Dados tres puntos, verifique si se encuentran en una línea recta (colineal) o no
. Ejemplos:
Input : (1, 1), (1, 4), (1, 5) Output : Yes The points lie on a straight line Input : (1, 5), (2, 5), (4, 6) Output : No The points do not lie on a straight line
Primera aproximación
Tres puntos están en la línea recta si el área formada por el triángulo de estos tres puntos es cero. Así comprobaremos si el área formada por el triángulo es cero o no
Formula for area of triangle is : 0.5 * [x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)] The formula is basically half of determinant value of following. x1 x2 x3 y1 y2 y3 1 1 1 The above formula is derived from shoelace formula. If this equals zero then points lie on a straight line
C++
// C++ program to check if three
// points are collinear or not
// using area of triangle.
#include <bits/stdc++.h>
#include <math.h>
#include <stdlib.h>
using namespace std;
// function to check if point
// collinear or not
void collinear(int x1, int y1, int x2,
int y2, int x3, int y3)
{
// Calculation the area of
// triangle. We have skipped
// multiplication with 0.5
// to avoid floating point
// computations
int a = x1 * (y2 - y3) +
x2 * (y3 - y1) +
x3 * (y1 - y2);
if (a == 0)
cout << "Yes";
else
cout << "No";
}
// Driver Code
int main()
{
int x1 = 1, x2 = 1, x3 = 1,
y1 = 1, y2 = 4, y3 = 5;
collinear(x1, y1, x2, y2, x3, y3);
return 0;
}
// This code is contributed
// by Akanksha Rai(Abby_akku)
C
// C program to check if three
// points are collinear or not
// using area of triangle.
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
// function to check if point
// collinear or not
void collinear(int x1, int y1, int x2,
int y2, int x3, int y3)
{
// Calculation the area of
// triangle. We have skipped
// multiplication with 0.5
// to avoid floating point
// computations
int a = x1 * (y2 - y3) +
x2 * (y3 - y1) +
x3 * (y1 - y2);
if (a == 0)
printf("Yes");
else
printf("No");
}
// Driver Code
int main()
{
int x1 = 1, x2 = 1, x3 = 1,
y1 = 1, y2 = 4, y3 = 5;
collinear(x1, y1, x2, y2, x3, y3);
return 0;
}
Java
// Java program to check if
// three points are collinear
// or not using area of triangle.
class GFG
{
// function to check if
// point collinear or not
static void collinear(int x1, int y1, int x2,
int y2, int x3, int y3)
{
/* Calculation the area of
triangle. We have skipped
multiplication with 0.5
to avoid floating point
computations */
int a = x1 * (y2 - y3) +
x2 * (y3 - y1) +
x3 * (y1 - y2);
if (a == 0)
System.out.println("Yes");
else
System.out.println("No");
}
// Driver Code
public static void main(String args[])
{
int x1 = 1, x2 = 1, x3 = 1,
y1 = 1, y2 = 4, y3 = 5;
collinear(x1, y1, x2, y2, x3, y3);
}
}
// This code is contributed by Sam007.
Python
# Python program to check # if three points are collinear # or not using area of triangle. # function to check if # point collinear or not def collinear(x1, y1, x2, y2, x3, y3): """ Calculation the area of triangle. We have skipped multiplication with 0.5 to avoid floating point computations """ a = x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2) if (a == 0): print "Yes" else: print "No" # Driver Code x1, x2, x3, y1, y2, y3 = 1, 1, 1, 1, 4, 5 collinear(x1, y1, x2, y2, x3, y3) # This code is contributed # by Sachin Bisht
C#
// C# program to check if
// three points are collinear
// or not using area of triangle.
using System;
class GFG
{
/* function to check if
point collinear or not */
static void collinear(int x1, int y1, int x2,
int y2, int x3, int y3)
{
/* Calculation the area of
triangle. We have skipped
multiplication with 0.5 to
avoid floating point computations */
int a = x1 * (y2 - y3) +
x2 * (y3 - y1) +
x3 * (y1 - y2);
if (a == 0)
Console.Write("Yes");
else
Console.Write("No");
}
// Driver code
public static void Main ()
{
int x1 = 1, x2 = 1, x3 = 1,
y1 = 1, y2 = 4, y3 = 5;
collinear(x1, y1, x2, y2, x3, y3);
}
}
// This code is contributed by Sam007.
PHP
<?php
// PHP or not using area of triangle.
/* function to check if
point collinear or not */
function collinear($x1, $y1, $x2,
$y2, $x3, $y3)
{
/* Calculation the area of
triangle. We have skipped
multiplication with 0.5 to
avoid floating point computations */
$a = $x1 * ($y2 - $y3) +
$x2 * ($y3 - $y1) +
$x3 * ($y1 - $y2);
if ($a == 0)
printf("Yes");
else
printf("No");
}
// Driver Code
$x1 = 1; $x2 = 1; $x3 = 1;
$y1 = 1; $y2 = 4; $y3 = 5;
collinear($x1, $y1, $x2, $y2, $x3, $y3);
// This code is contributed by Sam007.
?>
Javascript
<script>
// Javascript program to check if three
// points are collinear or not
// using area of triangle.
function collinear(x1, y1, x2, y2, x3, y3)
{
// Calculation the area of
// triangle. We have skipped
// multiplication with 0.5
// to avoid floating point
// computations
var a = x1 * (y2 - y3) +
x2 * (y3 - y1) +
x3 * (y1 - y2);
if (a == 0)
document.write("Yes");
else
document.write( "No");
}
var x1 = 1, x2 = 1, x3 = 1,y1 = 1, y2 = 4, y3 = 5;
collinear(x1, y1, x2, y2, x3, y3);
// This code is contributed by akshitsaxenaa09.
</script>
Producción :
Yes
Complejidad de tiempo: O(1)
Espacio Auxiliar: O(1)
Segunda aproximación
For three points, slope of any pair of points must be same as other pair. For example, slope of line joining (x2, y2) and (x3, y3), and line joining (x1, y1) and (x2, y2) must be same. (y3 - y2)/(x3 - x2) = (y2 - y1)/(x2 - x1) In other words, (y3 - y2)(x2 - x1) = (y2 - y1)(x3 - x2)
C++
// A C++ program
// Slope based solution to check
// if three points are collinear.
#include <bits/stdc++.h>
using namespace std;
/* function to check if
point collinear or not*/
void collinear(int x1, int y1, int x2, int y2, int x3,
int y3)
{
if ((y3 - y2) * (x2 - x1) == (y2 - y1) * (x3 - x2))
cout << "Yes" << endl;
else
cout << "No" << endl;
}
// Driver Code
int main()
{
int x1 = 1, x2 = 1, x3 = 0, y1 = 1, y2 = 6, y3 = 9;
collinear(x1, y1, x2, y2, x3, y3);
return 0;
}
// The code is contributed by Gautam goel (gautamgoel962)
C
// Slope based solution to check
// if three points are collinear.
#include <stdio.h>
#include <math.h>
/* function to check if
point collinear or not*/
void collinear(int x1, int y1, int x2,
int y2, int x3, int y3)
{
if ((y3 - y2) * (x2 - x1) ==
(y2 - y1) * (x3 - x2))
printf("Yes");
else
printf("No");
}
// Driver Code
int main()
{
int x1 = 1, x2 = 1, x3 = 0,
y1 = 1, y2 = 6, y3 = 9;
collinear(x1, y1, x2, y2, x3, y3);
return 0;
}
Java
// Slope based solution to check
// if three points are collinear.
import java.io.*;
class GFG {
/* function to check if
point collinear or not*/
static void cool_line(int x1, int y1, int x2,
int y2, int x3, int y3)
{
if ((y3 - y2) * (x2 - x1) ==
(y2 - y1) * (x3 - x2))
System.out.println("Yes");
else
System.out.println("No");
}
// Driver Code
public static void main (String[] args) {
int a1 = 1, a2 = 1, a3 = 0,
b1 = 1, b2 = 6, b3 = 9;
cool_line(a1, b1, a2, b2, a3, b3);
}
}
//This Code is Contributed by ajit
Python
# Slope based solution to check if three
# points are collinear.
# function to check if
# point collinear or not
def collinear(x1, y1, x2, y2, x3, y3):
if ((y3 - y2)*(x2 - x1) == (y2 - y1)*(x3 - x2)):
print ("Yes")
else:
print ("No")
# Driver Code
x1, x2, x3, y1, y2, y3 = 1, 1, 0, 1, 6, 9
collinear(x1, y1, x2, y2, x3, y3);
# This code is contributed
# by Sachin Bisht
C#
// Slope based solution to check
// if three points are collinear.
using System;
class GFG
{
/* function to check if
point collinear or not*/
static void cool_line(int x1, int y1, int x2,
int y2, int x3, int y3)
{
if ((y3 - y2) * (x2 - x1) ==
(y2 - y1) * (x3 - x2))
Console.WriteLine("Yes");
else
Console.WriteLine("No");
}
// Driver Code
static public void Main ()
{
int a1 = 1, a2 = 1, a3 = 0,
b1 = 1, b2 = 6, b3 = 9;
cool_line(a1, b1, a2, b2, a3, b3);
}
}
// This code is contributed by ajit
PHP
<?php
// Slope based solution to check
// if three points are collinear.
/* function to check if
point collinear or not*/
function collinear($x1, $y1, $x2,
$y2, $x3, $y3)
{
if (($y3 - $y2) * ($x2 - $x1) ==
($y2 - $y1) * ($x3 - $x2))
echo ("Yes");
else
echo ("No");
}
// Driver Code
$x1 = 1;
$x2 = 1;
$x3 = 0;
$y1 = 1;
$y2 = 6;
$y3 = 9;
collinear($x1, $y1, $x2,
$y2, $x3, $y3);
// This code is contributed by ajit
?>
Javascript
<script>
// Slope based solution to check
// if three points are collinear.
/*
* function to check if point collinear or not
*/
function cool_line(x1 , y1 , x2 , y2 , x3 , y3)
{
if ((y3 - y2) * (x2 - x1) == (y2 - y1) * (x3 - x2))
document.write("Yes");
else
document.write("No");
}
// Driver Code
var a1 = 1, a2 = 1, a3 = 0, b1 = 1, b2 = 6, b3 = 9;
cool_line(a1, b1, a2, b2, a3, b3);
// This code is contributed by aashish1995
</script>
Producción :
No
Complejidad de tiempo: O(1)
Espacio Auxiliar: O(1)
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Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA