■ 이집트 분수를 사용하는 방법을 보여준다.
▶ MathHelper.cs
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using System; namespace TestProject { /// <summary> /// 수학 헬퍼 /// </summary> public static class MathHelper { //////////////////////////////////////////////////////////////////////////////////////////////////// Method ////////////////////////////////////////////////////////////////////////////////////////// Static //////////////////////////////////////////////////////////////////////////////// Public #region 최대 공약수 구하기 - GetGreatestCommonDivisor(a, b) /// <summary> /// 최대 공약수 구하기 /// </summary> /// <param name="a">A</param> /// <param name="b">B</param> /// <returns>최대 공약수</returns> public static long GetGreatestCommonDivisor(long a, long b) { a = Math.Abs(a); b = Math.Abs(b); if(a < b) { long temporary = a; a = b; b = temporary; } for(;;) { long remainder = a % b; if(remainder == 0) { return b; } a = b; b = remainder; } } #endregion #region 최소 공배수 구하기 - GetLeastCommonMultiple(a, b) /// <summary> /// 최소 공배수 구하기 /// </summary> /// <param name="a">A</param> /// <param name="b">B</param> /// <returns>최소 공배수</returns> public static long GetLeastCommonMultiple(long a, long b) { long gcd = GetGreatestCommonDivisor(a, b); return ((a / gcd) * (b / gcd)) * gcd; } #endregion } } |
▶ Fraction.cs
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namespace TestProject { /// <summary> /// 분수 /// </summary> public class Fraction { //////////////////////////////////////////////////////////////////////////////////////////////////// Field ////////////////////////////////////////////////////////////////////////////////////////// Public #region Field /// <summary> /// 분자 /// </summary> public long Numerator; /// <summary> /// 분모 /// </summary> public long Denominator; #endregion //////////////////////////////////////////////////////////////////////////////////////////////////// Constructor ////////////////////////////////////////////////////////////////////////////////////////// Public #region 생성자 - Fraction(text) /// <summary> /// 생성자 /// </summary> /// <param name="text">텍스트</param> public Fraction(string text) { string[] valueArray = text.Split('/'); Numerator = long.Parse(valueArray[0]); Denominator = long.Parse(valueArray[1]); Simplify(); } #endregion #region 생성자 - Fraction(numerator, denominator) /// <summary> /// 생성자 /// </summary> /// <param name="numerator">분자</param> /// <param name="denominator">분모</param> public Fraction(long numerator, long denominator) { Numerator = numerator; Denominator = denominator; Simplify(); } #endregion //////////////////////////////////////////////////////////////////////////////////////////////////// Method ////////////////////////////////////////////////////////////////////////////////////////// Static //////////////////////////////////////////////////////////////////////////////// Public #region - 연산자 재정의하기 - -(a) /// <summary> /// - 연산자 재정의하기 /// </summary> /// <param name="a">분수 A</param> /// <returns>분수</returns> public static Fraction operator -(Fraction a) { return new Fraction(-a.Numerator, a.Denominator); } #endregion #region + 연산자 재정의하기 - +(a, b) /// <summary> /// + 연산자 재정의하기 /// </summary> /// <param name="a">분수 A</param> /// <param name="b">분수 B</param> /// <returns>분수</returns> public static Fraction operator +(Fraction a, Fraction b) { long gcd = MathHelper.GetGreatestCommonDivisor(a.Denominator, b.Denominator); long numerator = a.Numerator * (b.Denominator / gcd) + b.Numerator * (a.Denominator / gcd); long denominator = a.Denominator * (b.Denominator / gcd); return new Fraction(numerator, denominator); } #endregion #region - 연산자 재정의하기 - -(a, b) /// <summary> /// - 연산자 재정의하기 /// </summary> /// <param name="a">분수 A</param> /// <param name="b">분수 B</param> /// <returns>분수</returns> public static Fraction operator -(Fraction a, Fraction b) { return a + -b; } #endregion #region * 연산자 재정의하기 - *(a, b) /// <summary> /// * 연산자 재정의하기 /// </summary> /// <param name="a">분수 A</param> /// <param name="b">분수 B</param> /// <returns>분수</returns> public static Fraction operator *(Fraction a, Fraction b) { Fraction result1 = new Fraction(a.Numerator, b.Denominator); Fraction result2 = new Fraction(b.Numerator, a.Denominator); return new Fraction ( result1.Numerator * result2.Numerator, result1.Denominator * result2.Denominator ); } #endregion #region / 연산자 재정의하기 - /(a, b) /// <summary> /// / 연산자 재정의하기 /// </summary> /// <param name="a">분수 A</param> /// <param name="b">분수 B</param> /// <returns>분수</returns> public static Fraction operator /(Fraction a, Fraction b) { return a * new Fraction(b.Denominator, b.Numerator); } #endregion #region < 연산자 재정의하기 - <(a, b) /// <summary> /// < 연산자 재정의하기 /// </summary> /// <param name="a">분수 A</param> /// <param name="b">분수 B</param> /// <returns>처리 결과</returns> public static bool operator <(Fraction a, Fraction b) { return (double)a < (double)b; } #endregion #region > 연산자 재정의하기 - >(a, b) /// <summary> /// > 연산자 재정의하기 /// </summary> /// <param name="a">분수 A</param> /// <param name="b">분수 B</param> /// <returns>처리 결과</returns> public static bool operator >(Fraction a, Fraction b) { return (double)a > (double)b; } #endregion #region == 연산자 재정의하기 - ==(a, b) /// <summary> /// == 연산자 재정의하기 /// </summary> /// <param name="a">분수 A</param> /// <param name="b">분수 B</param> /// <returns>처리 결과</returns> public static bool operator ==(Fraction a, Fraction b) { return ((a.Numerator == b.Numerator) && (a.Denominator == b.Denominator)); } #endregion #region != 연산자 재정의하기 - !=(a, b) /// <summary> /// != 연산자 재정의하기 /// </summary> /// <param name="a">분수 A</param> /// <param name="b">분수 B</param> /// <returns>처리 결과</returns> public static bool operator !=(Fraction a, Fraction b) { return (!(a == b)); } #endregion #region 실수 암시적 변환 정의하기 - double(a) /// <summary> /// 실수 암시적 변환 정의하기 /// </summary> /// <param name="a">분수 A</param> public static implicit operator double(Fraction a) { return (double)a.Numerator / a.Denominator; } #endregion #region 분수 암시적 변환 정의하기 - Fraction(value) /// <summary> /// 분수 암시적 변환 정의하기 /// </summary> /// <param name="value">값</param> public static implicit operator Fraction(long value) { return new Fraction(value, 1); } #endregion ////////////////////////////////////////////////////////////////////////////////////////// Instance //////////////////////////////////////////////////////////////////////////////// Public #region 해시 코드 구하기 - GetHashCode() /// <summary> /// 해시 코드 구하기 /// </summary> /// <returns>해시 코드</returns> public override int GetHashCode() { return Numerator.GetHashCode() ^ Denominator.GetHashCode(); } #endregion #region 동일 여부 구하기 - Equals(source) /// <summary> /// 동일 여부 구하기 /// </summary> /// <param name="source">소스</param> /// <returns>동일 여부</returns> public override bool Equals(object source) { if(!(source is Fraction)) { return false; } Fraction b = source as Fraction; return (this == b); } #endregion #region 문자열 구하기 - ToString() /// <summary> /// 문자열 구하기 /// </summary> /// <returns>문자열</returns> public override string ToString() { if(Denominator == 1) { return Numerator.ToString(); } return Numerator.ToString() + "/" + Denominator.ToString(); } #endregion //////////////////////////////////////////////////////////////////////////////// Private #region 단순화 하기 - Simplify() /// <summary> /// 단순화 하기 /// </summary> private void Simplify() { if(Denominator < 0) { Numerator = -Numerator; Denominator = -Denominator; } if(Numerator == 0) { return; } long gcd = MathHelper.GetGreatestCommonDivisor(Numerator, Denominator); Numerator = Numerator / gcd; Denominator = Denominator / gcd; } #endregion } } |
▶ MainForm.cs
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using System; using System.Collections.Generic; using System.Text; using System.Windows.Forms; namespace TestProject { /// <summary> /// 메인 폼 /// </summary> public partial class MainForm : Form { //////////////////////////////////////////////////////////////////////////////////////////////////// Constructor ////////////////////////////////////////////////////////////////////////////////////////// Public #region 생성자 - MainForm() /// <summary> /// 생성자 /// </summary> public MainForm() { InitializeComponent(); #region 이벤트를 설정한다. this.calculateButton.Click += calculateButton_Click; #endregion } #endregion //////////////////////////////////////////////////////////////////////////////////////////////////// Method ////////////////////////////////////////////////////////////////////////////////////////// Private //////////////////////////////////////////////////////////////////////////////// Event #region 계산하기 버튼 클릭시 처리하기 - calculateButton_Click(sender, e) /// <summary> /// 계산하기 버튼 클릭시 처리하기 /// </summary> /// <param name="sender">이벤트 발생자</param> /// <param name="e">이벤트 인자</param> private void calculateButton_Click(object sender, EventArgs e) { Fraction sourceFraction = new Fraction(this.fractionTextBox.Text); if(sourceFraction < 0) { sourceFraction = -sourceFraction; } List<Fraction> fractionList = GetEgyptianFraction(sourceFraction); StringBuilder stringBuilder = new StringBuilder(); foreach(Fraction fraction in fractionList) { if(stringBuilder.Length > 0) { stringBuilder.Append(" + "); } stringBuilder.Append(fraction.ToString()); } this.resultTextBox.Text = stringBuilder.ToString(); } #endregion //////////////////////////////////////////////////////////////////////////////// Function #region 이집트 분수 구하기 - GetEgyptianFraction(sourceFraction) /// <summary> /// 이집트 분수 구하기 /// </summary> /// <param name="sourceFraction">소스 분수</param> /// <returns>분수 리스트</returns> private List<Fraction> GetEgyptianFraction(Fraction sourceFraction) { List<Fraction> resultFractionList = new List<Fraction>(); int wholePart = (int)(sourceFraction.Numerator / sourceFraction.Denominator); if(wholePart > 0) { resultFractionList.Add(wholePart); sourceFraction = sourceFraction - wholePart; } long denominator = 2; while(sourceFraction > 0) { Fraction fraction = new Fraction(1, denominator); while(fraction > sourceFraction) { denominator++; fraction = new Fraction(1, denominator); } resultFractionList.Add(fraction); sourceFraction -= fraction; denominator++; } return resultFractionList; } #endregion } } |
