24點演算法源碼（C#）__演算法

using System;using System.Collections.Generic;using System.Text;using System.Collections;namespace HeroAssociation{    /// <summary>    /// 24 點    /// </summary>    public class TwentyFourPoint    {        /// <summary>        /// 分數類，用於分數運算。        /// </summary>        class Fraction        {            /// <summary>            /// 分子            /// </summary>            private int numerator;            /// <summary>            /// 分母            /// </summary>            private int denominator;            public Fraction(int number)                : this(number, 1)            { }            public Fraction(int numerator, int denominator)            {                if (denominator == 0)                {                    throw new DivideByZeroException("分母不能為0");                }                int sign = numerator * denominator < 0 ? -1 : 1;                numerator = Abs(numerator);                denominator = Abs(denominator);                this.numerator = sign * numerator / Gcd(numerator, denominator);                this.denominator = denominator / Gcd(numerator, denominator);            }            public static Fraction operator +(Fraction a, Fraction b)            {                if (a.denominator == b.denominator)                {                    return new Fraction(a.numerator + b.numerator, a.denominator);                }                else                {                    return new Fraction(a.numerator * b.denominator + b.numerator * a.denominator, a.denominator * b.denominator);                }            }            public static Fraction operator -(Fraction a, Fraction b)            {                if (a.denominator == b.denominator)                {                    return new Fraction(a.numerator - b.numerator, a.denominator);                }                else                {                    return new Fraction(a.numerator * b.denominator - b.numerator * a.denominator, a.denominator * b.denominator);                }            }            public static Fraction operator *(Fraction a, Fraction b)            {                return new Fraction(a.numerator * b.numerator, a.denominator * b.denominator);            }            public static Fraction operator /(Fraction a, Fraction b)            {                return new Fraction(a.numerator * b.denominator, a.denominator * b.numerator);            }            public override bool Equals(object obj)            {                Fraction a = (Fraction)obj;                return this.numerator == a.numerator && this.denominator == a.denominator;            }            public override int GetHashCode()            {                return this.numerator.GetHashCode() ^ this.denominator.GetHashCode();            }            /// <summary>            /// 是否是整數            /// </summary>            /// <returns></returns>            public bool IsInteger()            {                return numerator % denominator == 0;            }            /// <summary>            /// 最大公約數            /// </summary>            /// <param name="a"></param>            /// <param name="b"></param>            /// <returns></returns>            private static int Gcd(int a, int b)            {                return b == 0 ? a : Gcd(b, a % b);            }            private static int Abs(int a)            {                return a < 0 ? -a : a;            }            public int Result()            {                return numerator / denominator;            }            public bool IsZero()            {                return numerator == 0;            }        }        /// <summary>        /// 算術運算組合列舉程式,不改變各分數的排列順序        /// </summary>        class ArithmeticIterator : IEnumerable<Fraction>        {            private Fraction[] fractions;            /// <summary>            /// 構造算術枚舉對象            /// </summary>            /// <param name="fractions">分數數組</param>            public ArithmeticIterator(Fraction[] fractions)            {                this.fractions = fractions;            }            public IEnumerator<Fraction> GetEnumerator()            {                if (fractions.Length == 1)                {                    yield return fractions[0];                    yield break;                }                for (int i = 1; i < fractions.Length; i++)                {                    Fraction[] leftFractions = new Fraction[i];                    Fraction[] rightFractions = new Fraction[fractions.Length - i];                    Array.Copy(fractions, 0, leftFractions, 0, leftFractions.Length);                    Array.Copy(fractions, i, rightFractions, 0, rightFractions.Length);                    foreach (Fraction leftFraction in new ArithmeticIterator(leftFractions))                    {                        foreach (Fraction rightFraction in new ArithmeticIterator(rightFractions))                        {                            yield return leftFraction + rightFraction;                            yield return leftFraction - rightFraction;                            yield return leftFraction * rightFraction;                            if (!rightFraction.IsZero())                            {                                yield return leftFraction / rightFraction;                            }                        }                    }                }            }            IEnumerator IEnumerable.GetEnumerator()            {                return GetEnumerator();            }        }        /// <summary>        /// 分數全排列迭代器        /// </summary>        class FractionsPermutationIterator : IEnumerable<Fraction[]>        {            private Fraction[] fractions;            /// <summary>            /// 構造分數全排列迭代器            /// </summary>            /// <param name="fractions">分數數組</param>            public FractionsPermutationIterator(Fraction[] fractions)            {                this.fractions = fractions;            }            public IEnumerator<Fraction[]> GetEnumerator()            {                if (fractions.Length == 1)                {                    yield return fractions;                    yield break;                }                for (int idx = 0; idx < fractions.Length; idx++)                {                    Fraction[] result = new Fraction[fractions.Length];                    result[0] = fractions[idx];                    Fraction[] subFractions = RemoveAt(fractions, idx);                    foreach (Fraction[] frs in new FractionsPermutationIterator(subFractions))                    {                        Array.Copy(frs, 0, result, 1, frs.Length);                        yield return result;                    }                }            }            /// <summary>            /// 刪除素組指定位置的元素，返回新的數組。            /// </summary>            /// <param name="array">原數組。不改變原數組</param>            /// <param name="idx"></param>            /// <returns></returns>            private static Fraction[] RemoveAt(Fraction[] array, int idx)            {                Fraction[] subFractions = new Fraction[array.Length - 1];                if (idx > 0)                {                    //前部分                    Array.Copy(array, 0, subFractions, 0, idx);                }                if (idx < array.Length - 1)                {                    //後半部分                    Array.Copy(array, idx + 1, subFractions, idx, subFractions.Length - idx);                }                return subFractions;            }            IEnumerator IEnumerable.GetEnumerator()            {                return GetEnumerator();            }        }        private int a, b, c, d;        public static bool Can24(int a, int b, int c, int d)        {            return new TwentyFourPoint(a, b, c, d).Can24();        }        public TwentyFourPoint(int a, int b, int c, int d)        {            this.a = a;            this.b = b;            this.c = c;            this.d = d;        }        public bool Can24()        {            Fraction[] fractions = new Fraction[4];            fractions[0] = new Fraction(this.a);            fractions[1] = new Fraction(this.b);            fractions[2] = new Fraction(this.c);            fractions[3] = new Fraction(this.d);            foreach (Fraction[] oneFractions in new FractionsPermutationIterator(fractions))            {                foreach (Fraction fra in new ArithmeticIterator(oneFractions))                {                    if (fra.IsInteger() && fra.Result() == 24)                    {                        return true;                    }                }            }            return false;        }    }}