USACO：frac1

基本思路是受到了M路歸併的啓發。

從這裏也看得出來基礎的重要性。

 

/*
ID: fairyroad
TASK: frac1
LANG:C++
*/

#include<fstream>
#include<algorithm>
using namespace std;
ifstream fin("frac1.in");
ofstream fout("frac1.out");
#define LEN 160
int n;

struct fraction{
    int up, down;
    fraction() : up(0), down(0) {}
    fraction(int a, int b) : up(a), down(b) {}
};
fraction fs[LEN];

inline bool comp(const fraction& f1, const fraction& f2 ){
    return f1.up * f2.down > f1.down * f2.up;
}

bool check(int a, int b){ // relatively prime or not
    int t;
    if(a < b){ t = a; a = b; b = t;}
    while(t = a%b) {
        a = b;
        b = t;
    }
    return b == 1 ? true : false;
}

inline void print(const fraction& f) { fout<<f.up<<"/"<<f.down<<"\n"; }

int main()
{
    fin>>n;
    print(fraction(0, 1));
    int i;
    for(i = 1; i < n; ++i){
        int t = n;
        while(!check(i,t)) --t;
        fs[i-1] = fraction(i, t);
    }

    make_heap(fs, fs+n-2, comp);
    int size = n-1, j;
    while(fs[0].up!=n-1)
    {
        print(fs[0]);
        pop_heap(fs, fs+size, comp);
        bool flag = false;
        for(j = fs[size-1].down-1; j > fs[size-1].up; --j) // M路歸併的思路就體現在這裏了
            if(check(fs[size-1].up, j)){
                fs[size-1] = fraction(fs[size-1].up, j);
                flag = true;
                break;
            }
        if(!flag) --size;
        push_heap(fs, fs+size, comp);
    }
    if(size != 0)print(fs[0]);
    print(fraction(1,1));
    return 0;
}