hdu 2136 Largest prime factor(素数筛选)

Largest prime factor

Time Limit: 5000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 10043    Accepted Submission(s): 3552

Problem Description

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.

 

Input

Each line will contain one integer n(0 < n < 1000000).

 

Output

Output the LPF(n).

 

Sample Input

1
2
3
4
5

 

Sample Output

0
1
2
1
3

题意：任何数都可以由素数的乘积构成，问你最大质因数是第几个素数

思路：用素数筛选可以求出每个素数的位置，再求出最大质因数，O（1）就可以做到查找了

代码：

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <cstring>
using namespace std;
#define N 1000010
int prime[N],notprime[N];
void init()
{
    memset(notprime,0,sizeof(notprime));
    prime[0]=0;prime[1]=0;
    for(int i=2;i<N;i++)
    {
        if(!notprime[i])
        {
            prime[i]=++prime[0];
            for(long long j=(long long)i*i;j<N;j+=i)
                notprime[j]=1;
        }
    }
}
int Devie(int n)
{
    int maxn=-1;
    for(int i=2;i*i<=n;i++)
    {
        if(n%i==0)
            {
                if(maxn<i) maxn=i;
                while(n%i==0)
                    n/=i;
            }
    }
    if(n>1) return max(maxn,n);
    return maxn;
}
int main()
{
    int n;
    init();
    while(~scanf("%d",&n))
    {
        if(n==1) printf("0\n");
        else
        {
            int m=Devie(n);
       printf("%d\n",prime[m]);
        }
    }
    return 0;
}