
result:=s;
L:=length(s);
i:=firstaddsub(s,sigh);
if (i=0) or (s[i]<>sigh)  then exit;
le:=leftsigh(s,i);
j:=leftnum(s,i);
k:=rightnum(s,i);
ri:=rightsigh(s,i);
if (sigh<>'+')   and  (sigh<>'-')  then  break;
if sigh='+'  then
if j+k>=0 then
s:=leftstr(s,le-1)+floattostr(j+k)+rightstr(s,L-ri)
else
s:=leftstr(s,le-1)+'('+floattostr(j+k)+')'+rightstr(s,L-ri);
if sigh='-'  then
if j-k>=0 then
s:=leftstr(s,le-1)+floattostr(j-k)+rightstr(s,L-ri)
else
s:=leftstr(s,le-1)+'('+floattostr(j-k)+')'+rightstr(s,L-ri);
end;
result:=s;
end;
function nosub(s:string):string ;
var
i,L,le,ri:integer;
j,k:double ;
begin
s:=nospace(s);
result:=s;
L:=length(s);
i:=firstMinussignEX(s);
if (i=0) or (s[i]<>'-')  then exit;
le:=leftsigh(s,i);
j:=leftnum(s,i);
k:=rightnum(s,i);
ri:=rightsigh(s,i);
if j-k>=0 then
result:=nosub(leftstr(s,le-1)+floattostr(j-k)+rightstr(s,L-ri))
else
result:=nosub(leftstr(s,le-1)+'('+floattostr(j-k)+')'+rightstr(s,L-ri))

end;
function alltoone(s:string):string ;
begin
 s:=nomultidiv(s);
 s:=noaddsub(s);
 result:=s;
end;

function  myexpress(s:string):string;
var
c,j,L:integer;
le,ri,al,substr,s0:string;
tryit:double;
begin
while 1=1 do
begin
s:=nospace(s);
s0:=s;
L:=length(s);
//if (s[1]<>'(') or (s[L]<>')')  then
//s:='('+s+')';
//if (s[1]='(') and (s[L]=')') and((s[2]='-')  or (isminus(s,L)))  then
//s:='('+s+')';
L:=length(s);
j:=firstJ(s);
c:=firstc(s,j);
if j>c then
begin
substr:=copy(s,c+1,j-c-1);
//le:=leftstr(s,c-1);
//ri:= rightstr(s,L-j);
le:=leftstr(s,c-1);
le:=rightstr(le,length(le));
ri:= rightstr(s,L-j);
ri:=leftstr(ri,length(ri));
//showmessage(substr);
al:=alltoone(substr);
//showmessage(le+al+ri);
s:=le+al+ri;
end
else
begin
s:=alltoone(s0);
 break;
end;
end;
result:=s;
if (result[1]='(')  and (result[length(result)]=')') then
result:=copy(result,2,length(result)-2);
end;
procedure TForm1.Button1Click(Sender: TObject);
begin
Edit2.Text:=myexpress(edit1.text);
end;

 

end.