package com.company;

public class EuclideanAlgorithm {
    /**
     * 欧几里得算法求最大公约数
     * 也叫辗转相除法
     * 这是基于数学原理
     * 两个整数的最大公约数等于其中较小的数和两数的差的最大公约数
     * 实现的
     * @param one
     * @param another
     */
    static public void euclidean(int one,int another) {
        if (one <= 0 || another <= 0) {
            System.out.println("参数不合法");
            return;
        }
        //确保one >= another
        if (one < another) {
            int tempVariable = another;
            another = one;
            one = tempVariable;
        }
        int reminder = one % another;
        while (reminder != 0) {
            one = another;
            another = reminder;
            reminder = one % another;
        }
        System.out.println("最大公约数是 : " + another);
    }

    /**
     * 求最小公倍数的方法
     * 现在假设最大公约数已知为c。
     * 这2个数为x和y
     * 那么x=ac，y=bc。
     * 其中a和b没有任何公约数了
     * 根据小学求公约数的方法来计算。
     * 则最小公倍数为abc=acb=xb=xbc/c=xy/c
     * 最后得出结论
     * 最小公倍数是xy/c
     * @param one
     * @param another
     */
    static public void minCommonultiple(int one,int another) {
        if (one <= 0 || another <= 0) {
            System.out.println("参数不合法");
            return;
        }
        int oneVariable = one;
        int anotherVariable = another;
        //确保oneVariable >= anotherVariable
        if (oneVariable < anotherVariable) {
            int tempVariable = anotherVariable;
            anotherVariable = oneVariable;
            oneVariable = tempVariable;
        }
        int reminder = oneVariable % anotherVariable;
        while (reminder != 0) {
            oneVariable = anotherVariable;
            anotherVariable = reminder;
            reminder = oneVariable % anotherVariable;
        }
        System.out.println("最小公倍数是 : " + one * another / anotherVariable);
    }
}