Anonymous user
Fraction reduction: Difference between revisions
no edit summary
No edit summary |
|||
Line 69:
:* Wikipedia entry: [https://en.wikipedia.org/wiki/Anomalous_cancellation anomalous cancellation and/or accidental cancellation].
<br><br>
=={{header|Ada}}==
{{trans|Python}}
<lang Ada>with Ada.Integer_Text_IO;
with Ada.Text_IO; use Ada.Text_IO;
procedure Fraction_Reduction is
type Int_Array is array (Natural range <>) of Integer;
procedure Put (Item : Integer;
Width : Field := 0; -- Override default width
Base : Number_Base := Ada.Integer_Text_IO.Default_Base)
renames Ada.Integer_Text_IO.Put;
function indexOf(haystack : Int_Array; needle : Integer) return Integer is
idx : Integer := 0;
begin
for straw of haystack loop
if straw = needle then
return idx;
else
idx := idx + 1;
end if;
end loop;
return -1;
end IndexOf;
function getDigits(n, le : in Integer;
digit_array : in out Int_Array) return Boolean is
n_local : Integer := n;
le_local : Integer := le;
r : Integer;
begin
while n_local > 0 loop
r := n_local mod 10;
if r = 0 or indexOf(digit_array, r) >= 0 then
return False;
end if;
le_local := le_local - 1;
digit_array(le_local) := r;
n_local := n_local / 10;
end loop;
return True;
end getDigits;
function removeDigit(digit_array : Int_Array;
le, idx : Integer) return Integer is
sum : Integer := 0;
pow : Integer := 10 ** (le - 2);
begin
for i in 0 .. le - 1 loop
if i /= idx then
sum := sum + digit_array(i) * pow;
pow := pow / 10;
end if;
end loop;
return sum;
end removeDigit;
lims : constant array (0 .. 3) of Int_Array (0 .. 1) :=
((12, 97), (123, 986), (1234, 9875), (12345, 98764));
count : Int_Array (0 .. 4) := (others => 0);
omitted : array (0 .. 4) of Int_Array (0 .. 9) :=
(others => (others => 0));
begin
for i in lims'Range loop
declare
nDigits, dDigits : Int_Array (0 .. i + 1);
digit, dix, rn, rd : Integer;
begin
for n in lims(i)(0) .. lims(i)(1) loop
nDigits := (others => 0);
if getDigits(n, i + 2, nDigits) then
for d in n + 1 .. lims(i)(1) + 1 loop
dDigits := (others => 0);
if getDigits(d, i + 2, dDigits) then
for nix in nDigits'Range loop
digit := nDigits(nix);
dix := indexOf(dDigits, digit);
if dix >= 0 then
rn := removeDigit(nDigits, i + 2, nix);
rd := removeDigit(dDigits, i + 2, dix);
-- 'n/d = rn/rd' is same as 'n*rd = rn*d'
if n*rd = rn*d then
count(i) := count(i) + 1;
omitted(i)(digit) :=
omitted(i)(digit) + 1;
if count(i) <= 12 then
Put (n);
Put ("/");
Put (d);
Put (" = ");
Put (rn);
Put ("/");
Put (rd);
Put (" by omitting ");
Put (digit);
Put_Line ("'s");
end if;
end if;
end if;
end loop;
end if;
end loop;
end if;
end loop;
end;
New_Line;
end loop;
for i in 2 .. 5 loop
Put ("There are ");
Put (count(i - 2));
Put (" ");
Put (i);
Put_Line ("-digit fractions of which:");
for j in 1 .. 9 loop
if omitted(i - 2)(j) /= 0 then
Put (omitted(i - 2)(j), Width => 6);
Put (" have ");
Put (j);
Put_Line ("'s omitted");
end if;
end loop;
New_Line;
end loop;
end Fraction_Reduction;</lang>
=={{header|C}}==
| |||