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euler.pas
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euler.pas
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(* Project Euler in pascal (specifically targeting the GNU pascal compiler)
To compile:
% gpc euler.pas -o euler
*)
program euler;
(* Euler #1
Answer: 233168
If we list all the natural numbers below 10 that are multiples of 3 or 5,
we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000.
*)
function euler1 : integer;
var
n : integer = 0;
i : integer;
begin
for i := 1 to 999 do
begin
if (i mod 3 = 0) or (i mod 5 = 0) then
begin
n := n + i;
end;
end;
euler1 := n;
end;
(* Euler #2
Answer: 4613732
Each new term in the Fibonacci sequence is generated by adding the previous
two terms. By starting with 1 and 2, the first 10 terms will be:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
Find the sum of all the even-valued terms in the sequence which do not
exceed four million.
*)
function euler2 : integer;
var
n : integer = 2;
a : integer = 1;
b : integer = 2;
c : integer;
begin
while true do
begin
c := a + b;
if c > 4000000 then
break;
if c mod 2 = 0 then
n := n + c;
a := b;
b := c;
end;
euler2 := n
end;
function ceil(d : double) : integer;
begin
(* There is probably a more clever way to do this, but this gets the job done for now. *)
if frac(d) >= 0.5 then
ceil := round(d)
else
ceil := trunc(d)
end;
(* Euler #3
Answer: 6857
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143 ?
*)
function is_prime(n : integer) : boolean;
var
i : integer;
result : boolean = true;
begin
if n <> 2 then
for i := 2 to ceil(sqrt(n)) do
begin
if n mod i = 0 then
begin
result := false;
break;
end;
end;
is_prime := result;
end;
function euler3 : integer;
const
target : LongInt = 600851475143;
var
i : integer;
stop : boolean = true;
begin
for i := ceil(sqrt(target)) downto 2 do
if (target mod i = 0) and is_prime(i) then
begin
euler3 := i;
break;
end;
end;
(* Problem #4
Answer: 906609 - doesn't work yet.
A palindromic number reads the same both ways. The largest
palindrome made from the product of two 2-digit numbers is 9009 =
91 99.
Find the largest palindrome made from the product of two 3-digit
numbers.
*)
(* ghetto *)
procedure swap(var s : string; i : integer; j : integer);
var
tmp : char;
begin
tmp := s[i];
s[i] := s[j];
s[j] := tmp;
end;
function reverse(s : string) : string;
var
i : integer;
len : integer;
begin
len := length(s);
for i := 1 to trunc(len/2.0) do
swap(s, i, len + 1 - i);
reverse := s;
end;
function is_palindromic_number(n :integer) : boolean;
var
s : String[6];
begin
Str(n, s);
is_palindromic_number := s = reverse(s);
end;
function euler4 : integer;
var
i : integer;
j : integer;
p : integer;
result : integer = 0;
begin
for i := 100 to 999 do
for j := 100 to 999 do
begin;
p := i * j;
if (p > result) and is_palindromic_number(p) then
result := p;
end;
euler4 := result;
end;
begin
writeln(euler1());
writeln(euler2());
writeln(euler3());
writeln(euler4());
end.