Max Factor（素数筛法+把一个数进行素数分解） HDU2710

最新推荐文章于 2024-08-29 11:58:30 发布

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最新推荐文章于 2024-08-29 11:58:30 发布

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分类专栏： ACM训练18周 HDU_OJ 数论/概率学/组合学/离散数学/(线性)代数

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本文介绍了一种通过素数筛选来高效找出一组数字中具有最大素因子的方法，并提供了两种实现思路，一种是通过预处理得到所有素数再进行分解，另一种则是直接筛选并记录每个数字的最大素因子。

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/*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
4
36
38
40
42

Sample Output
38
 */

 /*
 题意：求素因子最大的数
 考察：素数筛选   把x素数分解（得到的因子为全部可整除的素数）
 */
#include<stdio.h>
#include<string.h>
#define MAXN 20000
int prime[MAXN+1];
int getPrime()//得到小于等于MAXN的素数，prime[0]存放的是个数
{
    memset(prime,0,sizeof(prime));
    for(int i=2;i<=MAXN;i++)
    {
        if(!prime[i]) prime[++prime[0]]=i;
        for(int j=1;j<=prime[0]&&prime[j]<=MAXN/i;j++)
        {
            prime[prime[j]*i]=1;
            if(i%prime[j]==0) break;
        }
    }
    return prime[0];
}
long long factor[100][2];
int facCnt;
int getFactors(long long x)//把x进行素数分解
{
    facCnt=0;
    long long tmp=x;
    for(int i=1;tmp!=1;i++)
    {
        factor[facCnt][1]=0;
        if(tmp%prime[i]==0)
        {
            factor[facCnt][0]=prime[i];
            while(tmp%prime[i]==0)
            {
                   factor[facCnt][1]++;
                   tmp/=prime[i];
            }
            facCnt++;
        }
    }
    return facCnt;
}




int main()
{
    int n;
    getPrime();
    int num;
    while(scanf("%d",&n)!=EOF)
    {
        int ans=0;
        int temp=0;
        for(int i=0;i<n;i++)
        {
            scanf("%d",&num);
            if(num==1)//1的时候要单独处理一下
            {
                if(temp<1)
                {
                    temp=1;
                    ans=1;
                }
                continue;
            }
            getFactors(num);
            if(temp<factor[facCnt-1][0])
            {
                temp=factor[facCnt-1][0];
                ans=num;
            }
        }
        printf("%d\n",ans);
    }
    return 0;
}

//另一种方法

#include <cstdio>
#include <cstring>
#include <iostream>
using namespace std;
int array[20001];
int main(){
	int n;
	int number;
	int max,result;//最大素数因子和结果
	memset(array,0,sizeof(array));
	array[1]=1;
	for(int i=2;i<=20000;i++){//此处素数筛法很巧妙，最后array的每个元素均为该处下标的最大因子
		if(!array[i]){
			for(int j=i;j<=20000;j+=i)
				array[j]=i;
		}
	}
	while(cin>>n){
		max=0;
		for(int i=1;i<=n;i++){
			cin>>number;
		    if(array[number]>max){
			   max=array[number];
			   result=number;
		    }
		}
		cout<<result<<'\n';
	}
	return 0;
}