Task: Heronian triangles


C++: #include <algorithm>
#include <cmath>
#include <iostream>
#include <tuple>
#include <vector>

int gcd(int a, int b)
{
    int rem = 1, dividend, divisor;
    std::tie(divisor, dividend) = std::minmax(a, b);
    while (rem != 0) {
        rem = dividend % divisor;
        if (rem != 0) {
            dividend = divisor;
            divisor = rem;
        }
    }
    return divisor;
}

struct Triangle
{
    int a;
    int b;
    int c;
};

int perimeter(const Triangle& triangle)
{
    return triangle.a + triangle.b + triangle.c;
}

double area(const Triangle& t)
{
    double p_2 = perimeter(t) / 2.;
    double area_sq = p_2 * ( p_2 - t.a ) * ( p_2 - t.b ) * ( p_2 - t.c );
    return sqrt(area_sq);
}

std::vector<Triangle> generate_triangles(int side_limit = 200)
{
    std::vector<Triangle> result;
    for(int a = 1; a <= side_limit; ++a)
        for(int b = 1; b <= a; ++b)
            for(int c = a+1-b; c <= b; ++c) 
            {
                Triangle t{a, b, c};
                double t_area = area(t);
                if(t_area == 0) continue;
                if( std::floor(t_area) == std::ceil(t_area) && gcd(a, gcd(b, c)) == 1)
                    result.push_back(t);
            }
    return result;
}

bool compare(const Triangle& lhs, const Triangle& rhs)
{
    return std::make_tuple(area(lhs), perimeter(lhs), std::max(lhs.a, std::max(lhs.b, lhs.c))) <
           std::make_tuple(area(rhs), perimeter(rhs), std::max(rhs.a, std::max(rhs.b, rhs.c)));
}

struct area_compare
{
    bool operator()(const Triangle& t, int i) { return area(t) < i; }
    bool operator()(int i, const Triangle& t) { return i < area(t); }
};

int main()
{
    auto tri = generate_triangles();
    std::cout << "There are " << tri.size() << " primitive Heronian triangles with sides up to 200\n\n";

    std::cout << "First ten when ordered by increasing area, then perimeter, then maximum sides:\n";
    std::sort(tri.begin(), tri.end(), compare);
    std::cout << "area\tperimeter\tsides\n";
    for(int i = 0; i < 10; ++i)
        std::cout << area(tri[i]) << '\t' << perimeter(tri[i]) << "\t\t" <<
                     tri[i].a << 'x' << tri[i].b << 'x' << tri[i].c << '\n';

    std::cout << "\nAll with area 210 subject to the previous ordering:\n";
    auto range = std::equal_range(tri.begin(), tri.end(), 210, area_compare());
    std::cout << "area\tperimeter\tsides\n";
    for(auto it = range.first; it != range.second; ++it)
        std::cout << area(*it) << '\t' << perimeter(*it) << "\t\t" <<
                     it->a << 'x' << it->b << 'x' << it->c << '\n';
}







VB: Function heroArea(a As Integer, b As Integer, c As Integer) As Double
    s = (a + b + c) / 2
    On Error GoTo Err
    heroArea = Sqr(s * (s - a) * (s - b) * (s - c))
    Exit Function
Err:
    heroArea = -1
End Function
 
Function hero(h As Double) As Boolean
    hero = (h - Int(h) = 0) And h > 0
End Function
 
Public Sub main()
    Dim list() As Variant, items As Integer
    Dim a As Integer, b As Integer, c As Integer
    Dim hArea As Double
    Dim tries As Long
    For a = 1 To 200
        For b = 1 To a
            For c = 1 To b
                tries = tries + 1
                If gcd(gcd(a, b), c) = 1 Then
                    hArea = heroArea(a, b, c)
                    If hero(hArea) Then
                        ReDim Preserve list(items)
                        list(items) = Array(CStr(hArea), CStr(a + b + c), CStr(a), CStr(b), CStr(c))
                        items = items + 1
                    End If
                End If
            Next c
        Next b
    Next a
    list = sort(list)
    Debug.Print "Primitive Heronian triangles with sides up to 200:"; UBound(list) + 1; "(of"; tries; "tested)"
    Debug.Print
    Debug.Print "First 10 ordered by area/perimeter/sides:"
    Debug.Print "area       perimeter        sides"
    For i = 0 To 9
        Debug.Print Format(list(i)(0), "@@@"), Format(list(i)(1), "@@@"),
        Debug.Print list(i)(2); "x"; list(i)(3); "x"; list(i)(4)
    Next i
    Debug.Print
    Debug.Print "area = 210:"
    Debug.Print "area       perimeter        sides"
    For i = 0 To UBound(list)
        If Val(list(i)(0)) = 210 Then
            Debug.Print Format(list(i)(0), "@@@"), Format(list(i)(1), "@@@"),
            Debug.Print list(i)(2); "x"; list(i)(3); "x"; list(i)(4)
        End If
    Next i
End Sub