我的有道难题算法－双倍超立方数

题目要求：双倍超立方数是指一个正整数可以正好被拆分为两种不同的a^3+b^3的方式，其中a,b均为整数且0<a<=b。对于任何一个指定的 int n, 返回所有的小于等于n的双倍超立方数的个数。

Definition
      Class:  TwiceSuperCubic
Method:  count
Parameters:  int
Returns:  int
Method signature:  int count(int n)
(be sure your method is public)

      
 
Constraints
-  n取值范围为1到1,000,000,000(含)
Examples
0)  
      1

Returns: 0

1)  
      1729

Returns: 1
1729=1^3+12^3
1729=9^3+10^3

2)  
      475574

Returns: 27

因为题中大量使用3次方计算，这里我们也可以减少重复计算。原理公式为：

(n + 1)^2 = n^2 + 2n + 2
(n + 1)^3 = n^3 + 3n^2 + 3n + 1

所以我的实现算法如下：

 

    class Program
    {
        static void Main(string[] args)
        {
            TwiceSuperCubic twice = new TwiceSuperCubic();
            System.Diagnostics.Stopwatch watch = new System.Diagnostics.Stopwatch();
            Dictionary<int, List<int[]>> ret = null;
            watch.Start();
            for (int i = 0; i < 1000; i++)
            {
                twice.CalcCount(475574, out ret);
            }

            watch.Stop();

            Console.WriteLine("======================");
            foreach (KeyValuePair<int, List<int[]>> pair in ret)
            {
                if (pair.Value.Count == 2)
                {
                    foreach (int[] val in pair.Value)
                    {
                        Console.WriteLine("{0}^3 + {1}^3 = {2}", val[0], val[1], pair.Key);
                    }
                }
            }
            Console.WriteLine("======================");
            Console.WriteLine(twice.CalcCount(1729));
            Console.WriteLine(twice.CalcCount(475574));
            Console.WriteLine("用时：{0}毫秒", watch.ElapsedMilliseconds);

            Console.WriteLine("======================");
            Console.WriteLine(T2.count(1729));
            Console.WriteLine(T2.count(475574));
            watch.Start();
            for (int i = 0; i < 1000; i++)
            {
                T2.count(475574);
            }

            watch.Stop();
            Console.WriteLine("用时：{0}毫秒", watch.ElapsedMilliseconds);

            Console.ReadKey();

        }
    }

    /// <summary>
    /// evlon算法
    /// </summary>
    public class TwiceSuperCubic
    {
        private static List<int> pow2 = new List<int>(new int[]{0});
        private static List<int> pow3 = new List<int>(new int[]{0});

        public int CalcCount(int n)
        {
            Dictionary<int, List<int[]>> debugInfo;
            return CalcCount(n, out debugInfo);
        }

        public int CalcCount(int n, out Dictionary<int, List<int[]>> debugInfo)
        {
            debugInfo = new Dictionary<int, List<int[]>>();
            int maxi = Convert.ToInt32(Math.Pow(n, 1.0 / 3)) + 1;
            for(int i = pow2.Count; i < maxi; ++i)
            {
                int pos = i - 1;
                pow2.Add(pow2[pos] + (pos << 1) + 1);         //  (n + 1)^2 = n^2 + 2n + 2
                pow3.Add(pow3[pos] + (pow2[pos] << 1) + pow2[pos] + (pos << 1) + pos + 1);     //  (n + 1)^3 = n^3 + 3n^2 + 3n + 1 
            }

            int count = 0;

            for(int x = 1; x < maxi; ++x)
            {
                bool found = false;
                for(int y = x; y < maxi; ++y)
                {
                    int z = pow3[x] + pow3[y];
                    if( z <= n)
                    {
                        if (!debugInfo.ContainsKey(z))
                        {
                            debugInfo.Add(z, new List<int[]>(new int[][] { new int[] { x, y } }));
                            found = true;
                        }
                        else
                        {
                            List<int[]> val = debugInfo[z];
                            val.Add(new int[] { x, y });

                            if (val.Count == 2)
                                count++;
                            else
                                count--;
                        }
                    }
                    else
                    {
                        break;
                    }
                }

                if(!found)
                    break;
            }


            return count;
        }


    }

    /// <summary>
    /// ealget的算法 
    /// </summary>
    class T2
    {
        static List<int> _CubeCache = new List<int>();
        static Dictionary<int, int> _CubeCountDict = new Dictionary<int, int>();

        /**/
        /// <summary>
        /// 
        /// </summary>
        /// <param name="n"></param>
        /// <returns></returns>
        /// <author>eaglet</author>
        static public int count(int n)
        {
            if (n < 0)
            {
                return 0;
            }

            _CubeCountDict.Clear();

            //b <= n 的 3 次方根
            int max_b = (int)Math.Pow((double)n, 1f / 3);

            //构造整数三次方计算缓存
            for (int i = _CubeCache.Count; i <= max_b; i++)
            {
                _CubeCache.Add(i * i * i);
            }


            int count = 0;
            int a = 1; //正整数
            int b = a;
            int sumCube;
            sumCube = _CubeCache[a] + _CubeCache[b];

            do
            {
                //计算 a^3+b^3
                while (sumCube <= n)
                {
                    int hit;

                    //看hash表中有没有已经存在的记录
                    if (_CubeCountDict.TryGetValue(sumCube, out hit))
                    {
                        //存在，且只击中了1次,则计数加1
                        if (hit == 1)
                        {
                            count++;
                        }

                        //击中超过1次,计数减1
                        //存在三组或以上组合相等的情况时走到这个分支
                        if (hit == 2)
                        {
                            count--;
                        }

                        //击中数加一
                        _CubeCountDict[sumCube]++;
                    }
                    else
                    {
                        _CubeCountDict.Add(sumCube, 1);
                    }

                    b++;

                    if (b > max_b)
                    {
                        break;
                    }

                    sumCube = _CubeCache[a] + _CubeCache[b];
                }

                a++;
                b = a;

                if (b > max_b)
                {
                    break;
                }

                sumCube = _CubeCache[a] + _CubeCache[b];
            }
            while (sumCube <= n);

            return count;
        }
    }