Dados dos segmentos de línea AB y CD que tienen A(x 1 , y 1 ), B(x 2 , y 2 ), C(x 3 , y 3 ) y D(x 4 , y 4 ). La tarea es verificar si estas dos líneas son ortogonales o no. Dos rectas se llaman ortogonales si son perpendiculares en el punto de intersección.
Ejemplos:
Input: x1 = 0, y1 = 3, x2 = 0, y2 = -5
x3 = 2, y3 = 0, x4 = -1, y4 = 0
Output: Yes
Input: x1 = 0, y1 = 4, x2 = 0, y2 = -9
x3 = 2, y3 = 0, x4 = -1, y4 = 0
Output: Yes
Enfoque: si las pendientes de las dos líneas son m 1 y m 2 , entonces para que sean ortogonales, debemos verificar si:
- Ambas rectas tienen pendiente infinita, entonces la respuesta es no.
- Una línea tiene pendiente infinita y si otra línea tiene pendiente 0, la respuesta es sí, de lo contrario, no.
- Ambas rectas tienen pendiente finita y su producto es -1 entonces la respuesta es sí.
A continuación se muestra la implementación del enfoque anterior:
C++
// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;
// Function to check if two straight
// lines are orthogonal or not
bool checkOrtho(int x1, int y1, int x2, int y2,
int x3, int y3, int x4, int y4)
{
int m1, m2;
// Both lines have infinite slope
if (x2 - x1 == 0 && x4 - x3 == 0)
return false;
// Only line 1 has infinite slope
else if (x2 - x1 == 0) {
m2 = (y4 - y3) / (x4 - x3);
if (m2 == 0)
return true;
else
return false;
}
// Only line 2 has infinite slope
else if (x4 - x3 == 0) {
m1 = (y2 - y1) / (x2 - x1);
if (m1 == 0)
return true;
else
return false;
}
else {
// Find slopes of the lines
m1 = (y2 - y1) / (x2 - x1);
m2 = (y4 - y3) / (x4 - x3);
// Check if their product is -1
if (m1 * m2 == -1)
return true;
else
return false;
}
}
// Driver code
int main()
{
int x1 = 0, y1 = 4, x2 = 0, y2 = -9;
int x3 = 2, y3 = 0, x4 = -1, y4 = 0;
checkOrtho(x1, y1, x2, y2, x3, y3, x4, y4) ? cout << "Yes"
: cout << "No";
return 0;
}
Java
//Java implementation of above approach
import java.io.*;
class GFG {
// Function to check if two straight
// lines are orthogonal or not
static boolean checkOrtho(int x1, int y1, int x2, int y2,
int x3, int y3, int x4, int y4)
{
int m1, m2;
// Both lines have infinite slope
if (x2 - x1 == 0 && x4 - x3 == 0)
return false;
// Only line 1 has infinite slope
else if (x2 - x1 == 0)
{
m2 = (y4 - y3) / (x4 - x3);
if (m2 == 0)
return true;
else
return false;
}
// Only line 2 has infinite slope
else if (x4 - x3 == 0)
{
m1 = (y2 - y1) / (x2 - x1);
if (m1 == 0)
return true;
else
return false;
}
else
{
// Find slopes of the lines
m1 = (y2 - y1) / (x2 - x1);
m2 = (y4 - y3) / (x4 - x3);
// Check if their product is -1
if (m1 * m2 == -1)
return true;
else
return false;
}
}
// Driver code
public static void main (String[] args)
{
int x1 = 0, y1 = 4, x2 = 0, y2 = -9;
int x3 = 2, y3 = 0, x4 = -1, y4 = 0;
if(checkOrtho(x1, y1, x2, y2, x3, y3, x4, y4)==true)
System.out.println ("Yes");
else
System.out.println("No" );
}
}
//This code is contributed by akt_mit..
Python3
# Python 3 implementation of above approach
# Function to check if two straight
# lines are orthogonal or not
def checkOrtho(x1, y1, x2, y2, x3, y3, x4, y4):
# Both lines have infinite slope
if (x2 - x1 == 0 and x4 - x3 == 0):
return False
# Only line 1 has infinite slope
elif (x2 - x1 == 0):
m2 = (y4 - y3) / (x4 - x3)
if (m2 == 0):
return True
else:
return False
# Only line 2 has infinite slope
elif (x4 - x3 == 0):
m1 = (y2 - y1) / (x2 - x1);
if (m1 == 0):
return True
else:
return False
else:
# Find slopes of the lines
m1 = (y2 - y1) / (x2 - x1)
m2 = (y4 - y3) / (x4 - x3)
# Check if their product is -1
if (m1 * m2 == -1):
return True
else:
return False
# Driver code
if __name__ == '__main__':
x1 = 0
y1 = 4
x2 = 0
y2 = -9
x3 = 2
y3 = 0
x4 = -1
y4 = 0
if(checkOrtho(x1, y1, x2, y2,
x3, y3, x4, y4)):
print("Yes")
else:
print("No")
# This code is contributed by
# Shashank_Sharma
C#
// C# implementation of above approach
using System;
class GFG
{
// Function to check if two straight
// lines are orthogonal or not
static bool checkOrtho(int x1, int y1, int x2, int y2,
int x3, int y3, int x4, int y4)
{
int m1, m2;
// Both lines have infinite slope
if (x2 - x1 == 0 && x4 - x3 == 0)
return false;
// Only line 1 has infinite slope
else if (x2 - x1 == 0)
{
m2 = (y4 - y3) / (x4 - x3);
if (m2 == 0)
return true;
else
return false;
}
// Only line 2 has infinite slope
else if (x4 - x3 == 0)
{
m1 = (y2 - y1) / (x2 - x1);
if (m1 == 0)
return true;
else
return false;
}
else
{
// Find slopes of the lines
m1 = (y2 - y1) / (x2 - x1);
m2 = (y4 - y3) / (x4 - x3);
// Check if their product is -1
if (m1 * m2 == -1)
return true;
else
return false;
}
}
// Driver code
public static void Main ()
{
int x1 = 0, y1 = 4, x2 = 0, y2 = -9;
int x3 = 2, y3 = 0, x4 = -1, y4 = 0;
if(checkOrtho(x1, y1, x2, y2, x3, y3, x4, y4) == true)
Console.WriteLine("Yes");
else
Console.WriteLine("No" );
}
}
// This code is contributed by Ryuga
PHP
<?php
// PHP implementation of above approach
// Function to check if two straight
// lines are orthogonal or not
function checkOrtho($x1, $y1, $x2, $y2,
$x3, $y3, $x4, $y4)
{
// Both lines have infinite slope
if ($x2 - $x1 == 0 && $x4 - $x3 == 0)
return false;
// Only line 1 has infinite slope
else if ($x2 - $x1 == 0)
{
$m2 = (int)(($y4 - $y3) / ($x4 - $x3));
if ($m2 == 0)
return true;
else
return false;
}
// Only line 2 has infinite slope
else if ($x4 - $x3 == 0)
{
$m1 = (int)(($y2 - $y1) / ($x2 - $x1));
if ($m1 == 0)
return true;
else
return false;
}
else
{
// Find slopes of the lines
$m1 = (int)(($y2 - $y1) / ($x2 - $x1));
$m2 = (int)(($y4 - $y3) / ($x4 - $x3));
// Check if their product is -1
if ($m1 * $m2 == -1)
return true;
else
return false;
}
}
// Driver code
$x1 = 0; $y1 = 4;
$x2 = 0; $y2 = -9;
$x3 = 2; $y3 = 0;
$x4 = -1; $y4 = 0;
if(checkOrtho($x1, $y1, $x2, $y2,
$x3, $y3, $x4, $y4))
print("Yes");
else
print("No");
// This code is contributed by chandan_jnu
?>
Javascript
<script>
// Javascript implementation of above approach
// Function to check if two straight
// lines are orthogonal or not
function checkOrtho(x1, y1, x2, y2, x3, y3, x4, y4)
{
let m1, m2;
// Both lines have infinite slope
if (x2 - x1 == 0 && x4 - x3 == 0)
return false;
// Only line 1 has infinite slope
else if (x2 - x1 == 0)
{
m2 = parseInt((y4 - y3) / (x4 - x3), 10);
if (m2 == 0)
return true;
else
return false;
}
// Only line 2 has infinite slope
else if (x4 - x3 == 0)
{
m1 = parseInt((y2 - y1) / (x2 - x1), 10);
if (m1 == 0)
return true;
else
return false;
}
else
{
// Find slopes of the lines
m1 = parseInt((y2 - y1) / (x2 - x1), 10);
m2 = parseInt((y4 - y3) / (x4 - x3), 10);
// Check if their product is -1
if (m1 * m2 == -1)
return true;
else
return false;
}
}
let x1 = 0, y1 = 4, x2 = 0, y2 = -9;
let x3 = 2, y3 = 0, x4 = -1, y4 = 0;
if(checkOrtho(x1, y1, x2, y2, x3, y3, x4, y4) == true)
document.write("Yes");
else
document.write("No" );
</script>
Producción:
Yes
Complejidad de tiempo: O(1)
Espacio Auxiliar: O(1)
Publicación traducida automáticamente
Artículo escrito por saurabh_shukla y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA