[WikiOI] 2.3.1 最大公约数和最小公倍数

[Problem]

输入二个正整数x0,y0(2<=x0<100000,2<=y0<=1000000),求出满足下列条件的P,Q的个数

条件:  1.P,Q是正整数

2.要求P,Q以x0为最大公约数,以y0为最小公倍数.

试求:满足条件的所有可能的两个正整数的个数.

[Solution]

#include <vector>
#include <iostream>
using namespace std;

/**
* swap
*/
void swap(int &a, int &b){
a ^= b;
b ^= a;
a ^= b;
}

/**
* greatest common divisor and least common multiple
*/
void GCD_LCM(int a, int b, int &gcd, int &lcm){
lcm = a * b;
if(a > b){
swap(a, b);
}
while(b % a != 0){
b %= a;
if(a > b){
swap(a, b);
}
}
gcd = a;
lcm /= a;
}

/**
* main
*/
int main(){
int a, b;
while(cin >> a >> b){
vector<int> tmp;

// generate candidates
for(int i = 1; i*a <= b; ++i){
if(b % (i*a) == 0){
tmp.push_back(i*a);
}
}

// check result
int result = 0;
for(int i = 0; i < tmp.size(); ++i){
for(int j = i + 1; j < tmp.size(); ++j){
int gcd = 0, lcm = 0;
GCD_LCM(tmp[i], tmp[j], gcd, lcm);
if(gcd == a && lcm == b){
if(tmp[i] != tmp[j]){
result += 2;
}
else{
result++;
}
}
}
}

// output result
cout << result << endl;
}
return 0;
}