Promblem12

using System;using System.Collections.Generic;using System.Linq;using System.Text;using System.Collections;//输出结果为//结果为：76576500 约数个数：575//The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be://1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...//Let us list the factors of the first seven triangle numbers:// 1: 1// 3: 1,3// 6: 1,2,3,6//10: 1,2,5,10//15: 1,3,5,15//21: 1,3,7,21//28: 1,2,4,7,14,28//We can see that 28 is the first triangle number to have over five divisors.//What is the value of the first triangle number to have over five hundred divisors?//解决思路：首先找出一个数字的质数的分解，然后进行统计例如28=2*2*7，有两个2，一个7，则组合有2的情况:一个不取，区一个，取//两个共三种情况，7的情况：一个不取，取一个，所以约数共有2*3 = 6个；namespace Problem12{ class Program { static void Main(string[] args) { int i = 1, j = 0, k = 0; while (true) { j = GetSum(i); k = GetDivisors(j); Console.WriteLine("该数为：{0}，约数为：{1}", j, k); if (k >= 500) { break; } i++; } Console.WriteLine("该数字为：{0}", j); } //获取每个数字的值 public static int GetSum(int n) { return (n + 1) * n / 2; } //判断是不是素数 public static bool IsPrime(long l) { for (long i = 2; i < (long)Math.Sqrt(l) + 1; i++) { if (l % i == 0) { return false; } } return true; } //求出一个数的约数的个数 public static int GetDivisors(int sum) { //利用键值对来存储素数的个数 Hashtable dt = GetPrime(sum); int divisors = 1; foreach (DictionaryEntry de in dt) { divisors *= ((int)de.Value + 1); } return divisors - 1; } public static Hashtable GetPrime(int sum) { Hashtable dt = new Hashtable(); int sum1 = sum; if (sum == 1) { dt.Add(1, 1); return dt; } #region while循环体 while (sum != 1) { for (int i = 2; i <= sum; i++) { if (IsPrime(i) && sum % i == 0) { sum1 = sum / i; AddToHash(dt, i); } sum = sum1; } if (IsPrime(sum)&∑!=1) { AddToHash(dt, sum); break; } } #endregion return dt; } private static void AddToHash(Hashtable dt, int i) { if (!dt.ContainsKey(i)) { dt.Add(i, 1); } else { try { int tmp = (int)dt[i]; dt.Remove(i); dt.Add(i, tmp + 1); } catch (Exception e) { Console.WriteLine(e.StackTrace); } } } }}