[这货不是游戏]细胞分裂

【题目描述】

      Hanks 博士是BT (Bio-Tech,生物技术) 领域的知名专家。现在,他正在为一个细胞实验做准备工作:培养细胞样本。
      Hanks 博士手里现在有N 种细胞,编号从1~N,一个第i 种细胞经过1 秒钟可以分裂为Si 个同种细胞(Si 为正整数)。现在他需要选取某种细胞的一个放进培养皿,让其自由分裂,进行培养。一段时间以后,再把培养皿中的所有细胞平均分入M 个试管,形成M 份样本,用于实验。Hanks 博士的试管数M 很大,普通的计算机的基本数据类型无法存储这样大的M 值,但万幸的是,M 总可以表示为m1 的m2 次方,即M = m1^m2 ,其中m1,m2 均为基本数据类型可以存储的正整数。
      注意,整个实验过程中不允许分割单个细胞,比如某个时刻若培养皿中有4 个细胞,Hanks 博士可以把它们分入2 个试管,每试管内2 个,然后开始实验。但如果培养皿中有5个细胞,博士就无法将它们均分入2 个试管。此时,博士就只能等待一段时间,让细胞们继续分裂,使得其个数可以均分,或是干脆改换另一种细胞培养。
      为了能让实验尽早开始,Hanks 博士在选定一种细胞开始培养后,总是在得到的细胞“刚好可以平均分入M 个试管”时停止细胞培养并开始实验。现在博士希望知道,选择哪种细胞培养,可以使得实验的开始时间最早。

【输入格式】

  输入文件共有三行。
  第一行有一个正整数 N,代表细胞种数。
  第二行有两个正整数 m1,m2,以一个空格隔开, m1^m2即表示试管的总数M。
  第三行有 N 个正整数,第i 个数Si 表示第i 种细胞经过1 秒钟可以分裂成同种细胞的个数。

【输出格式】

  输出文件共一行,为一个整数,表示从开始培养细胞到实验能够开始所经过的最少时间(单位为秒)。
  如果无论 Hanks 博士选择哪种细胞都不能满足要求,则输出整数-1。

【输入样例】

【输入样例 1】

1

2 1

3

【输入样例 2】

2

24 1

30 

12

【输出样例】

【输出样例 1】

-1

【输出样例 2】

2

【分析】

  将m1分解质因数,然后每个因子的个数乘以m2。

  对于每个si,我们算出m1的质因数x在si中的个数y,那么对于一个x来说,能整除的次数就是y乘以多少才可以比x在M中的个数大。然后所有x的最大值就是si需要分裂的次数。

  庞大的质数表。

 

#include <stdio.h>
#define MAXSU 5133
#define MAXINT 100000000
int su[MAXSU] = 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int yin[MAXSU + 10],yins[MAXSU + 10],tot;
long long n,m1,m2,s,ans,te_ans,tem,temp;
void swap(long long &a,long long &b) {
  int t;
  t = a;
  a = b;
  b = t;
}
int main() {
  freopen("cell.in","r",stdin);
  freopen("cell.out","w",stdout);
  scanf("%lld%lld%lld",&n,&m1,&m2);
  for (int i = 0;su[i] * su[i] <= m1;++i)
    if (m1 % su[i] == 0) {
      yin[++tot] = su[i];
      while (m1 % su[i] == 0) {
        ++yins[tot];
        m1 /= su[i];
      }
    }
  if (m1 != 1) {
    yin[++tot] = m1;
    yins[tot] = 1;
  }
  for (int i = 1;i <= tot;++i)
    yins[i] *= m2;
  ans = MAXINT;
  for (int t = 0;t < n;++t) {
    scanf("%lld",&s);
    te_ans = 0;
    for (int i = 1;i <= tot;++i)
      if (s % yin[i] == 0) {
        tem = 0;
        while (s % yin[i] == 0) {
          ++tem;
          s /= yin[i];
        }
        temp = yins[i] / tem;
        if (yins[i] % tem)
          ++temp;
        if (temp > te_ans)
          te_ans = temp;
      } else {
        te_ans = MAXINT;
        break;
      }
    if (te_ans < ans)
      ans = te_ans;
  }
  if (ans == MAXINT)
    ans = -1;
  printf("%lld\n",ans);
  return 0;
}

 

posted @ 2010-10-12 09:39  Sephiroth.L.  阅读(699)  评论(0编辑  收藏  举报