SPOJ NWERC11A_Binomial coefficients

╰半橙微兮° 2022-05-14 13:54 144阅读 0赞

[http://acm.hust.edu.cn/vjudge/contest/view.action?cid=34912\#problem/A][http_acm.hust.edu.cn_vjudge_contest_view.action_cid_34912_problem_A]

解法:  
枚举k,二分n  
  
关键点:  
1.枚举时候只考虑n - k >= k的情况,另一半由对称性得到  
2.大数求组合数时,注意处理超范围的情况  
  
细节处理:  
1.对于C(2k' - 1, k'), n - k = k' - 1 < k' 所以枚举的时候对于一个k,n >= 2k  
2.给定一个k值,那么C(2k, k)是最小值,如果最小值大于给定的值,那么结束枚举.可以发现,C(2k, k)增长的速度很快,所以枚举很快就能结束  
3.二分n求组合数时,先一直乘,如果大于long long的最大值,那么除

#include <cstdio>
    #include <ctime>
    #include <cstdlib>
    #include <cstring>
    #include <queue>
    #include <string>
    #include <set>
    #include <stack>
    #include <map>
    #include <cmath>
    #include <vector>
    #include <iostream>
    #include <algorithm>
    #include <bitset>
    #include <fstream>
    using namespace std;
    
    
    //LOOP
    #define FF(i, a, b) for(int i = (a); i < (b); ++i)
    #define FE(i, a, b) for(int i = (a); i <= (b); ++i)
    #define FED(i, b, a) for(int i = (b); i>= (a); --i)
    #define REP(i, N) for(int i = 0; i < (N); ++i)
    #define CLR(A,value) memset(A,value,sizeof(A))
    #define FC(it, c) for(__typeof((c).begin()) it = (c).begin(); it != (c).end(); it++)
    
    
    //OTHER
    #define SZ(V) (int)V.size()
    #define PB push_back
    #define MP make_pair
    #define all(x) (x).begin(),(x).end()
    
    
    //INPUT
    #define RI(n) scanf("%d", &n)
    #define RII(n, m) scanf("%d%d", &n, &m)
    #define RIII(n, m, k) scanf("%d%d%d", &n, &m, &k)
    #define RIV(n, m, k, p) scanf("%d%d%d%d", &n, &m, &k, &p)
    #define RV(n, m, k, p, q) scanf("%d%d%d%d%d", &n, &m, &k, &p, &q)
    #define RS(s) scanf("%s", s)
    
    
    //OUTPUT
    #define WI(n) printf("%d\n", n)
    #define WS(n) printf("%s\n", n)
    
    
    //debug
    //#define online_judge
    #ifndef online_judge
    #define debugt(a) cout << (#a) << "=" << a << " ";
    #define debugI(a) debugt(a) cout << endl
    #define debugII(a, b) debugt(a) debugt(b) cout << endl
    #define debugIII(a, b, c) debugt(a) debugt(b) debugt(c) cout << endl
    #define debugIV(a, b, c, d) debugt(a) debugt(b) debugt(c) debugt(d) cout << endl
    #else
    #define debugI(v)
    #define debugII(a, b)
    #define debugIII(a, b, c)
    #define debugIV(a, b, c, d)
    #endif
    
    typedef long long LL;
    typedef unsigned long long ULL;
    typedef vector <int> VI;
    const int INF = 0x3f3f3f3f;
    const double eps = 1e-10;
    const int MOD = 100000007;
    const int MAXN = 1000010;
    const double PI = acos(-1.0);
    
    const LL LL_MAX = (~(unsigned long long)0) >> 1;
    const LL MAX = (LL)1e15 + 100;
    const int MAX_INDEX = 1001;
    LL f[MAX_INDEX][MAX_INDEX];
    
    LL ipt;
    typedef pair<LL, LL> PLL;
    vector<PLL> v;
    #define MP make_pair
    
    LL C(LL a, LL b)
    {
        LL ret = 1, ta = a - b + 1, tb = 1;
        while (ta <= a && tb <= b)
        {
            if (ret > LL_MAX / a)
                ret /= tb++;
            else
                ret *= a--;
        }
        if (ta > a)
            while (tb <= b) ret /= tb++;
        else
            return ipt + 1;
        return ret;
    }
    
    LL bse(LL l, LL r, LL k)
    {
        LL m;
        while (l <= r)
        {
            m = (l + r) >> 1;
            if (C(m, k) <= ipt) l = m + 1;
            else r = m - 1;
        }
        return r;
    }
    
    void fun(LL n)
    {
        int k = 2;
        while (C(2 * k, k) <= ipt)
        {
            LL t = bse(2 * k, 1000000000, k);
            if (C(t, k) == ipt)
            {
                v.push_back(MP(t, k));
                v.push_back(MP(t, t - k));
            }
            k++;
        }
    }
    
    
    int main()
    {
    //    freopen("in.txt", "r", stdin);
    //    freopen("out.txt", "w", stdout);
        int kase;
        RI(kase);
        while (kase--)
        {
            v.clear();
    
            cin >> ipt;
            v.push_back(MP(ipt, 1));
            v.push_back(MP(ipt, ipt - 1));
            fun(ipt);
    
            sort(v.begin(), v.end());
            int size = unique(v.begin(), v.end()) - v.begin();
            cout << size << endl;
            REP(i, size)
            {
                if (i != 0) putchar(' ');
                cout << '(' << v[i].first << ',' << v[i].second << ')';
            }
            cout << endl;
        }
        return 0;
    }

[http_acm.hust.edu.cn_vjudge_contest_view.action_cid_34912_problem_A]: http://acm.hust.edu.cn/vjudge/contest/view.action?cid=34912#problem/A