--學習記錄

論壇問題帖:http://bbs.csdn.net/topics/390416116 

思路: 設輸入數字為S; 有N個連續整數(N>1),最小整數為M(M>=1),則第二為M+1...第N個則為M+N-1(也可以改設最大數) 通過分解可拆為:S=(1+2+...+N-1)+N*M之和,再利用公式求和即為:(1+(N-1))*(N-1)/2+MN=N*(N-1)/2+MN=S N範圍:N(N-1)=2S-2MN-->N平方<2S-2MN-->N<SQRT(2S-2MN) M範圍:M=(2S-N(N-1))/2N

--MSSQL實現--
--支援MASTER..SPT_VALUES 表裡面TYPE='P'的最大NUMBER.
CREATE FUNCTION DBO.FN_連續整數和為某值(@SUM INT)
RETURNS TABLE
AS
RETURN
(
 SELECT 
   A.NUMBER AS 連續個數,B.NUMBER AS 起始值,A.NUMBER +B.NUMBER-1 AS 結束值
 FROM 
   MASTER..SPT_VALUES A,MASTER..SPT_VALUES B
 WHERE
   A.NUMBER BETWEEN 2 AND SQRT (2*@SUM-2) AND A.TYPE='P' AND B.TYPE='P'
 AND
   B.NUMBER BETWEEN 1 AND CEILING(((2*@SUM*1.00)-A.NUMBER*(A.NUMBER-1))/(2*A.NUMBER))

 AND
   2*@SUM=A.NUMBER*(A.NUMBER-1)+2*A.NUMBER*B.NUMBER
)

 

-----C#實現---
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Diagnostics;

namespace ConsoleApplication2
{
    class Program
    {
        static void Main(string[] args)
        {
          
            Console.WriteLine("請輸入一個整數：");
            string str = Console.ReadLine();
            int y = Convert.ToInt32(str);
          
            Stopwatch sw1 = new Stopwatch();
            sw1.Start();
            PrintNum(y);
            Console.WriteLine("計算時間為：" + sw1.ElapsedMilliseconds.ToString() + "ms");
            sw1.Stop();
            Console.WriteLine();
            Console.ReadLine();
        }

        public static int MaxCount(int sum)
        {
            int n =Convert.ToInt32(Math.Ceiling( System.Math.Sqrt(Convert.ToDouble(sum*2-4))));
            return n;
        }

        public static void PrintNum(int sum)
        {
            string str = "";
            int n=MaxCount(sum);
            int tempj = 0, tempi = 0;
            for (int i = 2; i < n; i++)
            {
                int m = Convert.ToInt32(System.Math.Ceiling((Convert.ToDouble(2*sum)-i*(i-1)) / (2*i)));
                for (int j = 1; j <= m; j++)
                {
                    if (i * (i - 1) + 2 * i*j == 2 * sum)
                    {
                        tempj = j;
                        tempi = i;
                        str = "";
                    }
                }
                if (tempj > 0)
                {
                    str = "";
                    for (int k = tempj; k < tempj + i; k++)
                    {
                        str = str + k.ToString() + "+";
                    }
                    Console.WriteLine(tempi.ToString() + "個數:" + str.TrimEnd( '+') + "=" + sum.ToString());
                }
                tempj = 0; tempi = 0;
            }
            if (string.IsNullOrEmpty(str))
            {
                Console.WriteLine("沒有連續數字的和等於此值");
            }
        }

    }
    
}