蓝桥杯_数学模板

1.试除法判定质数

#include <iostream>
using namespace std;bool is_zs(int x)
{if(x<2) return false;for(int i=2;i<=x/i;i++)if(x%i==0)return false;return true;
}int main()
{int n; cin>>n;while(n--){int x; cin>>x;if(is_zs(x)) cout<<"Yes\n";elsecout<<"No\n";	}return 0;
}

2.阶乘

int fac(int x)
{if(x<=1) return 1;else return x*fac(x-1);
}

3.分解质因数

#include <iostream>
using namespace std;void div(int x)
{for(int i=2;i<=x/i;i++){if(x%i==0){int s = 0;while(x%i==0) x/=i,s++;cout<<i<<" "<<s<<endl;}}if(x>1) cout<<x<<" "<<1<<endl;printf("\n");
}int main()
{int n; cin>>n;while(n--){int x; cin>>x;div(x);}return 0;
}

4.筛质数
4_1暴力做法(会超时)

#include <iostream>
using namespace std;bool is_zs(int x)
{if(x<2) return false;for(int i=2;i<=x/i;i++)if(x%i==0)return false;return true;
}int c_zs(int n)
{int cnt = 0;for(int i=1;i<=n;i++){if(is_zs(i)) cnt++;}return cnt;}int main()
{int n; cin>>n;	int cnt = c_zs(n);cout<<cnt<<endl;return 0;
}

4_2(完美做法):

#include <iostream>
using namespace std;const int N = 1000010;int p[N],cnt;
bool st[N];void get_zs(int n)
{for(int i=2;i<=n;i++){if(st[i]) continue;p[cnt++] = i;for(int j=i+i;j<=n;j+=i)st[j] = true;}
}int main()
{int n; cin>>n;get_zs(n);cout<<cnt<<endl;return 0;
}

5.试除法求约数

#include <iostream>
#include <algorithm>
#include <vector>
using namespace std;int main()
{int m; cin>>m;while(m--){int n; cin>>n;vector<int> vt;for(int i=1;i<=n/i;i++){if(n%i==0){vt.push_back(i);if(n/i != i) vt.push_back(n/i);}}sort(vt.begin(),vt.end());for(int it:vt) cout<<it<<" ";printf("\n");}return 0;
}