求个算法________________________________________________________

Question

两个条件：
1:输入一个数 X 和: 20<=X<=165;
2:一个数N：个数  1<=N<=5;
例如
X=100； N=5；
因为N=5 所以就有  X1+X2+X3+X4+X5=100；
X1到X5 都是小于等于35大于等于1的，且彼此不重复
再例如:X=120;N=3
那么就是  X1+X2+X3=120；X1到X3 都是小于等于35 大于等于1的，且彼此不重复
依次类推！
要求把所有的可能都列举出来！不能遗漏

Answer 1

X1+X2+X3=120，是举例吧！这个值就算是35+35+35也不等于120呀！

Answer 2

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;namespace XN {
    class Program {
        private static int m_level = 0;
        private static int m_x = 20;
        private static int m_n = 1;
        private static int m_s = 1;        private static int[] m_numbers = new int[6];        static void Main(string[] args) {
            Console.Write("Input X(20 <= X <= 165): ");
            m_x = int.Parse(Console.ReadLine());
            Console.Write("Input N(1 <= X <= 5): ");
            m_n = int.Parse(Console.ReadLine());            Console.WriteLine("Running...");
            TryNextNumber(0);
            Console.WriteLine("OK.");            Console.ReadLine();
        }        static void TryNextNumber(int st) {
            ++m_level;            for (int i = st + 1; i <= 35; ++i) {
                m_numbers[m_level - 1] = i;                if (m_level == m_n) {
                    // 目标迭代层数
                    ValidateNumbers();
                } else {
                    TryNextNumber(i);
                }
            }            --m_level;
        }        static void ValidateNumbers() {
            int sum = 0;
            for (int i = 0; i < m_level; ++i) {
                sum += m_numbers[i];
            }            if (sum == m_x) {
                Console.Write("{0, 2:D}.  ", m_s++);
                for (int i = 0; i < m_level; ++i) {
                    Console.Write("{0,2:D}  ", m_numbers[i]);
                }
                Console.Write("\r\n");
            }
        }
    }
}

Answer 3

http://topic.csdn.net/u/20101012/13/a6381631-dd9d-4d0e-87b9-b3fb1ef6fc2e.html
思路差不多..

Answer 4

using System;
using System.Collections.Generic;
using System.Text;namespace addtest
{
    class Program
    {
        static int N, X;        static void Main(string[] args)
        {
            bool Nflag = true, Xflag = true;
            while (Nflag)
            {
                Console.WriteLine("请输入参数N(N大于等于1小于等于5):");
                string strN = Console.ReadLine();
                if (strN == "exit")
                {
                    return;
                }
                try
                {
                    N = Convert.ToInt16(strN);
                    Nflag = false;
                }
                catch
                {
                    N = 0;
                }
            }
            while (Xflag)
            {
                Console.WriteLine("请输入参数X(X大于等于20小于等于165):");
                string strX = Console.ReadLine();
                if (strX == "exit")
                {
                    return;
                }
                try
                {
                    X = Convert.ToInt16(strX);
                    Xflag = false;
                }
                catch
                {
                    X = 0;
                }
            }            
            for (int i = 1; i < 36; i++)
            {
                addx(0, i, 1, "");
            }            Console.ReadLine();
        }        public static void addx(int AddX, int thisX, int thisN, string writeStr)
        {
            string thiswriteStr;
            int thisAddX;
            if (thisN > N)
            {
                //thiswriteStr = writeStr + "N溢出！"
                //Console.WriteLine(thiswriteStr);
                return;
            }
            
            thiswriteStr = writeStr + "(X" + thisN.ToString() + ":" + thisX.ToString() + ")";
            thisAddX = AddX + thisX;
            
            if (thisAddX > (X - (N - thisN)))
            {
                //thiswriteStr = writeStr + "X溢出！"
                //Console.WriteLine(thiswriteStr);
                return;
            }            if ((thisN == N) && (thisAddX==X))
            {
                    Console.WriteLine(thiswriteStr);
            }
            for (int i = 1; i < 36; i++)
            {
                addx(thisAddX, i, thisN + 1, thiswriteStr);
            }
            return;
        }
    }
}

Answer 5

凑合能算，数再大的话，需要把剪枝部分（还有最后1个数的计算）优化一下，不考虑输出的话，速度提高个10倍是有可能的
using System;namespace CsdnTest
{
    class Program
    {
        static void Main(string[] args)
        {
            Solve(5, 100, 35, string.Empty);
            Console.ReadKey();
        }        static void Solve(int remain, int remainSum, int max, string selected)
        {
            if (remain * max < remainSum || max < 0 || remainSum < 0)
                return;            if (remain == 0 && remainSum == 0)
            {
                Console.WriteLine(selected);
                return;
            }            Solve(remain, remainSum, max - 1, selected);
            Solve(remain - 1, remainSum - max, max - 1, selected + max.ToString() + " ");
        }
    }
}

Answer 6

优化下using System;
using System.Collections.Generic;
using System.Text;namespace addtest
{
    class Program
    {
        static int N, X;        static void Main(string[] args)
        {
            bool Nflag = true, Xflag = true;
            while (Nflag)
            {
                Console.WriteLine("请输入参数N(N大于等于1小于等于5):");
                string strN = Console.ReadLine();
                if (strN == "exit")
                {
                    return;
                }
                try
                {
                    N = Convert.ToInt16(strN);
                    Nflag = false;
                }
                catch
                {
                    N = 0;
                }
            }
            while (Xflag)
            {
                Console.WriteLine("请输入参数X(X大于等于20小于等于165):");
                string strX = Console.ReadLine();
                if (strX == "exit")
                {
                    return;
                }
                try
                {
                    X = Convert.ToInt16(strX);
                    Xflag = false;
                }
                catch
                {
                    X = 0;
                }
            }            
            for (int i = 1; i < 36; i++)
            {
                if (addx(0, i, 1, ""))
                {
                    break;
                }
            }            Console.ReadLine();
        }        public static bool addx(int AddX, int thisX, int thisN, string writeStr)
        {
            string thiswriteStr;
            int thisAddX;
            if (thisN > N)
            {
                //thiswriteStr = writeStr + "N溢出！"
                //Console.WriteLine(thiswriteStr);
                return true;
            }
            
            thiswriteStr = writeStr + "(X" + thisN.ToString() + ":" + thisX.ToString() + ")";
            thisAddX = AddX + thisX;
            
            if (thisAddX > (X - (N - thisN)))
            {
                //thiswriteStr = writeStr + "X溢出！"
                //Console.WriteLine(thiswriteStr);
                return true;
            }            if ((thisN == N) && (thisAddX==X))
            {
                    Console.WriteLine(thiswriteStr);
            }
            for (int i = 1; i < 36; i++)
            {
                if (addx(thisAddX, i, thisN + 1, thiswriteStr))
                {
                    break;
                }
            }
            return false;
        }
    }
}

Answer 7

简单优化了一下，可以算稍微大一点的，比如10个不超过40的数，和为200，解的数量本身就是指数级的，不会有太好的方法。如果只求解的数量，可以用动态规划。using System;namespace CsdnTest
{
    class Program
    {
        static void Main(string[] args)
        {
            int selectCount = 10, sum = 200, max = 40;
            Solve(selectCount, sum, max, new int[selectCount]);
            Console.ReadKey();
        }        static void Solve(int remainCount, int remain, int max, int[] selected)
        {
            if (max < remainCount || remain < remainCount || remainCount * max < remain)
                return;            if (remainCount == 1 && remain <= max)
            {
                selected[remainCount - 1] = remain;
                //需要输出就去掉注释，为测试剪枝幅度，注释掉了
                //for(int i = selected.Length - 1; i >= 0; i--)
                //    Console.Write("{0} ", selected[i]);                //Console.WriteLine();
                return;
            }            Solve(remainCount, remain, max - 1, selected);
            selected[remainCount - 1] = max;
            Solve(remainCount - 1, remain - max, max - 1, selected);
        }
    }
}

Answer 8

把输出部分的注释去掉
using System;namespace CsdnTest
{
    class Program
    {
        static void Main(string[] args)
        {
            int selectCount = 5, sum = 100, max = 35;
            Solve(selectCount, sum, max, new int[selectCount]);
            Console.ReadKey();
        }        static void Solve(int remainCount, int remain, int max, int[] selected)
        {
            if (max < remainCount || remain < remainCount || remainCount * max < remain)
                return;            if (remainCount == 1 && remain <= max)
            {
                selected[remainCount - 1] = remain;
                //需要输出就去掉注释，为测试剪枝幅度，注释掉了
                for(int i = selected.Length - 1; i >= 0; i--)
                    Console.Write("{0} ", selected[i]);                Console.WriteLine();
                return;
            }            Solve(remainCount, remain, max - 1, selected);
            selected[remainCount - 1] = max;
            Solve(remainCount - 1, remain - max, max - 1, selected);
        }
    }
}