hdu 2136 数论+筛选质数+打表

题目来源：
http://acm.hdu.edu.cn/showproblem.php?pid=2136

Largest prime factor

Time Limit: 5000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 6237 Accepted Submission(s): 2206


[align=left]Problem Description[/align]
Everybody knows any number can be combined by the prime number.
Now, your task is telling me what position of the largest prime factor.
The position of prime 2 is 1, prime 3 is 2, and prime 5 is 3, etc.
Specially, LPF(1) = 0.

[align=left]Input[/align]
Each line will contain one integer n(0 < n < 1000000).

[align=left]Output[/align]
Output the LPF(n).

[align=left]Sample Input[/align]

1
2
3
4
5

[align=left]Sample Output[/align]

0 1 2 1 3
代码如下：

1 #include<iostream>
2 #include<stdlib.h>
3 #include<stdio.h>
4 #include<math.h>
5 #include<string.h>
6 #include<string>
7 #include<queue>
8 #include<algorithm>
9 #include<map>
10 #define N 1000005
11 using namespace std;
12 int elem
; // 记录n 的最大质因子的位置
13 int cnt;
14 int a
;
15 //  判断质数
16 int prime(int x)
17 {
18     if(x==0 || x==1) return 0;
19     if(x==2) return 1;
20     if(x%2==0) return 0; //剪枝,偶数都不是质数
21     for(int i=3; i*i <=x; i+=2)// 奇质数
22         if(x%i==0 ) return 0;
23     return 1;
24 }
25 // 筛选打表
26 void init()
27 {
28     elem[1]=0;
29     cnt=0;
30     for(int i=2;i<N ;i++) //质数筛选
31     {
32         if(prime(i))
33         {
34             cnt++;
35             for(int j=i;j<N ; j+=i)
36                 elem[j]=cnt;  // 记录j(j以 i 为因子) 的最大质因子的位置
37         }
38     }
39 }
40 int main()
41 {
42     init();
43     int n;
44     while(scanf("%d",&n) !=EOF)
45     {
46         printf("%d\n",elem
);
47     }
48     return 0;
49 }