zoukankan      html  css  js  c++  java
  • HDU 2824 The Euler function --------欧拉模板

    The Euler function

    Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
    Total Submission(s): 2986    Accepted Submission(s): 1221


    Problem Description
    The Euler function phi is an important kind of function in number theory, (n) represents the amount of the numbers which are smaller than n and coprime to n, and this function has a lot of beautiful characteristics. Here comes a very easy question: suppose you are given a, b, try to calculate (a)+ (a+1)+....+ (b)
     
    Input
    There are several test cases. Each line has two integers a, b (2<a<b<3000000).
     
    Output
    Output the result of (a)+ (a+1)+....+ (b)
     
    Sample Input
    3 100
     
    Sample Output
    3042
     
    第一种打表的方法是,素数和欧拉,分开来打表。250ms
    第二种打表只有一个,但是时间上更多。500ms
     
     1 #include<iostream>
     2 #include<cstdio>
     3 #include<cstdlib>
     4 #include<cstring>
     5 using namespace std;
     6 
     7 
     8 int prime[3000003],len;
     9 int   opl[3000003];
    10 bool s[3000003];
    11 
    12 void Getprime() //打素数表
    13 {
    14     int i,j;
    15     len=0;
    16     for(i=2;i<=3000000;i++)
    17     {
    18         if(s[i]==false)
    19         {
    20             prime[++len]=i;
    21             for(j=i*2;j<=3000000;j=j+i)
    22             s[j]=true;
    23         }
    24     }
    25 }
    26 
    27 void Euler() //欧拉打表。
    28 {
    29     int i,j;
    30     Getprime();
    31     for(i=2;i<=3000000;i++)
    32     opl[i]=i;
    33     opl[1]=0;
    34     for(i=1;i<=len;i++)
    35     {
    36         for(j=prime[i];j<=3000000;j=j+prime[i])
    37         opl[j]=opl[j]/prime[i]*(prime[i]-1); //利用的定理
    38 
    39     }
    40 }
    41 
    42 int main()
    43 {
    44     int n,m,i;
    45     __int64 num;
    46     Euler();
    47     while(scanf("%d%d",&n,&m)>0)
    48     {
    49         num=0;
    50         for(i=n;i<=m;i++)
    51         num=num+opl[i];
    52         printf("%I64d
    ",num);
    53     }
    54     return 0;
    55 }

     第二种方法。

     1 #include<iostream>
     2 #include<cstdio>
     3 #include<cstdlib>
     4 #include<cstring>
     5 using namespace std;
     6 
     7 
     8 int   opl[3000003];
     9 bool s[3000003];
    10 
    11 
    12 void Euler() //欧拉打表。
    13 {
    14     int i,j;
    15     for(i=2;i<=3000000;i++)
    16     opl[i]=i;
    17     opl[1]=0;
    18 
    19     for(i=2;i<=3000000;i++)
    20     if(s[i]==false)
    21     {
    22         for(j=i;j<=3000000;j=j+i)
    23         {
    24             opl[j]=opl[j]/i*(i-1);
    25             s[j]=true;
    26         }
    27     }
    28 }
    29 
    30 int main()
    31 {
    32     int n,m,i;
    33     __int64 num;
    34     Euler();
    35     while(scanf("%d%d",&n,&m)>0)
    36     {
    37         num=0;
    38         for(i=n;i<=m;i++)
    39         num=num+opl[i];
    40         printf("%I64d
    ",num);
    41     }
    42     return 0;
    43 }
     
  • 相关阅读:
    26 转义符 re模块 方法 random模块 collection模块的Counter方法
    25 正则表达式
    24 from 模块 import 名字
    24 from 模块 import 名字
    24 from 模块 import 名字
    23 析构方法 items系列 hash方法 eq方法
    21 isinstance issubclass 反射 _str_ _new_ _len_ _call_
    20 属性, 类方法, 静态方法. python2与python3的区别.
    python(1)
    python之字符串格式化
  • 原文地址:https://www.cnblogs.com/tom987690183/p/3243535.html
Copyright © 2011-2022 走看看