Faulhaber's triangle: Difference between revisions
Rename Perl 6 -> Raku, alphabetize, minor clean-up
Thundergnat (talk | contribs) (Rename Perl 6 -> Raku, alphabetize, minor clean-up) |
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0 -3/20 0 1/2 0 -7/10 0 3/4 1/2 1/10</pre>
=={{header|C
{{trans|Java}}
<lang csharp>using System;
Line 517 ⟶ 365:
}
}
}</lang>
{{out}}
<pre> 1
1/2 1/2
1/6 1/2 1/3
0 1/4 1/2 1/4
-1/30 0 1/3 1/2 1/5
0 -1/12 0 5/12 1/2 1/6
1/42 0 -1/6 0 1/2 1/2 1/7
0 1/12 0 -7/24 0 7/12 1/2 1/8
-1/30 0 2/9 0 -7/15 0 2/3 1/2 1/9
0 -3/20 0 1/2 0 -7/10 0 3/4 1/2 1/10</pre>
=={{header|C++}}==
{{trans|C#}}
Uses C++ 17
<lang cpp>#include <exception>
#include <iomanip>
#include <iostream>
#include <numeric>
#include <sstream>
#include <vector>
class Frac {
public:
Frac(long n, long d) {
if (d == 0) {
throw new std::runtime_error("d must not be zero");
}
long nn = n;
long dd = d;
if (nn == 0) {
dd = 1;
} else if (dd < 0) {
nn = -nn;
dd = -dd;
}
long g = abs(std::gcd(nn, dd));
if (g > 1) {
nn /= g;
dd /= g;
}
num = nn;
denom = dd;
}
Frac operator-() const {
return Frac(-num, denom);
}
Frac operator+(const Frac& rhs) const {
return Frac(num*rhs.denom + denom * rhs.num, rhs.denom*denom);
}
Frac operator-(const Frac& rhs) const {
return Frac(num*rhs.denom - denom * rhs.num, rhs.denom*denom);
}
Frac operator*(const Frac& rhs) const {
return Frac(num*rhs.num, denom*rhs.denom);
}
friend std::ostream& operator<<(std::ostream&, const Frac&);
static Frac ZERO() {
return Frac(0, 1);
}
private:
long num;
long denom;
};
std::ostream & operator<<(std::ostream & os, const Frac &f) {
if (f.num == 0 || f.denom == 1) {
return os << f.num;
}
std::stringstream ss;
ss << f.num << "/" << f.denom;
return os << ss.str();
}
Frac bernoulli(int n) {
if (n < 0) {
throw new std::runtime_error("n may not be negative or zero");
}
std::vector<Frac> a;
for (int m = 0; m <= n; m++) {
a.push_back(Frac(1, m + 1));
for (int j = m; j >= 1; j--) {
a[j - 1] = (a[j - 1] - a[j]) * Frac(j, 1);
}
}
// returns 'first' Bernoulli number
if (n != 1) return a[0];
return -a[0];
}
int binomial(int n, int k) {
if (n < 0 || k < 0 || n < k) {
throw new std::runtime_error("parameters are invalid");
}
if (n == 0 || k == 0) return 1;
int num = 1;
for (int i = k + 1; i <= n; i++) {
num *= i;
}
int denom = 1;
for (int i = 2; i <= n - k; i++) {
denom *= i;
}
return num / denom;
}
std::vector<Frac> faulhaberTraingle(int p) {
std::vector<Frac> coeffs;
for (int i = 0; i < p + 1; i++) {
coeffs.push_back(Frac::ZERO());
}
Frac q{ 1, p + 1 };
int sign = -1;
for (int j = 0; j <= p; j++) {
sign *= -1;
coeffs[p - j] = q * Frac(sign, 1) * Frac(binomial(p + 1, j), 1) * bernoulli(j);
}
return coeffs;
}
int main() {
using namespace std;
for (int i = 0; i < 10; i++) {
vector<Frac> coeffs = faulhaberTraingle(i);
for (auto it = coeffs.begin(); it != coeffs.end(); it++) {
cout << right << setw(5) << *it << " ";
}
cout << endl;
}
return 0;
}</lang>
{{out}}
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{ 0 -3/20 0 1/2 0 -7/10 0 3/4 1/2 1/10 }
</pre>
=={{header|FreeBASIC}}==
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56056972216555580111030077961944183400198333273050000</pre>
=={{header|Fōrmulæ}}==
In [https://wiki.formulae.org/Faulhaber this] page you can see the solution of this task.
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text ([http://wiki.formulae.org/Editing_F%C5%8Drmul%C3%A6_expressions more info]). Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for transportation effects more than visualization and edition.
The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code.
=={{header|Go}}==
Line 1,537:
56056972216555580111030077961944183400198333273050000
</pre>
=={{header|Kotlin}}==
Line 1,857 ⟶ 1,856:
56056972216555580111030077961944183400198333273050000
</pre>
=={{header|Phix}}==
Line 2,211 ⟶ 2,166:
{{out}}
<pre>'((1) (1/2 1/2) (1/6 1/2 1/3) (0 1/4 1/2 1/4) (-1/30 0 1/3 1/2 1/5) (0 -1/12 0 5/12 1/2 1/6) (1/42 0 -1/6 0 1/2 1/2 1/7) (0 1/12 0 -7/24 0 7/12 1/2 1/8) (-1/30 0 2/9 0 -7/15 0 2/3 1/2 1/9) (0 -3/20 0 1/2 0 -7/10 0 3/4 1/2 1/10))
56056972216555580111030077961944183400198333273050000</pre>
=={{header|Raku}}==
(formerly Perl 6)
{{works with|Rakudo|2017.05}}
{{trans|Sidef}}
<lang perl6># Helper subs
sub infix:<reduce> (\prev, \this) { this.key => this.key * (this.value - prev.value) }
sub next-bernoulli ( (:key($pm), :value(@pa)) ) {
$pm + 1 => [ map *.value, [\reduce] ($pm + 2 ... 1) Z=> 1 / ($pm + 2), |@pa ]
}
constant bernoulli = (0 => [1.FatRat], &next-bernoulli ... *).map: { .value[*-1] };
sub binomial (Int $n, Int $p) { combinations($n, $p).elems }
sub asRat (FatRat $r) { $r ?? $r.denominator == 1 ?? $r.numerator !! $r.nude.join('/') !! 0 }
# The task
sub faulhaber_triangle ($p) { map { binomial($p + 1, $_) * bernoulli[$_] / ($p + 1) }, ($p ... 0) }
# First 10 rows of Faulhaber's triangle:
say faulhaber_triangle($_)».&asRat.fmt('%5s') for ^10;
say '';
# Extra credit:
my $p = 17;
my $n = 1000;
say sum faulhaber_triangle($p).kv.map: { $^value * $n**($^key + 1) }</lang>
{{out}}
<pre> 1
1/2 1/2
1/6 1/2 1/3
0 1/4 1/2 1/4
-1/30 0 1/3 1/2 1/5
0 -1/12 0 5/12 1/2 1/6
1/42 0 -1/6 0 1/2 1/2 1/7
0 1/12 0 -7/24 0 7/12 1/2 1/8
-1/30 0 2/9 0 -7/15 0 2/3 1/2 1/9
0 -3/20 0 1/2 0 -7/10 0 3/4 1/2 1/10
56056972216555580111030077961944183400198333273050000</pre>
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