HDU2710:Max Factor-优快云博客

本文介绍了一种算法，用于从一组整数中找出拥有最大质因数的数字。通过筛选法预先计算出所有可能的质数，并利用这些质数来确定每个输入数字的最大质因数。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

Problem Description

To improve the organization of his farm, Farmer John labels each of his N (1 <= N <= 5,000) cows with a distinct serial number in the range 1..20,000. Unfortunately, he is unaware that the cows interpret some serial numbers as better than others. In particular, a cow whose serial number has the highest prime factor enjoys the highest social standing among all the other cows.

(Recall that a prime number is just a number that has no divisors except for 1 and itself. The number 7 is prime while the number 6, being divisible by 2 and 3, is not).

Given a set of N (1 <= N <= 5,000) serial numbers in the range 1..20,000, determine the one that has the largest prime factor.

Input

* Line 1: A single integer, N

* Lines 2..N+1: The serial numbers to be tested, one per line

Output

* Line 1: The integer with the largest prime factor. If there are more than one, output the one that appears earliest in the input file.

Sample Input

Sample Output

38

没什么好说的，题目意思也比较好懂，最主要的是要注意1这个因子

#include <iostream>
#include <string.h>
using namespace std;
#define N 20010
int main()
{
    int n,a[N],s[N],i,j;
    memset(s,1,sizeof(s));
    for(i = 2;i<N;i++)
    {
        if(s[i])
        for(j = i+i;j<N;j+=i)
        s[j] = 0;
    }
    for(i = 2,j = 2;i<N;i++)
    {
        if(s[i])
        a[j++] = i;
    }
    a[1] = 1;
    memset(s,0,sizeof(s));
    while(cin >> n)
    {
        int max = 0,flag;
        for(i = 1;i<=n;i++)
        cin >> s[i];
        for(i = 1;i<=n;i++)
        {
            for(j = 1;a[j]<=s[i];j++)
            {
                if(s[i]%a[j] == 0)
                {
                    if(max < a[j])
                    {
                    max = a[j];
                    flag = i;
                    }
                }
            }
        }
        cout << s[flag] << endl;
    }


    return 0;
}