Problem 61 - Pascal

Pascal is one of those languages that comes up all the time as an older language that used to be hip and cool, but nobody uses anymore. So, that makes it a perfect target for use in this blog. My experience seemed to validate Pascal's current status: its a fine language and all, but its a bit stiff and has a lot of weird features that have been smoothed out in later languages (variable declarations need to go in a certain place, function parameters are grouped by type, semicolons are necessary in weird places, and must be omitted in even weirder places [defining weird as unnatural to my sensibilities, though the rules do themselves make some sense]). Anyway, most of my difficulty with this problem came not in difficulties with Pascal, but rather difficulties with a corner case of the problem itself: it is necessary to find a cycle of numbers where one is triangular, one square, one pentagonal, one hexagonal, one heptagonal, and one octagonal. I originally decided to make the beginning of my cycle an octagonal number, as there are the fewest of them, but I realized this to be foolhardy due to an issue involving all hexagonal numbers also being triangular. This was solved by beginning cycles with triangular numbers. Anyway, my Pascal solution is below, and it runs fairly quickly (~ 20ms on my machine). Also, if anyone noticed, yes, I skipped problem 60. I'll get to it soon enough.

program Euler61;

var
    temp : integer;
    ans  : integer;
    t    : integer;
    i    : integer;

function nthTri(x : integer) : integer;
begin
    nthTri := (x * (x + 1)) div  2
end;
function isTri(x : integer) : Boolean;
begin
    temp  := round(sqrt(2*x + 1/4) + 1/2);
    isTri := temp * (temp + 1) / 2 = x
end;

function isSquare(x : integer) : Boolean;
begin
    temp     := round(sqrt(x));
    isSquare := temp * temp = x
end;

function isPent(x : integer) : Boolean;
begin
    temp   := round(sqrt(2/3 * x + 1 / 36) + 1/6);
    isPent := temp * (3 * temp - 1) / 2 = x
end;

function isHex(x : integer) : Boolean;
begin
    temp  := round(sqrt(x / 2 + 1 / 16) + 1/4);
    isHex := temp * (2 * temp - 1) = x
end;

function isHept(x : integer) : Boolean;
begin
    temp   := round(sqrt(2 / 5 * x + 9 / 100) + 3 / 10);
    isHept := temp * (5 * temp - 3) / 2 = x
end;

function isOct(x : integer) : Boolean;
begin
    temp  := round(sqrt(x / 3 + 1/9) + 1/3);
    isOct := temp * (3 * temp - 2) = x
end;

function shape(x,found : integer) : integer;
begin
    if isHept(x) then
        shape := 5
    else
        if isHex(x) then
            shape := 4
        else
            if isPent(x) then
                shape := 3
            else
                if isSquare(x) then
                    shape := 2
                else
                    if isOct(x) then 
                        shape := 1
                    else
                        shape := 0;
end;

function Next(x, found, sum, origin : integer) : integer;
var
    base : integer;
    s : integer;
    r : integer;
    test : integer;
    tfound : integer;
    tsum : integer;
begin
    r := 10;
    base := (x mod 100) * 100;
    while r <= 99 do
    begin
        s := 1 shl shape(base + r, found);
        if (found and s) = 0 then
        begin
            tfound := found + s;
            tsum   := sum + (base + r);
            if tfound = 63 then
            begin
                if r = origin div 100 then
                    Next := tsum
                else
                    Next := 0;
                exit;
            end

            else
            begin
                test := Next(base + r, tfound, tsum, origin);
                if test > 0 then
                begin
                    Next := test;
                    exit
                end;
            end;
        end;
        r := r + 1;
    end;
    Next := 0
end;

begin
    ans := 0;
    i := 45;
    while ans = 0 do
    begin
        t   := nthTri(i);
        if t mod 100 > 10 then
            ans := Next(t,1,t,t);
        i   := i + 1;
        if t > 9999 then
            exit;
    end;
    writeln(ans)
end.