Research on the algorithm for finding the greatest common divisor in C language

Exploration on the algorithm for finding the greatest common divisor in C language

Introduction:
The Greatest Common Divisor (GCD for short) is a common concept in mathematics , refers to the largest common divisor of two or more integers. In computer science, finding the greatest common divisor is a common requirement. This article will explore several algorithms for finding the greatest common divisor in C language and provide specific code examples.

1. Euclidean algorithm (euclidean division):
Euclidean algorithm is an ancient and simple algorithm, which divides two numbers modulo repeatedly until the remainder is zero, the smaller number is the greatest common divisor. The following is a code example for implementing the Euclidean algorithm in C language:

int gcd_euclidean(int a, int b)
{
    if (b == 0)
        return a;
    else
        return gcd_euclidean(b, a % b);
}

2. Phase-changing subtraction technique:
Phase-changing subtraction technique is another ancient method of finding the greatest common divisor. By repeatedly subtracting the larger number and the smaller number until the two numbers are equal. The following is a code example to implement the euclidean subtraction method in C language:

int gcd_subtraction(int a, int b)
{
    while (a != b)
    {
        if (a > b)
            a = a - b;
        else
            b = b - a;
    }
    return a;
}

3. Euclidean subtraction method:
The euclidean subtraction method is an improvement on the Euclidean algorithm. In all cases, the operation is performed by subtracting the smaller number from the larger number. The following is a code example to implement the euclidean subtraction method in C language:

int gcd_subtraction(int a, int b)
{
    if (a < b)
        return gcd_subtraction(b, a);
    else if (b == 0)
        return a;
    else
        return gcd_subtraction(a - b, b);
}

4. Optimized Euclidean algorithm (euclidean division method):
In order to solve the possible recursion depth of the Euclidean algorithm For larger problems, the Euclidean algorithm can be optimized. This optimization method uses iteration instead of recursion, which can improve the efficiency of the algorithm. The following is a code example for implementing optimized Euclidean algorithm in C language:

int gcd_euclidean_optimized(int a, int b)
{
    while (b != 0)
    {
        int temp = b;
        b = a % b;
        a = temp;
    }
    return a;
}

Conclusion:
This article introduces several algorithms for finding the greatest common divisor in C language and provides the corresponding code Example. Different algorithms may have different applicability in specific application scenarios, and readers can choose the appropriate algorithm according to actual needs. At the same time, factors such as the efficiency and boundary conditions of the algorithm need to be considered in actual use. I hope this article will be helpful to readers in their understanding and application of the greatest common divisor algorithm.

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