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  • hdu2973-YAPTCHA-(欧拉筛+威尔逊定理+前缀和)

    YAPTCHA

    Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
    Total Submission(s): 1490    Accepted Submission(s): 811


    Problem Description
    The math department has been having problems lately. Due to immense amount of unsolicited automated programs which were crawling across their pages, they decided to put Yet-Another-Public-Turing-Test-to-Tell-Computers-and-Humans-Apart on their webpages. In short, to get access to their scientific papers, one have to prove yourself eligible and worthy, i.e. solve a mathematic riddle.


    However, the test turned out difficult for some math PhD students and even for some professors. Therefore, the math department wants to write a helper program which solves this task (it is not irrational, as they are going to make money on selling the program).

    The task that is presented to anyone visiting the start page of the math department is as follows: given a natural n, compute

    where [x] denotes the largest integer not greater than x.
     
    Input
    The first line contains the number of queries t (t <= 10^6). Each query consist of one natural number n (1 <= n <= 10^6).
     
    Output
    For each n given in the input output the value of Sn.
     
    Sample Input
    13 1 2 3 4 5 6 7 8 9 10 100 1000 10000
     
    Sample Output
    0 1 1 2 2 2 2 3 3 4 28 207 1609
    翻译:求Sn。中括号([])表示取整。
    解题过程:
    令p=3*k+7。
    威尔逊定理:当且仅当p为素数,(p-1)! ≡ -1 (mod p) → (p-1)!+1 ≡ 0 (mod p)
    1.若p是素数, ( (p-1)!+1 )/p是个整数,设为x,则(p-1)!/p比这个整数小一点点,取整后是x-1,
    则[  ( (p-1)!+1 )/p - [(p-1)!/p] ]=1;
    2.若p是合数,(p-1)!/p是个整数,设为y,则( (p-1)!+1 )/p比这个整数大一点点,取整后还是y,
    则[  ( (p-1)!+1 )/p - [(p-1)!/p] ]=0;
    3.前缀和打表Sn。
     1 #include <iostream>
     2 #include<stdio.h>
     3 #include <algorithm>
     4 #include<string.h>
     5 #include<cstring>
     6 #include<math.h>
     7 #define inf 0x3f3f3f3f
     8 #define ll long long
     9 using namespace std;
    10 const int maxx=3000086;
    11 int prime[2000086];
    12 bool vis[3000086];
    13 int ans[1000086];
    14 int cnt;
    15 
    16 void init()
    17 {
    18     cnt=0;
    19     memset(vis,true,sizeof(vis));
    20     vis[0]=vis[1]=false;
    21     for(int i=2;i<=maxx;i++)//欧拉筛
    22     {
    23         if(vis[i])
    24             prime[cnt++]=i;
    25         for(int j=0;j<cnt && prime[j]*i<=maxx;j++)
    26         {
    27             vis[ prime[j]*i ]=false;
    28             if( i%prime[j]==0 ) break;
    29         }
    30     }
    31     memset(ans,0,sizeof(ans));
    32     int p;
    33     for(int k=1;k<=1000005;k++)
    34     {
    35         p=3*k+7;
    36         if(vis[p])
    37             ans[k]=ans[k-1]+1;
    38         else
    39             ans[k]=ans[k-1];
    40     }
    41 }
    42 
    43 int main()///hdu2973,威尔逊定理+前缀和
    44 {
    45     init();
    46     int t,n;
    47     scanf("%d",&t);
    48     while(t--)
    49     {
    50         scanf("%d",&n);
    51         printf("%d
    ",ans[n]);
    52     }
    53     return 0;
    54 }
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  • 原文地址:https://www.cnblogs.com/shoulinniao/p/10366910.html
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