因数分解（也称为质因子分解）：将一个大整数分解它的质因子之乘积的算法。
Pollard Rho算法的基本思路：先判断当前数是否是素数（质数），如果是，则直接返回。如果不是，继续找到当前数的一个因子（可以不是质因子）。然后递归对该因子和约去这个因子的另一个因子进行分解。
运行效果：
源代码：
using System;
using System.Collections;
using System.Collections.Generic;
namespace Legalsoft.Truffer.Algorithm
{
/// <summary>
/// 用Pollard-Rho算法求合成质数因子
/// </summary>
public static class Prime_Factorization
{
/// <summary>
/// 随机数发生器
/// </summary>
private static Random rand = new Random((int)DateTime.Now.Ticks);
/// <summary>
/// 计算 x 幂取模
/// </summary>
/// <param name="x"></param>
/// <param name="exponent"></param>
/// <param name="modulus"></param>
/// <returns></returns>
private static long ModularPow(long x, int exponent, long modulus)
{
long result = 1;
while (exponent > 0)
{
// 如果 y 是奇数！
if ((exponent % 2) == 1)
{
result = (result * x) % modulus;
}
exponent = (exponent >> 1);
x = (x * x) % modulus;
}
return result;
}
/// <summary>
/// 计算 n 的分解质因子（除）算法
/// </summary>
/// <param name="n"></param>
/// <returns></returns>
public static long PollardRho(long n)
{
if (n == 1)
{
return n;
}
// 偶数
if ((n % 2) == 0)
{
return 2;
}
// 设置一个取值范围
long x = (long)(rand.Next(0, -(int)n + 1));
long y = x;
long c = (long)(rand.Next(1, -(int)n));
// 初始化候选除数（或结果），直到未获得素数因子。
long d = 1L;
while (d == 1)
{
x = (ModularPow(x, 2, n) + c + n) % n;
y = (ModularPow(y, 2, n) + c + n) % n;
y = (ModularPow(y, 2, n) + c + n) % n;
d = GCD(Math.Abs(x - y), n);
if (d == n)
{
return PollardRho(n);
}
}
return d;
}
public static long GCD(long a, long b)
{
return ((b == 0) ? a : GCD(b, (a % b)));
}
}
}
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TRUFFER.CN
using System;
using System.Collections;
using System.Collections.Generic;namespace Legalsoft.Truffer.Algorithm
{/// <summary>/// 用Pollard-Rho算法求合成质数因子/// </summary>public static class Prime_Factorization{/// <summary>/// 随机数发生器/// </summary>private static Random rand = new Random((int)DateTime.Now.Ticks);/// <summary>/// 计算 x 幂取模/// </summary>/// <param name="x"></param>/// <param name="exponent"></param>/// <param name="modulus"></param>/// <returns></returns>private static long ModularPow(long x, int exponent, long modulus){long result = 1;while (exponent > 0){// 如果 y 是奇数！if ((exponent % 2) == 1){result = (result * x) % modulus;}exponent = (exponent >> 1);x = (x * x) % modulus;}return result;}/// <summary>/// 计算 n 的分解质因子（除）算法/// </summary>/// <param name="n"></param>/// <returns></returns>public static long PollardRho(long n){if (n == 1){return n;}// 偶数if ((n % 2) == 0){return 2;}// 设置一个取值范围long x = (long)(rand.Next(0, -(int)n + 1));long y = x;long c = (long)(rand.Next(1, -(int)n));// 初始化候选除数（或结果），直到未获得素数因子。long d = 1L;while (d == 1){x = (ModularPow(x, 2, n) + c + n) % n;y = (ModularPow(y, 2, n) + c + n) % n;y = (ModularPow(y, 2, n) + c + n) % n;d = GCD(Math.Abs(x - y), n);if (d == n){return PollardRho(n);}}return d;}public static long GCD(long a, long b){return ((b == 0) ? a : GCD(b, (a % b)));}}
}
