[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 candidatesfor(int i = 1; i*a <= b; ++i){if(b % (i*a) == 0){tmp.push_back(i*a);}}// check resultint 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 resultcout << result << endl;}return 0;}