Encuentra dos vértices de un triángulo isósceles en el que hay un rectángulo con esquinas opuestas (0, 0) y (X, Y)

Dados dos enteros X e Y . La tarea es encontrar dos vértices de un triángulo isósceles ABC (ángulo recto en B) que tiene un vértice en el punto B (0, 0). Y hay un rectángulo con lados opuestos (0, 0) y (X, Y). Todos los puntos de este rectángulo están ubicados dentro o en el borde del triángulo. Imprime 4 enteros x1, y1, x2, y2, donde A(x1, y1) y B(x2, y2).
Ejemplos: 
 

Entrada: X = 3, Y = 3 
Salida: 6 0 0 6 
 

Entrada: X = -3, y = -2 
Salida: -5 0 0 -5 
 

 

Enfoque: 
Sea Val = |x| + |y|. Entonces el primer punto es (Val * sign(x), 0) y el segundo punto es (0, Val * sign(y)). 
Veamos cómo funciona para x > 0 y y > 0. Otros casos se pueden demostrar de manera similar. 
Necesitamos mostrar que (x, y) pertenece a nuestro triángulo (incluidos sus bordes). De hecho (x, y) pertenece al segmento, conectando (x + y, 0) con (0, x + y). La recta que pasa por (x + y, 0) y (0, x + y) es Y = – X + x + y. El uso de coordenadas (x, y) en esta ecuación prueba nuestra respuesta.
A continuación se muestra la implementación del enfoque anterior: 
 

// C++ program to find two vertices of an
// isosceles triangle in which there is
// rectangle with opposite side (0, 0) and (x, y)
#include <bits/stdc++.h>
using namespace std;
 
// Function to find two vertices of an
// isosceles triangle in which there is
// rectangle with opposite side (0, 0) and (x, y)
int Vertices(int x, int y)
{
    // Required value;
    int val = abs(x) + abs(y);
 
    // print x1 and y1
    cout << val * (x < 0 ? -1 : 1) << " 0 ";
 
    // print x2 and y3
    cout << "0 " << val * (y < 0 ? -1 : 1);
}
 
// Driver code
int main()
{
    int x = 3, y = 3;
 
    // Function call
    Vertices(x, y);
 
    return 0;
}

// Java program to find two vertices of an
// isosceles triangle in which there is
// rectangle with opposite side (0, 0) and (x, y)
class GFG
{
 
// Function to find two vertices of an
// isosceles triangle in which there is
// rectangle with opposite side (0, 0) and (x, y)
static void Vertices(int x, int y)
{
    // Required value;
    int val = Math.abs(x) + Math.abs(y);
 
    // print x1 and y1
    System.out.print(val * (x < 0 ? -1 : 1) + " 0 ");
 
    // print x2 and y3
    System.out.print("0 " + val * (y < 0 ? -1 : 1));
}
 
// Driver code
public static void main(String[] args)
{
    int x = 3, y = 3;
 
    // Function call
    Vertices(x, y);
}
}
 
// This code is contributed by Rajput-Ji

# Python3 program to find two vertices of an
# isosceles triangle in which there is
# rectangle with opposite side (0, 0) and (x, y)
 
# Function to find two vertices of an
# isosceles triangle in which there is
# rectangle with opposite side (0, 0) and (x, y)
def Vertices(x, y) :
 
    # Required value;
    val = abs(x) + abs(y);
 
    # print x1 and y1
    if x < 0 :
        x = -1
    else :
        x = 1
         
    print(val * x,"0",end = " ");
 
    # print x2 and y3
    if y < 0 :
        y = -1
    else :
        y = 1
     
    print("0",val * y);
 
 
# Driver code
if __name__ == "__main__" :
 
    x = 3; y = 3;
 
    # Function call
    Vertices(x, y);
 
# This code is contributed by AnkitRai01

// C# program to find two vertices of an
// isosceles triangle in which there is
// rectangle with opposite side (0, 0) and (x, y)
using System;
     
class GFG
{
 
// Function to find two vertices of an
// isosceles triangle in which there is
// rectangle with opposite side (0, 0) and (x, y)
static void Vertices(int x, int y)
{
    // Required value;
    int val = Math.Abs(x) + Math.Abs(y);
 
    // print x1 and y1
    Console.Write(val * (x < 0 ? -1 : 1) + " 0 ");
 
    // print x2 and y3
    Console.Write("0 " + val * (y < 0 ? -1 : 1));
}
 
// Driver code
public static void Main(String[] args)
{
    int x = 3, y = 3;
 
    // Function call
    Vertices(x, y);
}
}
 
// This code is contributed by Rajput-Ji

<script>
 
// JavaScript program to find two vertices of an
// isosceles triangle in which there is
// rectangle with opposite side (0, 0) and (x, y)
 
// Function to find two vertices of an
// isosceles triangle in which there is
// rectangle with opposite side (0, 0) and (x, y)
function Vertices(x, y)
{
    // Required value;
    let val = Math.abs(x) + Math.abs(y);
 
    // print x1 and y1
    document.write(val * (x < 0 ? -1 : 1) + " 0 ");
 
    // print x2 and y3
    document.write("0 " + val * (y < 0 ? -1 : 1));
}
 
// Driver code
 
    let x = 3, y = 3;
 
    // Function call
    Vertices(x, y);
 
 
// This code is contributed by Surbhi Tyagi.
 
</script>

6 0 0 6

Complejidad de tiempo : O(1)

Espacio Auxiliar: O(1)