Premise: I didn't go through your entire implementation, thou' at first
sight looks much better than the current one.
I know roman numerals since I was 8 or 9 yo, that makes a quick and dirt
result of about 35 years.
Thing is:
1. in the roman numerals, not all the digits can be subtracted from the
others
2. no more than three same roman numerals can appear in a row.
so that XM is as invalid as CCCC.
(although this amenity can be seen on some - in my opinion poor -
wristwatches' face that uses roman numerals, for the 4h, showing IIII
instead of the correct IV, but this is another story)
in roman numerals we have only these digits:
I(1) V(5)
X(10) L(50)
C(100) D(500)
M(1000) (sorry, no digit for the expected progression, for 5000)
the only digits that can be subtracted are I, X and C (only those on the
left side of the "table" above), and they can only from the 2 digits
immediately following them in the system, so that:
I can be subtracted only from V and X
X can be subtracted only from L and C
C can be subtracted only from D and M
so that 45 cannot be written as VL (50 - 5, as one might suspect) but
must be written as XLV, or to better understand, as (XL)V = 40 + 5
The maximum roman numeral that can be represented is 4999, that is NOT
MMMIM, but instead: MMM(CM)(XC)(IX)
1000+1000+1000+(1000-900)+(100-10)+(10-1)
After this, roman numerals always begin with bigger numbers to sum up,
and proceed to smaller, so you cannot start adding up 10, then 500, then
again 1; like XDI (whether it be intended to be 491 or 511 - just no way)
I did an implementation some time ago, for pure fun, and provided I find
it out (or maybe I can just rewrite it, on the basis of this knowledge)
I will be - repository allowing ;-) - wery happy to contribute with my
2c for it.
Cheers, A.
On 20/09/13 21:49, Bart wrote:
On 9/20/13, Reinier Olislagers<reinierolislag...@gmail.com> wrote:
The question however becomes "what is the
algorithm for deciding invalid characters" which IMO will become a mess
very quickly. Much better to just consider the entire input as invalid.
Here's my implementation:
program test;
{$mode objfpc}
{$H+}
uses
SysUtils, StrUtils;
function TryRomanToInt(S: String; out N: Integer): Boolean;
var
i, Len: Integer;
Terminated: Boolean;
begin
Result := (False);
S := UpperCase(S); //don't use AnsiUpperCase please
Len := Length(S);
if (Len = 0) then Exit;
i := 1;
N := 0;
Terminated := False;
//leading M's
while (i<= Len) and (S[i] = 'M') do
begin
//writeln('TryRomanToInt: Found 1000');
Inc(i);
N := N + 1000;
end;
//then CM or or CD or D or (C, CC, CCC, CCCC)
if (i<= Len) and (S[i] = 'D') then
begin
//writeln('TryRomanToInt: Found 500');
Inc(i);
N := N + 500;
end
else if (i + 1<= Len) and (S[i] = 'C') then
begin
if (S[i+1] = 'M') then
begin
//writeln('TryRomanToInt: Found 900');
Inc(i,2);
N := N + 900;
end
else if (S[i+1] = 'D') then
begin
//writeln('TryRomanToInt: Found 400');
Inc(i,2);
N := N + 400;
end;
end ;
//next max 4 C's
if (i<= Len) and (S[i] = 'C') then
begin
//find max 4 C's
//writeln('TryRomanToInt: Found 100');
Inc(i);
N := N + 100;
if (i<= Len) and (S[i] = 'C') then
begin
//writeln('TryRomanToInt: Found 100');
Inc(i);
N := N + 100;
end;
if (i<= Len) and (S[i] = 'C') then
begin
//writeln('TryRomanToInt: Found 100');
Inc(i);
N := N + 100;
end;
if (i<= Len) and (S[i] = 'C') then
begin
//writeln('TryRomanToInt: Found 100');
Inc(i);
N := N + 100;
end;
end;
//then XC or XL
if (i + 1<= Len) and (S[i] = 'X') then
begin
if (S[i+1] = 'C') then
begin
//writeln('TryRomanToInt: Found 90');
Inc(i,2);
N := N + 90;
end
else if (S[i+1] = 'L') then
begin
//writeln('TryRomanToInt: Found 40');
Inc(i,2);
N := N + 40;
end;
end;
//then L
if (i<= Len) and (S[i] = 'L') then
begin
//writeln('TryRomanToInt: Found 50');
Inc(i);
N := N + 50;
end;
//then (X, xx, xxx, xxxx)
if (i<= Len) and (S[i] = 'X') then
begin
//find max 4 X's
//writeln('TryRomanToInt: Found 10');
Inc(i);
N := N + 10;
if (i<= Len) and (S[i] = 'X') then
begin
//writeln('TryRomanToInt: Found 10');
Inc(i);
N := N + 10;
end;
if (i<= Len) and (S[i] = 'X') then
begin
//writeln('TryRomanToInt: Found 10');
Inc(i);
N := N + 10;
end;
if (i<= Len) and (S[i] = 'X') then
begin
//writeln('TryRomanToInt: Found 10');
Inc(i);
N := N + 10;
end;
end;
//then IX or IV
if (i + 1<= Len) and (S[i] = 'I') then
begin
if (S[i+1] = 'X') then
begin
Terminated := (True);
//writeln('TryRomanToInt: Found 9');
Inc(i,2);
N := N + 9;
end
else if (S[i+1] = 'V') then
begin
Terminated := (True);
//writeln('TryRomanToInt: Found 4');
Inc(i,2);
N := N + 4;
end;
end;
//then V
if (not Terminated) and (i<= Len) and (S[i] = 'V') then
begin
//writeln('TryRomanToInt: Found 5');
Inc(i);
N := N + 5;
end;
//then I
if (not Terminated) and (i<= Len) and (S[i] = 'I') then
begin
Terminated := (True);
//writeln('TryRomanToInt: Found 1');
Inc(i);
N := N + 1;
//Find max 3 closing I's
if (i<= Len) and (S[i] = 'I') then
begin
//writeln('TryRomanToInt: Found 1');
Inc(i);
N := N + 1;
end;
if (i<= Len) and (S[i] = 'I') then
begin
//writeln('TryRomanToInt: Found 1');
Inc(i);
N := N + 1;
end;
if (i<= Len) and (S[i] = 'I') then
begin
//writeln('TryRomanToInt: Found 1');
Inc(i);
N := N + 1;
end;
end;
//writeln('TryRomanToInt: Len = ',Len,' i = ',i);
Result := (i> Len);
//if Result then writeln('TryRomanToInt: N = ',N);
end;
var
S: String;
N1, N2: Integer;
B: Boolean;
begin
repeat
write('Enter Roman numeral: ');
readln(S);
B := TryRomanToInt(S, N1);
if B then
write('TryRomanToInt(''',S,''') -> ',N1)
else
write('TryRomanToInt(''',S,''') FAIL');
writeln;
N2 := StrUtils.RomanToInt(S);
writeln('StrUtils.RomanToInt(''',S,''') = ',N2);
if B and (N1<> N2) then writeln('StrUtils.RomanToInt<> TryRomanToInt');
writeln;
until S = '';
end.
Bart
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_______________________________________________
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http://lists.freepascal.org/mailman/listinfo/fpc-pascal
