[daily question in summer] Luogu p2026 find the analytic formula of primary function

Topic link ：P2026 Find the analytic expression of a function - Luogu | New ecology of computer science education (luogu.com.cn)

Background

Complaints about doing math winter vacation homework ……

Title Description

Given the coordinates of two integral points , Find the analytic function of the line where they are located （ Once function ）.

Input format

There are two lines of input .

The first line has two integers x1,y1. The coordinates of the first integral point are (x1,y1)

The second line has two integers x2,y2. The coordinate of the second integral point is (x2,y2)

Output format

The output is one line , That is, the analytic expression of this function .

Examples #1

The sample input #1

3 6
2 4

Sample output #1

y=2x

Examples #2

The sample input #2

3 5
2 7

Sample output #2

y=-2x+11

Examples #3

The sample input #3

3 -1
5 -2

Sample output #3

y=-1/2*x+1/2

Tips

Mahayana and Hinayana X Expressed as 2x

Half multiply X Expressed as 1/2\*x

AC code:

#include<iostream>
#include<algorithm>

using namespace std;

// y=k*x+b;
// k=(y2-y1)/(x2-x1) 
// b=y-k*x;
int main()
{
	int x1,y1;
	cin>>x1>>y1;
	int x2,y2;
	cin>>x2>>y2;
	int k_fz,k_fm; //  Slope molecule , The denominator 
	k_fz=y2-y1;
	k_fm=x2-x1;
	
	//  The slope is an integer （ Intercept must also be an integer ） 
	if(k_fz%k_fm==0) 
	{
		int b=y1-(k_fz/k_fm)*x1;
		if(b>0)
			cout<<"y="<<k_fz/k_fm<<"x"<<"+"<<b<<endl;
		else if(b<0)
			cout<<"y="<<k_fz/k_fm<<"x"<<b<<endl;
		else
			cout<<"y="<<k_fz/k_fm<<"x"<<endl;
		return 0;
	}
	
	//  The slope is a fraction  
	if(k_fz*1.0/k_fm>0) //  The slope is positive  
	{
		k_fz=abs(y2-y1);
		k_fm=abs(x2-x1);
	//   The slope is reduced to the simplest fraction  
		k_fz=k_fz/__gcd(k_fz,k_fm);
		k_fm=k_fm/__gcd(k_fz,k_fm);
		
		int b_fz,b_fm; //  Intercept molecule , The denominator  
		b_fz=y1*k_fm-k_fz*x1;
		b_fm=k_fm;
		
		if(b_fz%b_fm==0) //  Intercept is an integer  
		{
			if(b_fz*1.0/b_fm>0)
				cout<<"y="<<abs(k_fz)<<"/"<<abs(k_fm)<<"*x"<<"+"<<b_fz/b_fm<<endl;
			else if(b_fz*1.0/b_fm<0)
				cout<<"y="<<abs(k_fz)<<"/"<<abs(k_fm)<<"*x"<<b_fz/b_fm<<endl;
			else
				cout<<"y="<<abs(k_fz)<<"/"<<abs(k_fm)<<"*x"<<endl;
			return 0; 
		}
		
		if(b_fz*1.0/b_fm>0)
			cout<<"y="<<abs(k_fz)<<"/"<<abs(k_fm)<<"*x"<<"+"<<abs(b_fz)/__gcd(abs(b_fz),abs(b_fm))<<"/"<<abs(b_fm)/__gcd(abs(b_fz),abs(b_fm))<<endl;
		else if(b_fz*1.0/b_fm<0)
			cout<<"y="<<abs(k_fz)<<"/"<<abs(k_fm)<<"*x"<<"-"<<abs(b_fz)/__gcd(abs(b_fz),abs(b_fm))<<"/"<<abs(b_fm)/__gcd(abs(b_fz),abs(b_fm))<<endl;		
		else
			cout<<"y="<<abs(k_fz)<<"/"<<abs(k_fm)<<"*x"<<endl;	
	}
	else //  The slope is negative  
	{
		k_fz=abs(y2-y1);
		k_fm=abs(x2-x1);
	//   The slope is reduced to the simplest fraction  
		k_fz=k_fz/__gcd(k_fz,k_fm);
		k_fm=k_fm/__gcd(k_fz,k_fm);
		
		int b_fz,b_fm; //  Intercept molecule , The denominator  
		b_fz=y1*k_fm+k_fz*x1; //  Note that this is  "+"  Number  （ Because the slope is negative ） 
		b_fm=k_fm;
		
		if(b_fz%b_fm==0) //  Intercept is an integer  
		{
			if(b_fz*1.0/b_fm>0)
				cout<<"y="<<"-"<<abs(k_fz)<<"/"<<abs(k_fm)<<"*x"<<"+"<<b_fz/b_fm<<endl;
			else if(b_fz*1.0/b_fm<0)
				cout<<"y="<<"-"<<abs(k_fz)<<"/"<<abs(k_fm)<<"*x"<<b_fz/b_fm<<endl;
			else
				cout<<"y="<<"-"<<abs(k_fz)<<"/"<<abs(k_fm)<<"*x"<<endl;
			return 0;
		}
		
		if(b_fz*1.0/b_fm>0)
			cout<<"y="<<"-"<<abs(k_fz)<<"/"<<abs(k_fm)<<"*x"<<"+"<<abs(b_fz)/__gcd(abs(b_fz),abs(b_fm))<<"/"<<abs(b_fm)/__gcd(abs(b_fz),abs(b_fm))<<endl;
		else if(b_fz*1.0/b_fm<0) 
			cout<<"y="<<"-"<<abs(k_fz)<<"/"<<abs(k_fm)<<"*x"<<"-"<<abs(b_fz)/__gcd(abs(b_fz),abs(b_fm))<<"/"<<abs(b_fm)/__gcd(abs(b_fz),abs(b_fm))<<endl;
		else
			cout<<"y="<<"-"<<abs(k_fz)<<"/"<<abs(k_fm)<<"*x"<<endl;
	}
	
	return 0; 
}