王道机试指南6.2素数6.3分解质因数

例题6.7素数判定（哈尔滨工业大学上机）

#include<iostream>
#include<cstdio>
using namespace std;
int main(){
    int n, flag = 0;
    while(cin >> n){
        if(n == 1 || n == 0 || n < 0){
            flag =1;
        }
        for(int i = 2; i * i <= n; i++){
            if(n % i == 0){
                flag = 1;
                break;
            } 
        }
        if(flag == 1) cout << "no" << endl;
        else cout << "yes" << endl;
    }
    return 0;
}  

例题6.8素数（北京航空航天大学上机）

#include<iostream>
#include<cstdio>
using namespace std;
int flag[10001] = {0};
int main(){
    int n;
    while(cin >> n){
        for(int i = 2; i <= n; i++){
            if(flag[i] == 0){
                for(int j = 2; j * i <= n; j++){
                    flag[i * j] = 1;
                }
            }
        }
        int space = 0;
        int none = 0;
        for(int i = 2; i <= n; i++){
            if(i % 10 == 1 && flag[i] == 0){
                if(space == 1){
                    cout << " " ;
                }
                cout << i;
                space = 1;
                none = 1;
            }
        }
        if(none == 0) cout << -1;
    }
    return 0;
}  

例题6.9质因数个数（清华大学复试上机）
下面的代码本地通过了，但是没有AC提示段错误，不调用函数不显示段错误，应该是调用层数太多了，需要重构

#include<iostream>
#include<cstdio>
#include<vector>
using namespace std;
int flag[1000] = {0};
vector<int> v;
void primnum(int n){
    for(int i = 2; i * i <= n; i++){
        if(flag[i] == 0){
           for(int j = 2; j * i <= n; j++){
                flag[j * i] = 1;
            }
        }
     }
     for(int i = 2; i < n; i++){
         if(flag[i] == 0){
             v.push_back(i);
        }
    }
}
int main(){
    int n;
    while(cin >> n){
        int sum = 0;
        v.clear();
        primnum(n);
        for(int i = 0; i < v.size(); i++){
            while(n % v[i] == 0){
                n /= v[i];
                sum++;
            }
        }
        cout << sum << endl; 
    }
    return 0;
}  

参考了别人代码后，进行了重构

#include<iostream>
#include<cstdio>
#include<vector>
using namespace std;
int main(){
    int n;
    while(cin >> n){
        int sum = 0;
        for(int i = 2; i * i< n; i++){
            while(n % i == 0){
                n /= i;
                sum++;
            }
        }
        if(n > 1) sum++;//
        cout << sum << endl; 
    }
    return 0;
}    

习题6.7约数个数（清华大学复试上机）

#include<iostream>
#include<cstdio>
#include<cmath>
using namespace std;
int main(){
   int n;
    while(scanf("%d",&n) != EOF){
        for(int i = 0; i < n; i++){
            int temp, count = 0;
            scanf("%d", &temp);
            int bound = (int)sqrt((double)temp) + 1;
            for(int j = 1; j <= bound; j++){
                if(temp % j == 0){
                    count++;
                    if(temp / j > bound) count++;
                }
            }
            printf("%d\n", count);
        }
        n--;
    }
    return 0;
}