Dada una curva [y = x(A – x)] , la tarea es encontrar la normal en un punto dado (x, y) en esa curva, donde A es un número entero y x, y también cualquier número entero.
Ejemplos:
Input: A = 2, x = 2, y = 0
Output: 2y = x - 2
Since y = x(2 - x)
y = 2x - x^2 differentiate it with respect to x
dy/dx = 2 - 2x put x = 2, y = 0 in this equation
dy/dx = 2 - 2* 2 = -2
equation => (Y - 0 ) = ((-1/-2))*( Y - 2)
=> 2y = x -2
Input: A = 3, x = 4, y = 5
Output: Not possible
Point is not on that curve
Enfoque: Primero necesitamos encontrar que el punto dado está en esa curva o no si el punto está en esa curva entonces:
- Necesitamos diferenciar esa ecuación en ese punto. No pienses demasiado en la diferenciación de esta ecuación si analizas y encuentras que dy/dx siempre se convierte en A – 2x.
- Ponga x, y en dy/dx.
- La ecuación de la normalidad es Y – y = -(1/( dy/dx )) * (X – x).
A continuación se muestra la implementación del enfoque anterior:
C++
// C++ program for find curve
// at given point
#include <bits/stdc++.h>
using namespace std;
// function for find normal
void findNormal(int A, int x, int y)
{
// differentiate given equation
int dif = A - x * 2;
// check that point on the curve or not
if (y == (2 * x - x * x)) {
// if differentiate is negative
if (dif < 0)
cout << 0 - dif << "y = "
<< "x" << (0 - x) + (y * dif);
else if (dif > 0)
// differentiate is positive
cout << dif << "y = "
<< "-x+" << x + dif * y;
// differentiate is zero
else
cout << "x = " << x;
}
// other wise normal not found
else
cout << "Not possible";
}
// Driver code
int main()
{
// declare variable
int A = 2, x = 2, y = 0;
// call function findNormal
findNormal(A, x, y);
return 0;
}
Java
// Java program for find curve
// at given point
import java.io.*;
class GFG {
// function for find normal
static void findNormal(int A, int x, int y)
{
// differentiate given equation
int dif = A - x * 2;
// check that point on the curve or not
if (y == (2 * x - x * x)) {
// if differentiate is negative
if (dif < 0)
System.out.print( (0 - dif) + "y = "
+ "x" +((0 - x) + (y * dif)));
else if (dif > 0)
// differentiate is positive
System.out.print( dif + "y = "
+ "-x+" + (x + dif * y));
// differentiate is zero
else
System.out.print( "x = " +x);
}
// other wise normal not found
else
System.out.println( "Not possible");
}
// Driver code
public static void main (String[] args) {
// declare variable
int A = 2, x = 2, y = 0;
// call function findNormal
findNormal(A, x, y);;
}
}
// This Code is contributed by inder_verma..
Python3
# Python 3 program for find curve
# at given point
# function for find normal
def findNormal(A, x, y):
# differentiate given equation
dif = A - x * 2
# check that point on the curve or not
if (y == (2 * x - x * x)):
# if differentiate is negative
if (dif < 0):
print(0 - dif, "y =", "x",
(0 - x) + (y * dif))
elif (dif > 0):
# differentiate is positive
print(dif, "y =", "- x +",
x + dif * y)
# differentiate is zero
else:
print("x =", x)
# other wise normal not found
else:
print("Not possible")
# Driver code
if __name__ == '__main__':
# declare variable
A = 2
x = 2
y = 0
# call function findNormal
findNormal(A, x, y)
# This code is contributed By
# Surendra_Gangwar
C#
// C# program for find curve
// at given point
using System;
class GFG
{
// function for find normal
static void findNormal(int A,
int x, int y)
{
// differentiate given equation
int dif = A - x * 2;
// check that point on
// the curve or not
if (y == (2 * x - x * x))
{
// if differentiate is negative
if (dif < 0)
Console.Write((0 - dif) + "y = " +
"x" + ((0 - x) + (y * dif)));
else if (dif > 0)
// differentiate is positive
Console.Write(dif + "y = " +
"-x + " + (x + dif * y));
// differentiate is zero
else
Console.Write("x = " + x);
}
// other wise normal not found
else
Console.WriteLine("Not possible");
}
// Driver code
static public void Main ()
{
// declare variable
int A = 2, x = 2, y = 0;
// call function findNormal
findNormal(A, x, y);
}
}
// This code is contributed by ajit
PHP
<?php
// PHP program for find curve
// at given point
// function for find normal
function findNormal($A, $x, $y)
{
// differentiate given equation
$dif = $A - $x * 2;
// check that point on the
// curve or not
if ($y == (2 * $x - $x * $x))
{
// if differentiate is negative
if ($dif < 0)
echo (0 - $dif), "y = ",
"x" , (0 - $x) + ($y * $dif);
else if ($dif > 0)
// differentiate is positive
echo $dif , "y = ",
"-x+" ,( $x + $dif * $y);
// differentiate is zero
else
echo "x = " , $x;
}
// other wise normal not found
else
echo "Not possible";
}
// Driver code
// declare variable
$A = 2;
$x = 2;
$y = 0;
// call function findNormal
findNormal($A, $x, $y);
// This code is contributed by ajit
?>
Javascript
<script>
// Javascript program for find curve at given point
// function for find normal
function findNormal(A, x, y)
{
// differentiate given equation
let dif = A - x * 2;
// check that point on
// the curve or not
if (y == (2 * x - x * x))
{
// if differentiate is negative
if (dif < 0)
document.write((0 - dif) + "y = " +
"x" + ((0 - x) + (y * dif)));
else if (dif > 0)
// differentiate is positive
document.write(dif + "y = " +
"-x + " + (x + dif * y));
// differentiate is zero
else
document.write("x = " + x);
}
// other wise normal not found
else
document.write("Not possible");
}
// declare variable
let A = 2, x = 2, y = 0;
// call function findNormal
findNormal(A, x, y);
</script>
Producción:
2y = x-2
Complejidad de tiempo: O (1), ya que no estamos usando ningún bucle.
Espacio auxiliar: O (1), ya que no estamos usando ningún espacio adicional.