求最大公约数算法

求最大公约数

概述

求最大公约数算法比较经典，本文给出5个实现，从1-5依次变得更优。

代码

#include <iostream>
using namespace std;

/**
  * common method. The number of recursive is o(min(numberA,numberB))
  * @author Junpeng Zhu
  * @numberA the parameter of the first number
  * @numberB the parameter of the second number
*/
int gcd1(int numberA, int numberB){
    int greaterNumber = (numberA>=numberB)?numberA:numberB;
    int smallNumber = (numberA<=numberB)?numberA:numberB;

    int gcd = 1;
    int count = 0 ;
    for (int i = 2; i <= smallNumber; i++){
        if (greaterNumber % i == 0  && smallNumber % i ==0){
            gcd = i ;
            count++;
        }else{
            count++;
            continue;
        }
    }
    cout << "The number of gcd1 comparision is count:" << count << endl;
    return gcd;

}

/**
  * common method. The number of recursive is o(min(numberA,numberB)/2)
  * @author Junpeng Zhu
  * @numberA the parameter of the first number
  * @numberB the parameter of the second number
*/
int gcd2(int numberA, int numberB){
    int greaterNumber = (numberA>=numberB)?numberA:numberB;
    int smallNumber = (numberA<=numberB)?numberA:numberB;
    if (greaterNumber % smallNumber == 0){
        int gcd = smallNumber;
        int count = 0;
        count++;
        cout << "The number of gcd2 comparision is count:" << count << endl;
        return gcd;
    }else{
        int gcd = 1;
        int count = 0;
        for (int i = 2; i <= smallNumber/2; i++){
            if (greaterNumber % i == 0  && smallNumber % i ==0){
                gcd = i ;
                count++;
            }else{
                count++;
                continue;
            }
        }
        cout << "The number of gcd2 comparision is count:" << count << endl;
        return gcd;
    }
}


/**
  * Eclidean method. The number of recursive is o(log(max(numberA,numberB)))
  * @author Junpeng Zhu
  * @numberA the parameter of the first number
  * @numberB the parameter of the second number
*/
int gcd3(int numberA, int numberB){
    int greaterNumber = (numberA>=numberB)?numberA:numberB;
    int smallNumber = (numberA<=numberB)?numberA:numberB;
    if (greaterNumber % smallNumber == 0){
        int gcd = smallNumber;
        return gcd;
    }else{
        int gcd = gcd3(smallNumber,greaterNumber%smallNumber);
        return gcd;
    }
}

/**
  * Nine chapter arithmetic method. The number of recursive is o(log(max(numberA,numberB)))
  * @author Junpeng Zhu
  * @numberA the parameter of the first number
  * @numberB the parameter of the second number
*/
int gcd4(int numberA, int numberB){
    int greaterNumber = (numberA>=numberB)?numberA:numberB;
    int smallNumber = (numberA<=numberB)?numberA:numberB;
    if (greaterNumber == smallNumber){
        return smallNumber;
    }else{
        return gcd4(smallNumber,greaterNumber-smallNumber);
    }
}

int gcd5(int numberA, int numberB){
    int greaterNumber = (numberA>=numberB)?numberA:numberB;
    int smallNumber = (numberA<=numberB)?numberA:numberB;
    if (greaterNumber == smallNumber){
        return smallNumber;
    }else{
        if (!(greaterNumber&1) && !(smallNumber&1)){
            return gcd5(greaterNumber >> 1, smallNumber >> 1) << 1;
        }
        if (greaterNumber&1 && smallNumber&1){
            return gcd5(smallNumber,greaterNumber-smallNumber);
        }
        if (!(greaterNumber&1) && smallNumber&1){
            return gcd5(greaterNumber >> 1,smallNumber);
        }
        if (greaterNumber&1 && !(smallNumber&1)){
            return gcd5(greaterNumber,smallNumber>>1);
        }
    }
}

int main()
{
    int i = 168;
    int j = 34;
    int gcdA = gcd1(i,j);
    cout <<"gcd1:"<< gcdA << endl;

    int gcdB = gcd2(i,j);
    cout << "gcd2:"<< gcdB << endl;

    int gcdC = gcd3(i,j);
    cout << "gcd3:"<< gcdC << endl;

    int gcdD = gcd4(i,j);
    cout << "gcd4:"<< gcdD << endl;

    int gcdE = gcd5(i,j);
    cout << "gcd5:"<< gcdE << endl;
    return 0;
}