Special pythagorean triplet: Difference between revisions
C++ entry
Alextretyak (talk | contribs) (Added 11l) |
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Line 116:
200+375+425=1000
200*375*425=31875000
</pre>
=={{header|C++}}==
<lang cpp>#include <cmath>
#include <concepts>
#include <iostream>
#include <numeric>
#include <optional>
#include <tuple>
using namespace std;
optional<tuple<int, int ,int>> FindPerimeterTriplet(int perimeter)
{
unsigned long long perimeterULL = perimeter;
auto max_M = (unsigned long long)sqrt(perimeter/2) + 1;
for(unsigned long long m = 2; m < max_M; ++m)
{
for(unsigned long long n = 1 + m % 2; n < m; n+=2)
{
if(gcd(m,n) != 1)
{
continue;
}
// The formulas below will generate primitive triples if:
// 0 < n < m
// m and n are relatively prime (gcd == 1)
// m + n is odd
auto a = m * m - n * n;
auto b = 2 * m * n;
auto c = m * m + n * n;
auto primitive = a + b + c;
// check all multiples of the primitive at once
auto factor = perimeterULL / primitive;
if(primitive * factor == perimeterULL)
{
// the triplet has been found
if(b<a) swap(a, b);
return tuple{a * factor, b * factor, c * factor};
}
}
}
// the triplet was not found
return nullopt;
}
int main()
{
auto t1 = FindPerimeterTriplet(1000);
if(t1)
{
auto [a, b, c] = *t1;
cout << "[" << a << ", " << b << ", " << c << "]\n";
cout << "a * b * c = " << a * b * c << "\n";
}
else
{
cout << "Perimeter not found\n";
}
}</lang>
{{out}}
<pre>
[200, 375, 425]
a * b * c = 31875000
</pre>
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