HDU2136:Largest prime factor

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本文介绍了一个通过筛选法预处理质数，并快速查找任意正整数的最大质因数位置的算法实现。该算法适用于小于100万的整数范围。

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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

Sample Output

#include <stdio.h>
#include <string.h>

const int N = 1000000;
int hash[N+5];
int prime[N+5];

void sushu()
{
    int  i,j;
    memset(prime,0,sizeof(prime));
    hash[1] = 0;
    int flag = 0;
    for(i = 2; i<=N; i++)
    {
        if(!prime[i])
        {
            hash[i] = ++flag;
            for(j = i; j<=N; j+=i)
            {
                prime[j] = i;
            }
        }
    }
}

int main()
{
    int i;
    memset(hash,0,sizeof(hash));
    sushu();
    while(~scanf("%d",&i))
    {
        if(i == 1)
        printf("0\n");
        else
        {
            int k = prime[i];
            printf("%d\n",hash[k]);
        }
    }

    return 0;
}