*[topcoder]LCMSetEasy

http://community.topcoder.com/stat?c=problem_statement&pm=13040

DFS集合全排列+LCM和GCD。但事实上，有更简单的算法，列在下面，就是观察到不能整除x的对我们无效。

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

class LCMSetEasy {
public:
    string include(vector <int> S, int x) {
        vector<int> vec;
        if (includeRe(S, x, 0, vec))
            return "Possible";
        else
            return "Impossible";
    }

    bool includeRe(const vector<int> &S, int x, int i, vector<int> &vec) {
        if (i == S.size()) {
            int r = lcm(vec);
            if (r == x)
                return true;
            return false;
        }
        vec.push_back(S[i]);
        bool res = includeRe(S, x, i + 1,vec);
        vec.pop_back();
        if (res)
            return true;
        res = includeRe(S, x, i + 1,vec);
        return res;
    }

    int lcm(vector<int> vec) {
        if (vec.size() == 0)
            return 1;
        int tmp = vec[0];
        for (int i = 1; i < vec.size(); i++) {
            tmp = lcm(tmp, vec[i]);
        }
        return tmp;
    }

    int lcm(int a, int b) {
        int c = gcd(a, b);
        return a * b /c;
    }

    int gcd(int a, int b) {
        if (a % b == 0)
            return b;
        int tmp = a % b;
        return gcd(b, tmp);
    }
};

　　

string include(vector <int> S, int x) {
        int r = 1;
        for (int i = 0; i < S.size(); i++) {
            if (x % S[i] == 0) {
                r = lcm(r, S[i]);
            }
        }
        if (r == x)
            return "Possible";
        else
            return "Impossible";
    }