Величайший общий делитель из набора из более чем 2 целых чисел

Question

Существует несколько вопросов о переполнении стека, в которых обсуждается, как найти наибольший общий делитель двух значений.Один хороший ответ показывает аккуратную рекурсивную функцию для этого.

Но как мне найти GCD из набора из более чем 2 целых чисел?Я не могу найти пример этого.

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Может кто-нибудь предложить наиболее эффективный код для реализации этой функции?

static int GCD(int[] IntegerSet)
{
    // what goes here?
}

Answer 1

Без использования LINQ.

    static int GCD(int a, int b)
    {
        if (b == 0) return a;
        return GCD(b, a % b);
    }

    static int GCD(params int[] numbers)
    {
        int gcd = 0;
        int a = numbers[0];
        for(int i = 1; i < numbers.Length; i++)
        {
            gcd = GCD(a, numbers[i]);
            a = numbers[i];
        }

        return gcd;
    }

Answer 2

Это три наиболее часто используемых:

public static uint FindGCDModulus(uint value1, uint value2)
{
    while(value1 != 0 && value2 != 0)
    {
            if (value1 > value2)
            {
                    value1 %= value2;
            }
            else
            {
                    value2 %= value1;
            }
    }
    return Math.Max(value1, value2);
       }

    public static uint FindGCDEuclid(uint value1, uint value2)
      {
    while(value1 != 0 && value2 != 0)
    {
            if (value1 > value2)
            {
                    value1 -= value2;
            }
            else
            {
                    value2 -= value1;
            }
    }
    return Math.Max(value1, value2);
  }

  public static uint FindGCDStein(uint value1, uint value2)
  {
    if (value1 == 0) return value2;
    if (value2 == 0) return value1;
    if (value1 == value2) return value1;

    bool value1IsEven = (value1 & 1u) == 0;
    bool value2IsEven = (value2 & 1u) == 0;

    if (value1IsEven && value2IsEven)
    {
            return FindGCDStein(value1 >> 1, value2 >> 1) << 1;
    }
    else if (value1IsEven && !value2IsEven)
    {
            return FindGCDStein(value1 >> 1, value2);
    }
    else if (value2IsEven)
    {
            return FindGCDStein(value1, value2 >> 1);
    }
    else if (value1 > value2)
    {
            return FindGCDStein((value1 - value2) >> 1, value2);
    }
    else
    {
            return FindGCDStein(value1, (value2 - value1) >> 1);
    }
  }

Answer 3

/*

Copyright (c) 2011, Louis-Philippe Lessard
All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

*/

unsigned gcd ( unsigned a, unsigned b );
unsigned gcd_arr(unsigned * n, unsigned size);

int main()
{
    unsigned test1[] = {8, 9, 12, 13, 39, 7, 16, 24, 26, 15};
    unsigned test2[] = {2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048};
    unsigned result;

    result = gcd_arr(test1, sizeof(test1) / sizeof(test1[0]));
    result = gcd_arr(test2, sizeof(test2) / sizeof(test2[0]));

    return result;
}


/**
* Find the greatest common divisor of 2 numbers
* See http://en.wikipedia.org/wiki/Greatest_common_divisor
*
* @param[in] a First number
* @param[in] b Second number
* @return greatest common divisor
*/
unsigned gcd ( unsigned a, unsigned b )
{
    unsigned c;
    while ( a != 0 )
    {
        c = a;
        a = b%a;
        b = c;
    }
    return b;
}

/**
* Find the greatest common divisor of an array of numbers
* See http://en.wikipedia.org/wiki/Greatest_common_divisor
*
* @param[in] n Pointer to an array of number
* @param[in] size Size of the array
* @return greatest common divisor
*/
unsigned gcd_arr(unsigned * n, unsigned size)
{
    unsigned last_gcd, i;
    if(size < 2) return 0;

    last_gcd = gcd(n[0], n[1]);

    for(i=2; i < size; i++)
    {
        last_gcd = gcd(last_gcd, n[i]);
    }

    return last_gcd;
}

Исходный код ссылки