Faulhaber's triangle: Difference between revisions

Content added Content deleted

Inline

@@ Line 387: / Line 387: @@
 #include <sstream>
 #include <vector>
 class Frac {
 public:
-	Frac(long n, long d) {
+    Frac() : num(0), denom(1) {}
+	Frac(int n, int d) {
 		if (d == 0) {
-			throw new std::runtime_error("d must not be zero");
+			throw std::runtime_error("d must not be zero");
 		}
-		long nn = n;
+		int sign_of_d = d < 0 ? -1 : 1;
-		long dd = d;
+		int g = std::gcd(n, d);
-		if (nn == 0) {
-			dd = 1;
-		} else if (dd < 0) {
-			nn = -nn;
-			dd = -dd;
-		}
+        num = sign_of_d * n / g;
-		long g = abs(std::gcd(nn, dd));
+        denom = sign_of_d * d / g;
-		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&);
+	Frac operator*(int rhs) const {
+		return Frac(num * rhs, denom);
-	static Frac ZERO() {
-		return Frac(0, 1);
 	}
+	friend std::ostream& operator<<(std::ostream&, const Frac&);
 private:
-	long num;
+	int num;
-	long denom;
+	int 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");
+		throw 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);
+			a[j - 1] = (a[j - 1] - a[j]) * j;
 		}
 	}
 	// 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");
+		throw 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;
+	std::vector<Frac> coeffs(p + 1);
-	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);
+		coeffs[p - j] = q * sign * binomial(p + 1, j) * bernoulli(j);
 	}
 	return coeffs;
 }
 int main() {
-	using namespace std;
 	for (int i = 0; i < 10; i++) {
-		vector<Frac> coeffs = faulhaberTraingle(i);
+		std::vector<Frac> coeffs = faulhaberTraingle(i);
-		for (auto it = coeffs.begin(); it != coeffs.end(); it++) {
+		for (auto frac : coeffs) {
-			cout << right << setw(5) << *it << "  ";
+			std::cout << std::right << std::setw(5) << frac << "  ";
 		}
-		cout << endl;
+		std::cout << std::endl;
 	}
 	return 0;
 }</lang>