79 lines
2.1 KiB
C#
79 lines
2.1 KiB
C#
using System;
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using System.Numerics;
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public class BigRational
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{
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public BigInteger Numerator { get; private set; }
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public BigInteger Denominator { get; private set; }
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public BigRational(BigInteger numerator, BigInteger denominator)
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{
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if (denominator == 0)
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throw new ArgumentException("Denominator cannot be zero.", nameof(denominator));
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BigInteger gcd = BigInteger.GreatestCommonDivisor(numerator, denominator);
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Numerator = numerator / gcd;
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Denominator = denominator / gcd;
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if (Denominator < 0)
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{
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Numerator = -Numerator;
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Denominator = -Denominator;
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}
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}
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public static BigRational operator +(BigRational a, BigRational b)
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{
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return new BigRational(a.Numerator * b.Denominator + b.Numerator * a.Denominator, a.Denominator * b.Denominator);
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}
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public override string ToString()
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{
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return $"{Numerator}/{Denominator}";
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}
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}
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class Program
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{
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static BigRational Harmonic(int n)
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{
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BigRational sum = new BigRational(0, 1);
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for (int i = 1; i <= n; i++)
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{
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BigRational r = new BigRational(1, i);
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sum += r;
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}
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return sum;
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}
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static void Main(string[] args)
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{
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Console.WriteLine("The first 20 harmonic numbers and the 100th, expressed in rational form, are:");
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int[] numbers = new int[21];
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for (int i = 1; i <= 20; i++)
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{
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numbers[i - 1] = i;
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}
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numbers[20] = 100;
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foreach (int i in numbers)
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{
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Console.WriteLine($"{i,3} : {Harmonic(i)}");
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}
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Console.WriteLine("\nThe first harmonic number to exceed the following integers is:");
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const int limit = 10;
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for (int i = 1, n = 1; i <= limit; n++)
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{
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double h = 0;
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for (int j = 1; j <= n; j++)
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{
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h += 1.0 / j;
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}
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if (h > i)
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{
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Console.WriteLine($"integer = {i,2} -> n = {n,6} -> harmonic number = {h,9:F6} (to 6dp)");
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i++;
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}
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}
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}
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}
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