zoukankan      html  css  js  c++  java
  • hdu-5894 hannnnah_j’s Biological Test(组合数学)

    题目链接:

    hannnnah_j’s Biological Test

    Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
    Total Submission(s): 412    Accepted Submission(s): 129


    Problem Description
    hannnnah_j is a teacher in WL High school who teaches biology.

    One day, she wants to test m students, thus she arranges n different seats around a round table.

    In order to prevent cheating, she thinks that there should be at least k empty seats between every two students.

    hannnnah_j is poor at math, and she wants to know the sum of the solutions.So she turns to you for help.Can you help her? The answer maybe large, and you need to mod 1e9+7.
     
    Input
    First line is an integer T(T≤1000).
    The next T lines were given n, m, k, respectively.
    0 < m < n < 1e6, 0 < k < 1000
     
    Output
    For each test case the output is only one integer number ans in a line.
     
    Sample Input
    2
    4 2 6
    5 2 1
     
    Sample Output
    0
    5
     
    题意:
     
    给出n个不同的围成一圈的座位,现在有m个人,要求每两个人之间要空至少k个座位,问有多少种方案;
     
    思路:
     
    m个人要坐m个座位,还要至少空m*k个座位,剩下的就是n-m*(k+1)个座位了,放在m个间隔中,就是相同的球放在不同的盒子那个模型了;
    C(n-m*k-1,m-1),然后n个不同的座位那么就可以有n种不同的开始方式,然后这其中的每一种方式都被算了m次;
    所以C(n-m*k-1,m-1)*n/m就是答案了;
     
    AC代码:
    #include <iostream>
    #include <cstdio>
    #include <cstring>
    #include <algorithm>
    #include <cmath>
    #include <bits/stdc++.h>
    #include <stack>
    #include <map>
      
    using namespace std;
      
    #define For(i,j,n) for(int i=j;i<=n;i++)
    #define mst(ss,b) memset(ss,b,sizeof(ss));
      
    typedef  long long LL;
      
    template<class T> void read(T&num) {
        char CH; bool F=false;
        for(CH=getchar();CH<'0'||CH>'9';F= CH=='-',CH=getchar());
        for(num=0;CH>='0'&&CH<='9';num=num*10+CH-'0',CH=getchar());
        F && (num=-num);
    }
    int stk[70], tp;
    template<class T> inline void print(T p) {
        if(!p) { puts("0"); return; }
        while(p) stk[++ tp] = p%10, p/=10;
        while(tp) putchar(stk[tp--] + '0');
        putchar('
    ');
    }
      
    const LL mod=1e9+7;
    const double PI=acos(-1.0);
    const LL inf=1e18;
    const int N=(1<<20)+10;
    const int maxn=1e6+10;
    const double eps=1e-12;
     
    int n,m,k;
    LL p[maxn];
    inline void Init()
    {
        p[0]=1;
        p[1]=1;
        for(int i=2;i<maxn;i++)p[i]=p[i-1]*(LL)i%mod;
    }
    LL pow_mod(LL x,LL y)
    {
        LL s=1,base=x;
        while(y)
        {
            if(y&1)s=s*base%mod;
            base=base*base%mod;
            y>>=1;
        }
        return s;
    }
    int main()
    {
        //freopen("int.txt","r",stdin);
        Init();
        int t;
        read(t);
        while(t--)
        {
            read(n);read(m);read(k);
            if(m==1){printf("%d
    ",n);continue;}
            if(n<m*(k+1))printf("0
    ");
            else 
            {
                int fn=n-k*m-1,fm=m-1;
                LL ans=p[fn]*pow_mod(p[fm]*p[fn-fm]%mod,mod-2)%mod;
                ans=ans*n%mod*pow_mod((LL)m,mod-2)%mod;
                printf("%lld
    ",ans);
            }
        }
        return 0;
    }
    

      

  • 相关阅读:
    《ECMAScript6入门》___阮一峰 笔记
    JS的常用正则表达式 验证密码(转载自用)
    微信小程序 写一个获取验证码 及setInterval 使用基本方法
    python中将图片从客户端(client)推到(POST)到服务器端(server)的方法
    用python将MSCOCO和Caltech行人检测数据集转化成VOC格式
    Tensorflow物体检测(Object Detection)API的使用
    opencv获取IP摄像头(IP-camera)实时视频流
    利用flask将opencv实时视频流输出到浏览器
    Tensorflow同时加载使用多个模型
    opencv在同一窗口打印多张图片
  • 原文地址:https://www.cnblogs.com/zhangchengc919/p/5885717.html
Copyright © 2011-2022 走看看