PAT 1059. Prime Factors (25) 质因子分解

题目链接 http://www.patest.cn/contests/pat-a-practise/1059

Given any positive integer N, you are supposed to find all of its prime factors, and write them in the format N = p₁^k₁ * p₂^k₂ *…*p_m^k_m.

Input Specification:

Each input file contains one test case which gives a positive integer N in the range of long int.

Output Specification:

Factor N in the format N = p₁^k₁ * p₂^k₂ *…*p_m^k_m, where p_i's are prime factors of N in increasing order, and the exponent k_i is the number of p_i -- hence when there is only one p_i, k_i is 1 and must NOT be printed out.（坑爹，这最后一句不是说满足情况不输出，可答案是要输出的，害我吓考虑2个case没过）

Sample Input:

97532468

Sample Output:

97532468=2^2*11*17*101*1291
---------------------------------------------------华丽的分割线---------------------------------------------------------------------------------------------

#include <iostream>
#include <cmath>
using namespace std;
const int maxn=100005;
int prime[maxn],pnum=0;
bool p[maxn]={0};
void Find_Prime(){
    p[0]=p[1]=true;
    for(int i=2;i<maxn;i++){
        if(p[i]==false){
            prime[pnum++]=i;
            for(int j=i+i;j<maxn;j+=i)
                p[j]=true;
        }
    }
}
struct factor{
    int x,cnt;
}fac[20];
int num;
void PrimeFactor(int n){
    int sqr=(int)sqrt(n);
    num=0;
    for(int i=0;i<maxn && prime[i]<=sqr;i++){
        if(n%prime[i]==0){
            fac[num].x=prime[i];
            fac[num].cnt=0;
            while(n%prime[i]==0){
                fac[num].cnt++;
                n/=prime[i];
            }
            num++;
        }
        if(n==1) break;
    }
    if(n!=1){
        fac[num].x=n;
        fac[num++].cnt=1;
    }
}
void Print_fac(int n){
    printf("%d=",n);
    for(int i=0;i<num;i++){
        if(i>0)
            printf("*");
        if(fac[i].cnt>1)
            printf("%d^%d",fac[i].x,fac[i].cnt);
        else
            printf("%d",fac[i].x);
    }
    printf("
");
}
int main()
{
    Find_Prime();
    int n;
    while(scanf("%d",&n)!=EOF){
        if(n==1)
            printf("1=1
");
        else{
            PrimeFactor(n);
            Print_fac(n);
        }

        /*
        int a=(1<<31)-1;
        cout<<a<<endl;
        cout<<"1"<<endl;
        PrimeFactor(a);
        cout<<"2"<<endl;
        Print_fac(a);
        cout<<"3"<<endl;
        cout<<num<<endl;
        */
    }
    return 0;
}
//97532468=2^2*11*17*101*1291