分数の構造体とつべで見つけた数学の問題 (C#) (original) (raw)
分数のクラスとかあったら便利じゃねと考えて、標準にあるだろうと思ったら無かった。
演算子をオーバーライドしたので構造体
分子・分母共に BigInteger を使う。
using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Numerics;
namespace Charlotte.Tools { public struct Fraction { public BigInteger Numer; public BigInteger Denom;
public Fraction(BigInteger numer, BigInteger denom)
{
this.Numer = numer;
this.Denom = denom;
}
public static implicit operator Fraction(long value)
{
return new Fraction(value, 1);
}
public static Fraction operator ++(Fraction instance)
{
return instance + new Fraction(1, 1);
}
public static Fraction operator --(Fraction instance)
{
return instance - new Fraction(1, 1);
}
public static Fraction operator +(Fraction a, Fraction b)
{
Reduction(ref a, ref b);
return new Fraction(a.Numer + b.Numer, b.Denom);
}
public static Fraction operator -(Fraction a, Fraction b)
{
Reduction(ref a, ref b);
return new Fraction(a.Numer - b.Numer, b.Denom);
}
public static Fraction operator *(Fraction a, Fraction b)
{
return new Fraction(a.Numer * b.Numer, a.Denom * b.Denom);
}
public static Fraction operator /(Fraction a, Fraction b)
{
return new Fraction(a.Numer * b.Denom, a.Denom * b.Numer);
}
public static bool operator ==(Fraction a, Fraction b)
{
Reduction(ref a, ref b);
return a.Numer == b.Numer;
}
public static bool operator !=(Fraction a, Fraction b)
{
Reduction(ref a, ref b);
return a.Numer != b.Numer;
}
public override bool Equals(object another)
{
return another is Fraction && this == (Fraction)another;
}
public override int GetHashCode()
{
return (this.Numer.GetHashCode() + ":" + this.Denom.GetHashCode()).GetHashCode();
}
public static bool operator <(Fraction a, Fraction b)
{
Reduction(ref a, ref b);
return a.Numer < b.Numer;
}
public static bool operator >(Fraction a, Fraction b)
{
Reduction(ref a, ref b);
return a.Numer > b.Numer;
}
public static bool operator <=(Fraction a, Fraction b)
{
Reduction(ref a, ref b);
return a.Numer <= b.Numer;
}
public static bool operator >=(Fraction a, Fraction b)
{
Reduction(ref a, ref b);
return a.Numer >= b.Numer;
}
public static void Reduction(ref Fraction a, ref Fraction b)
{
BigInteger d = a.Denom * b.Denom;
a.Numer *= b.Denom;
b.Numer *= a.Denom;
a.Denom = d;
b.Denom = d;
}
public void Simplify()
{
if (this.Denom == 0)
throw new Exception("Bad fraction");
if (this.Numer == 0)
{
this.Denom = 1;
return;
}
if (this.Numer < 0)
{
this.Numer *= -1;
this.Denom *= -1;
}
int sign = 1;
if (this.Denom < 0)
{
sign = -1;
this.Denom = BigInteger.Abs(this.Denom);
}
if (this.Numer == this.Denom)
{
this.Numer = sign;
this.Denom = 1;
return;
}
BigInteger d = GetGCD(this.Numer, this.Denom);
this.Numer /= d;
this.Denom /= d;
this.Numer *= sign;
}
private static BigInteger GetGCD(BigInteger a, BigInteger b)
{
if (a < b)
{
BigInteger t = a;
a = b;
b = t;
}
while (b != 0)
{
BigInteger r = a % b;
a = b;
b = r;
}
return a;
}
}}
で、これを使って...
www.youtube.com
...この問題を解いてみる。
source:
public void Test01()
{
const int MURABITO_NUM = 100;
List<Murabito_t> murabitoList = new List<Murabito_t>();
Fraction rem = 1;
for (int n = 1; n <= MURABITO_NUM; n++)
{
Fraction area = rem * new Fraction(n, MURABITO_NUM);
rem -= area;
area.Simplify();
rem.Simplify();
murabitoList.Add(new Murabito_t()
{
No = n,
Area = area,
});
}
murabitoList.Sort((a, b) => a.Area < b.Area ? 1 : (a.Area > b.Area ? -1 : 0));
Console.WriteLine("最も広い土地を貰ったのは " + murabitoList[0].No + " 番目の村人です。");
}
private class Murabito_t
{
public int No;
public Fraction Area;
}output:
最も広い土地を貰ったのは 10 番目の村人です。
それぞれの村人が貰った土地の面積を出力してみる。
source:
public void Test01()
{
const int MURABITO_NUM = 100;
List<Murabito_t> murabitoList = new List<Murabito_t>();
Fraction rem = 1;
for (int n = 1; n <= MURABITO_NUM; n++)
{
Fraction area = rem * new Fraction(n, MURABITO_NUM);
rem -= area;
area.Simplify();
rem.Simplify();
murabitoList.Add(new Murabito_t()
{
No = n,
Area = area,
});
}
murabitoList.Sort((a, b) => a.Area < b.Area ? 1 : (a.Area > b.Area ? -1 : 0));
foreach (Murabito_t x in murabitoList)
Console.WriteLine(string.Join("\t", x.No, x.Area.Numer, x.Area.Denom));
}
private class Murabito_t
{
public int No;
public Fraction Area;
}output:
面積の広い順
各行：村人番号 \t 面積の分子 \t 面積の分母
10 245373636545037 3906250000000000 11 24291990017958663 390625000000000000 9 24267722295663 390625000000000 12 589632848617723911 9765625000000000000 8 117235373409 1953125000000 13 28105832450778173091 488281250000000000000 7 8824167891 156250000000 14 1316650150963377493263 24414062500000000000000 6 80463537 1562500000 15 24263981353467956661561 488281250000000000000000 5 1411641 31250000 16 137495894336318421082179 3051757812500000000000000 17 49086034278065676326337903 1220703125000000000000000000 4 470547 12500000 18 2156898094453827071516141973 61035156250000000000000000000 19 186691512842170143190119399663 6103515625000000000000000000000 3 14553 500000 20 795895396853462189389456388037 30517578125000000000000000000000 21 16713803333922705977178584148777 762939453125000000000000000000000 2 99 5000 22 691633099865658642579437601204153 38146972656250000000000000000000000 23 56399535507226891126705048025465931 3814697265625000000000000000000000000 24 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グラフにしてみる。
しゃらくせえのでエクセルで、、、
貰った土地の面積(割合) / 村人番号
↑の source:
public void Test01()
{
const int MURABITO_NUM = 100;
List<Murabito_t> murabitoList = new List<Murabito_t>();
Fraction rem = 1;
for (int n = 1; n <= MURABITO_NUM; n++)
{
Fraction area = rem * new Fraction(n, MURABITO_NUM);
rem -= area;
area.Simplify();
rem.Simplify();
murabitoList.Add(new Murabito_t()
{
No = n,
Area = area,
});
}
using (CsvFileWriter writer = new CsvFileWriter(SCommon.NextOutputPath() + ".csv"))
{
foreach (Murabito_t x in murabitoList)
{
const int GAISANCHI_SEIDO = 1000000000;
double gaisanchi = (double)((x.Area.Numer * GAISANCHI_SEIDO) / x.Area.Denom) / GAISANCHI_SEIDO;
writer.WriteCell(x.No.ToString());
writer.WriteCell(gaisanchi.ToString("F9"));
writer.EndRow();
}
}
}
private class Murabito_t
{
public int No;
public Fraction Area;
}