一次函数

#include <iostream>
#include <cmath>

using namespace std;

int gcd(int a,int b)
{
   return b ? gcd(b, a % b) : a;
}

int main()
{
    int x1,y1,x2,y2,ky,kx,bx,by;
    double k,b;
    cin >> x1 >> y1 >> x2 >> y2;
    if(y1==y2)
    {
        cout << "y=" << y1;
        return 0;
    }
    k=(y1-y2)*1.0/(x1-x2);
    int k1=(y1-y2)/(x1-x2);
    if(k1!=k)
    {
        ky=abs(y1-y2);
        kx=abs(x1-x2);
        int s=gcd(ky,kx);
        ky/=s;
        kx/=s;
        if(k<0)
            ky*=-1;
        bx=abs(x1-x2);
        by=abs(x1*y2-x2*y1);
        s=gcd(by,bx);
        by/=s;
        bx/=s;
    }
    if(k1==k)
    {
         if(y1==k*x1)
         {
             if(k1==1)
                cout << "y=x";
             else if(k1==-1)
                cout << "y=-x";
             else
                cout << "y=" << k1 << "x";
         }
         else
         {
             b=y1-k*x1;
             if(b>0)
             {
                 if(k1==1)
                    cout << "y=x+" << b;
                 else if(k1==-1)
                    cout << "y=-x+" << b;
                 else
                    cout << "y=" << k1 << "x+" << b;
             }
             else
             {
                  if(k1==1)
                    cout << "y=x" << b;
                 else if(k1==-1)
                    cout << "y=-x" << b;
                 else
                    cout << "y=" << k1 << "x" << b;
             }
         }
    }
    else
    {
        if(y1-k*x1>0)
            cout << "y=" << ky << "/" << kx << "*x+" << by << "/" << bx;
        else if(y1-k*x1<0)
            cout << "y=" << ky << "/" << kx << "*x-" << by << "/" << bx;
        else
            cout << "y=" << ky << "/" << kx << "*x";
    }
    return 0;
}

因子分解

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cmath>

using namespace std;

const int N = 110;

typedef long long LL;

int primes[N], cnt; 
bool st[N];

void get_primes(){
    for (int i = 2; i <= 100; i ++ ){
        if (st[i]) continue;
        primes[cnt++] = i;
        for (int j = i + i; j <= 100; j += i)
            st[j] = true;
    }
}

int main(){
    get_primes();
    int n;
    cin >> n;
    int ok = 0;
    for (int i = 0; i < cnt; i ++ ){
        int x = primes[i];
        if (n % x == 0){
            int m = 0;
            while (n % x == 0){
                n /= x;
                m ++ ;
            }
            if (ok) cout << '*';
            cout << x;
            if (m > 1) cout << '^' << m;
            if (n == 1) break;
            ok = 1;
        }
    }
    return 0;
}

阶乘分解

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cmath>

using namespace std;

const int N = 1e5 + 10;

typedef long long LL;

int primes[N], cnt; 
bool st[N];

void get_primes(){
    for (int i = 2; i < N; i ++ ){
        if (st[i]) continue;
        primes[cnt++] = i;
        for (int j = i + i; j < N; j += i)
            st[j] = true;
    }
}

int main(){
    get_primes();
    int n;
    cin >> n;
    for (int i = 0; i < cnt; i ++ ){
        int x = primes[i];
        int t = 0;
        for (LL j = x; j <= n; j *= x)
            t += n / j;
        if (!t) break;
        cout << x << ' ' << t << endl;
    }
    return 0;
}