Given three integers a, b and c which represents coefficients of the equation of a line a * x + b * y – c = 0. Given two integer points (x1, y1) and (x2, y2). The task is to determine whether the points (x1, y1) and (x2, y2) lie on the same side of the given line or not.
Examples:
Input : a = 1, b = 1, c = 1, x1 = 1, y1 = 1, x2 = 1, y2 = 2
Output : yes
On applying (x1, y1) and (x2, y2) on a * x + b * y – c, gives 1 and 2 respectively both of which have the same sign, hence both the points lie on same side of the line.
Input : a = 1, b = 1, c = 1, x1 = 1, y1 = 1, x2 = 0, y2 = 0
Output : no
Approach : Apply both the points on given line equation and check if the obtained values belong to same parity or not.
Below is the implementation of the above approach:
// C++ program to check if two points // lie on the same side or not #include <bits/stdc++.h> using namespace std;
// Function to check if two points // lie on the same side or not bool pointsAreOnSameSideOfLine( int a, int b, int c,
int x1, int y1, int x2, int y2)
{ int fx1; // Variable to store a * x1 + b * y1 - c
int fx2; // Variable to store a * x2 + b * y2 - c
fx1 = a * x1 + b * y1 - c;
fx2 = a * x2 + b * y2 - c;
// If fx1 and fx2 have same sign
if ((fx1 * fx2) > 0)
return true ;
return false ;
} // Driver code int main()
{ int a = 1, b = 1, c = 1;
int x1 = 1, y1 = 1;
int x2 = 2, y2 = 1;
if (pointsAreOnSameSideOfLine(a, b, c, x1, y1, x2, y2))
cout << "Yes" ;
else
cout << "No" ;
} |
// Java program to check if two points // lie on the same side or not import java.util.*;
class GFG
{ // Function to check if two points // lie on the same side or not static boolean pointsAreOnSameSideOfLine( int a, int b,
int c, int x1,
int y1, int x2,
int y2)
{ int fx1; // Variable to store a * x1 + b * y1 - c
int fx2; // Variable to store a * x2 + b * y2 - c
fx1 = a * x1 + b * y1 - c;
fx2 = a * x2 + b * y2 - c;
// If fx1 and fx2 have same sign
if ((fx1 * fx2) > 0 )
return true ;
return false ;
} // Driver code public static void main(String[] args)
{ int a = 1 , b = 1 , c = 1 ;
int x1 = 1 , y1 = 1 ;
int x2 = 2 , y2 = 1 ;
if (pointsAreOnSameSideOfLine(a, b, c, x1, y1, x2, y2))
System.out.println( "Yes" );
else
System.out.println( "No" );
} } // This code is contributed by 29AjayKumar |
# Python3 program to check if two points # lie on the same side or not # Function to check if two points # lie on the same side or not def pointsAreOnSameSideOfLine(a, b, c, x1, y1, x2, y2):
fx1 = 0 # Variable to store a * x1 + b * y1 - c
fx2 = 0 # Variable to store a * x2 + b * y2 - c
fx1 = a * x1 + b * y1 - c
fx2 = a * x2 + b * y2 - c
# If fx1 and fx2 have same sign
if ((fx1 * fx2) > 0 ):
return True
return False
# Driver code a, b, c = 1 , 1 , 1
x1, y1 = 1 , 1
x2, y2 = 2 , 1
if (pointsAreOnSameSideOfLine(a, b, c,
x1, y1, x2, y2)):
print ( "Yes" )
else :
print ( "No" )
# This code is contributed by Mohit Kumar |
// C# program to check if two points // lie on the same side or not using System;
class GFG
{ // Function to check if two points // lie on the same side or not static bool pointsAreOnSameSideOfLine( int a, int b,
int c, int x1,
int y1, int x2,
int y2)
{ int fx1; // Variable to store a * x1 + b * y1 - c
int fx2; // Variable to store a * x2 + b * y2 - c
fx1 = a * x1 + b * y1 - c;
fx2 = a * x2 + b * y2 - c;
// If fx1 and fx2 have same sign
if ((fx1 * fx2) > 0)
return true ;
return false ;
} // Driver code public static void Main()
{ int a = 1, b = 1, c = 1;
int x1 = 1, y1 = 1;
int x2 = 2, y2 = 1;
if (pointsAreOnSameSideOfLine(a, b, c, x1, y1, x2, y2))
Console.WriteLine( "Yes" );
else
Console.WriteLine( "No" );
} } // This code is contributed by Code_Mech |
<script> // Javascript program to check if two points
// lie on the same side or not
// Function to check if two points
// lie on the same side or not
function pointsAreOnSameSideOfLine(a, b, c, x1, y1, x2, y2)
{
let fx1; // Variable to store a * x1 + b * y1 - c
let fx2; // Variable to store a * x2 + b * y2 - c
fx1 = a * x1 + b * y1 - c;
fx2 = a * x2 + b * y2 - c;
// If fx1 and fx2 have same sign
if ((fx1 * fx2) > 0)
return true ;
return false ;
}
let a = 1, b = 1, c = 1;
let x1 = 1, y1 = 1;
let x2 = 2, y2 = 1;
if (pointsAreOnSameSideOfLine(a, b, c, x1, y1, x2, y2))
document.write( "Yes" );
else
document.write( "No" );
// This code is contributed by divyesh072019. </script> |
Yes
Time complexity: O(1) because constant operations are done
Auxiliary space: O(1)