MathEx 数学计算帮助类

最大公约数

/// <summary>
/// 找到并返回最大公约数
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static int FindGCD(int a, int b)
{
    if (a==0)
    {
        return b;
    }
    if (b==0)
    {
        return a;
    }
    int _a = a, _b = b;
    int r = _a & _b;
    while (r!=0)
    {
        _a = _b;
        _b = r;
        r = _a & _b;
    }
    return _b;
}

相对质数

/// <summary>
/// 确定给定的两个数是相对质数
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static bool IsRelativelyPrime(int a ,int b)
{
    return FindGCD(a, b) == 1;
}

二项式系数 C(n,k)

从n个选取k个的方法总数

/// <summary>
/// 二项式系数 C(n,k)
/// </summary>
/// <param name="n"></param>
/// <param name="k"></param>
/// <returns></returns>
public static ulong BinomialCoefficients(uint n, uint k)
{
    ulong rslt = 1;
    if (k > n-k)
    {
        k = n - k;
    }
    for (int i = 0; i < k; i++)
    {
        rslt *= Convert.ToUInt64(n - i);
        rslt /= Convert.ToUInt64(i + 1);
    }
    return rslt;
}

逆平方根

/// <summary>
/// 逆平方根(浮点数的平方根倒数)
/// </summary>
/// <param name="number"></param>
/// <returns></returns>
public static float Q_rsqrt(float x)
{
    float xhalf = 0.5f * x;
    unsafe
    {
        int i = *(int*)&x;  // 浮点值当整数读取
        i = 0x5f3759df - (i >> 1);  // 给初始猜测
        x = *(float*)&i;    // 整数当浮点数读取
        x = x * (1.5f - xhalf * x * x);
        x = x * (1.5f - xhalf * x * x); // 第二次迭代，可删除
    }
    return x;
}
public static float Q_rsqrt2(float x)
{
    float xhalf = 0.5f * x;
    int i = Convert.ToInt32(FloatToBinary(x).Replace(" ", string.Empty), 2);
    i = 0x5f3759df - (i >> 1);  // 给初始猜测
    x = BinaryToFloat(Convert.ToString(i, 2));
    x = x * (1.5f - xhalf * x * x);
    x = x * (1.5f - xhalf * x * x); // 第二次迭代，可删除
    return x;
}

约瑟夫环

/// <summary>
/// 约瑟夫环问题:有n个人围成一个圈，每隔q个人踢掉一个人，问最后留下来的人是几号
/// O(logN)
/// </summary>
/// <param name="n"></param>
/// <param name="q"></param>
private static long JosephRing(long n, long q)
{
    long D = 1, end = (q - 1) * n;
    while (D <= end)
    {
        D = Ceil(q * D, q - 1);
    }
    return q * n + 1 - D;
}

private static long Ceil(long x, long y)
{
    return x / y + (x % y == 0 ? 0 : 1);
}

最大公共子字符串

/// <summary>
/// 最大公共子字符串
/// </summary>
/// <param name="str1">字符串1</param>
/// <param name="str2">字符串2</param>
/// <returns>子串</returns>
static string GetMaxCommonStr(string str1, string str2)
{
    if (string.IsNullOrEmpty(str1) || string.IsNullOrEmpty(str2))
    {
        return string.Empty;
    }
    var temp = new int[str1.Length, str2.Length];
    int max = -0;    // 相同子串的最大长度
    int n1End = -1;  // str1的长公共字符串的最后位置
    int n2End = -1;  // str2的长公共字符串的最后位置
    for (int i = 0; i < str1.Length; i++)
    {
        for (int j = 0; j < str2.Length; j++)
        {
            if (str1[i] != str2[j])
            {
                temp[i, j] = 0;
            }
            else
            {
                if (i == 0 || j == 0)
                {
                    temp[i, j] = 1;
                }
                else
                {
                    temp[i, j] = temp[i - 1, j - 1] + 1;
                }
                if (temp[i,j] > max)
                {
                    max = temp[i, j];
                    n1End = i;
                    n2End = j;
                }
            }
        }
    }
    var rslt = new StringBuilder();
    while (n1End >= 0 && n2End>= 0 && temp[n1End, n2End] > 0)
    {
        rslt.Insert(0, str1[n1End]);
        n1End--;
        n2End--;
    }
    return rslt.ToString();
}