Dadas tres coordenadas de un triángulo (x1, y1) , (x2, y2) , (x3, y3) . La tarea es averiguar si el triángulo se puede transformar en un triángulo rectángulo moviendo solo un punto exactamente la distancia 1.
Si es posible hacer que el triángulo sea rectángulo , imprima «POSIBLE» , de lo contrario imprima » NO ES POSIBLE” .
Si el triángulo ya es rectángulo , también se debe informar.
Ejemplos:
Entrada:
x1 = -1, y1 = 0
x2 = 2, y2 = 0
x3 = 0, y3 = 1
Salida: POSIBLE La
primera coordenada (-1, 0) puede cambiarse a (0, 0) y corregirse -angulado .
Entrada:
x1 = 36, y1 = 1
x2 = -17, y2 = -54
x3 = -19, y3 = 55
Salida: POSIBLE
Enfoque:
Como se sabe que para un triángulo de lados a , b y c , el triángulo será rectángulo si se cumple la siguiente ecuación: a 2 + b 2 = c 2
Entonces, para todas las coordenadas del triángulo, averigua todos los lados y para las 3 posibles permutaciones de ellos verifica si ya es un triangulo rectangulo y reportalo.
Si la condición anterior no se cumple, entonces se deben realizar las siguientes operaciones
: debemos cambiar todas las coordenadas por 1 una por una y verificar que sea una combinación válida para un triángulo rectángulo.
Mira que puede haber 4 combinaciones posibles para cambiar cada coordenada por 1. Son (-1, 0), (0, 1), (1, 0), (0, -1) . Así que ejecute un ciclo y aplique esos cambios uno por uno para cada coordenada y verifique que la fórmula a 2 + b 2 = c 2 sea verdadera o no.
Si es cierto, entonces es posible transformar el triángulo en un triángulo rectángulo , de lo contrario no.
A continuación se muestra la implementación del código anterior:
C++
// C++ implementation of
// the above approach
#include <bits/stdc++.h>
using namespace std;
// Storing all the possible
// changes to make the triangle
// right-angled
int dx[] = { -1, 0, 1, 0 };
int dy[] = { 0, 1, 0, -1 };
// Function to check if the triangle
// is right-angled or not
int ifRight(int x1, int y1,
int x2, int y2,
int x3, int y3)
{
int a = ((x1 - x2) * (x1 - x2))
+ ((y1 - y2) * (y1 - y2));
int b = ((x1 - x3) * (x1 - x3))
+ ((y1 - y3) * (y1 - y3));
int c = ((x2 - x3) * (x2 - x3))
+ ((y2 - y3) * (y2 - y3));
if ((a == (b + c) && a != 0 && b != 0 && c != 0)
|| (b == (a + c) && a != 0 && b != 0 && c != 0)
|| (c == (a + b) && a != 0 && b != 0 && c != 0)) {
return 1;
}
return 0;
}
// Function to check if the triangle
// can be transformed to right-angled
void isValidCombination(int x1, int y1,
int x2, int y2,
int x3, int y3)
{
int x, y;
// Boolean variable to
// return true or false
bool possible = 0;
// If it is already right-angled
if (ifRight(x1, y1,
x2, y2,
x3, y3)) {
cout << "ALREADY RIGHT ANGLED";
return;
}
else {
// Applying the changes on the
// co-ordinates
for (int i = 0; i < 4; i++) {
// Applying on the first
// co-ordinate
x = dx[i] + x1;
y = dy[i] + y1;
if (ifRight(x, y,
x2, y2,
x3, y3)) {
cout << "POSSIBLE";
return;
}
// Applying on the second
// co-ordinate
x = dx[i] + x2;
y = dy[i] + y2;
if (ifRight(x1, y1,
x, y,
x3, y3)) {
cout << "POSSIBLE";
return;
}
// Applying on the third
// co-ordinate
x = dx[i] + x3;
y = dy[i] + y3;
if (ifRight(x1, y1,
x2, y2,
x, y)) {
cout << "POSSIBLE";
return;
}
}
}
// If can't be transformed
if (!possible)
cout << "NOT POSSIBLE" << endl;
}
// Driver Code
int main()
{
int x1 = -49, y1 = 0;
int x2 = 0, y2 = 50;
int x3 = 0, y3 = -50;
isValidCombination(x1, y1,
x2, y2,
x3, y3);
return 0;
}
Java
// Java implementation of the approach
import java.util.*;
class GFG
{
// Storing all the possible
// changes to make the triangle
// right-angled
static int dx[] = { -1, 0, 1, 0 };
static int dy[] = { 0, 1, 0, -1 };
// Function to check if the triangle
// is right-angled or not
static boolean ifRight(int x1, int y1,
int x2, int y2,
int x3, int y3)
{
int a = ((x1 - x2) * (x1 - x2)) +
((y1 - y2) * (y1 - y2));
int b = ((x1 - x3) * (x1 - x3)) +
((y1 - y3) * (y1 - y3));
int c = ((x2 - x3) * (x2 - x3)) +
((y2 - y3) * (y2 - y3));
if ((a == (b + c) && a != 0 && b != 0 && c != 0) ||
(b == (a + c) && a != 0 && b != 0 && c != 0) ||
(c == (a + b) && a != 0 && b != 0 && c != 0))
{
return true;
}
return false;
}
// Function to check if the triangle
// can be transformed to right-angled
static void isValidCombination(int x1, int y1,
int x2, int y2,
int x3, int y3)
{
int x, y;
// Boolean variable to
// return true or false
boolean possible = false;
// If it is already right-angled
if (ifRight(x1, y1, x2, y2, x3, y3))
{
System.out.print("ALREADY RIGHT ANGLED");
return;
}
else
{
// Applying the changes on the
// co-ordinates
for (int i = 0; i < 4; i++)
{
// Applying on the first
// co-ordinate
x = dx[i] + x1;
y = dy[i] + y1;
if (ifRight(x, y, x2, y2, x3, y3))
{
System.out.print("POSSIBLE");
return;
}
// Applying on the second
// co-ordinate
x = dx[i] + x2;
y = dy[i] + y2;
if (ifRight(x1, y1, x, y, x3, y3))
{
System.out.print("POSSIBLE");
return;
}
// Applying on the third
// co-ordinate
x = dx[i] + x3;
y = dy[i] + y3;
if (ifRight(x1, y1, x2, y2, x, y))
{
System.out.print("POSSIBLE");
return;
}
}
}
// If can't be transformed
if (!possible)
System.out.println("NOT POSSIBLE");
}
// Driver Code
public static void main(String[] args)
{
int x1 = -49, y1 = 0;
int x2 = 0, y2 = 50;
int x3 = 0, y3 = -50;
isValidCombination(x1, y1, x2, y2, x3, y3);
}
}
// This code is contributed by Rajput-Ji
Python3
# Python3 implementation of the above approach
# Storing all the possible
# changes to make the triangle
# right-angled
dx = [-1, 0, 1, 0]
dy = [0, 1, 0, -1]
# Function to check if the triangle
# is right-angled or not
def ifRight(x1, y1, x2, y2, x3, y3):
a = ((x1 - x2) * (x1 - x2)) + \
((y1 - y2) * (y1 - y2))
b = ((x1 - x3) * (x1 - x3)) + \
((y1 - y3) * (y1 - y3))
c = ((x2 - x3) * (x2 - x3)) + \
((y2 - y3) * (y2 - y3))
if ((a == (b + c) and a != 0 and b != 0 and c != 0) or
(b == (a + c) and a != 0 and b != 0 and c != 0) or
(c == (a + b) and a != 0 and b != 0 and c != 0)):
return 1
# Function to check if the triangle
# can be transformed to right-angled
def isValidCombination(x1, y1, x2, y2, x3, y3):
x, y = 0, 0
# Boolean variable to
# return true or false
possible = 0
# If it is already right-angled
if (ifRight(x1, y1, x2, y2, x3, y3)):
print("ALREADY RIGHT ANGLED")
return
else:
# Applying the changes on the
# co-ordinates
for i in range(4):
# Applying on the first
# co-ordinate
x = dx[i] + x1
y = dy[i] + y1
if (ifRight(x, y, x2, y2, x3, y3)):
print("POSSIBLE")
return
# Applying on the second
# co-ordinate
x = dx[i] + x2
y = dy[i] + y2
if (ifRight(x1, y1, x, y, x3, y3)):
print("POSSIBLE")
return
# Applying on the third
# co-ordinate
x = dx[i] + x3
y = dy[i] + y3
if (ifRight(x1, y1, x2, y2, x, y)):
print("POSSIBLE")
return
# If can't be transformed
if (possible == 0):
print("NOT POSSIBLE")
# Driver Code
x1 = -49
y1 = 0
x2 = 0
y2 = 50
x3 = 0
y3 = -50
isValidCombination(x1, y1, x2, y2, x3, y3)
# This code is contributed by Mohit Kumar
C#
// C# implementation of the approach
using System;
class GFG
{
// Storing all the possible
// changes to make the triangle
// right-angled
static int []dx = { -1, 0, 1, 0 };
static int []dy = { 0, 1, 0, -1 };
// Function to check if the triangle
// is right-angled or not
static bool ifRight(int x1, int y1,
int x2, int y2,
int x3, int y3)
{
int a = ((x1 - x2) * (x1 - x2)) +
((y1 - y2) * (y1 - y2));
int b = ((x1 - x3) * (x1 - x3)) +
((y1 - y3) * (y1 - y3));
int c = ((x2 - x3) * (x2 - x3)) +
((y2 - y3) * (y2 - y3));
if ((a == (b + c) && a != 0 && b != 0 && c != 0) ||
(b == (a + c) && a != 0 && b != 0 && c != 0) ||
(c == (a + b) && a != 0 && b != 0 && c != 0))
{
return true;
}
return false;
}
// Function to check if the triangle
// can be transformed to right-angled
static void isValidCombination(int x1, int y1,
int x2, int y2,
int x3, int y3)
{
int x, y;
// Boolean variable to
// return true or false
bool possible = false;
// If it is already right-angled
if (ifRight(x1, y1, x2, y2, x3, y3))
{
Console.WriteLine("ALREADY RIGHT ANGLED");
return;
}
else
{
// Applying the changes on the
// co-ordinates
for (int i = 0; i < 4; i++)
{
// Applying on the first
// co-ordinate
x = dx[i] + x1;
y = dy[i] + y1;
if (ifRight(x, y, x2, y2, x3, y3))
{
Console.WriteLine("POSSIBLE");
return;
}
// Applying on the second
// co-ordinate
x = dx[i] + x2;
y = dy[i] + y2;
if (ifRight(x1, y1, x, y, x3, y3))
{
Console.WriteLine("POSSIBLE");
return;
}
// Applying on the third
// co-ordinate
x = dx[i] + x3;
y = dy[i] + y3;
if (ifRight(x1, y1, x2, y2, x, y))
{
Console.Write("POSSIBLE");
return;
}
}
}
// If can't be transformed
if (!possible)
Console.WriteLine("NOT POSSIBLE");
}
// Driver Code
static public void Main ()
{
int x1 = -49, y1 = 0;
int x2 = 0, y2 = 50;
int x3 = 0, y3 = -50;
isValidCombination(x1, y1, x2, y2, x3, y3);
}
}
// This code is contributed by AnkitRai01
Javascript
<script>
// Javascript implementation of
// the above approach
// Storing all the possible
// changes to make the triangle
// right-angled
let dx = [ -1, 0, 1, 0 ];
let dy = [ 0, 1, 0, -1 ];
// Function to check if the triangle
// is right-angled or not
function ifRight(x1, y1, x2, y2,
x3, y3)
{
let a = ((x1 - x2) * (x1 - x2))
+ ((y1 - y2) * (y1 - y2));
let b = ((x1 - x3) * (x1 - x3))
+ ((y1 - y3) * (y1 - y3));
let c = ((x2 - x3) * (x2 - x3))
+ ((y2 - y3) * (y2 - y3));
if ((a == (b + c) && a != 0 && b != 0 && c != 0)
|| (b == (a + c) && a != 0 && b != 0 && c != 0)
|| (c == (a + b) && a != 0 && b != 0 && c != 0)) {
return 1;
}
return 0;
}
// Function to check if the triangle
// can be transformed to right-angled
function isValidCombination(x1, y1,
x2, y2,
x3, y3)
{
let x, y;
// Boolean variable to
// return true or false
let possible = 0;
// If it is already right-angled
if (ifRight(x1, y1,
x2, y2,
x3, y3)) {
document.write("ALREADY RIGHT ANGLED");
return;
}
else {
// Applying the changes on the
// co-ordinates
for (let i = 0; i < 4; i++) {
// Applying on the first
// co-ordinate
x = dx[i] + x1;
y = dy[i] + y1;
if (ifRight(x, y,
x2, y2,
x3, y3)) {
document.write("POSSIBLE");
return;
}
// Applying on the second
// co-ordinate
x = dx[i] + x2;
y = dy[i] + y2;
if (ifRight(x1, y1,
x, y,
x3, y3)) {
document.write("POSSIBLE");
return;
}
// Applying on the third
// co-ordinate
x = dx[i] + x3;
y = dy[i] + y3;
if (ifRight(x1, y1,
x2, y2,
x, y)) {
document.write("POSSIBLE");
return;
}
}
}
// If can't be transformed
if (!possible)
document.write("NOT POSSIBLE<br>");
}
// Driver Code
let x1 = -49, y1 = 0;
let x2 = 0, y2 = 50;
let x3 = 0, y3 = -50;
isValidCombination(x1, y1,
x2, y2,
x3, y3);
</script>
Producción:
POSSIBLE
Complejidad de tiempo: O(1)
Espacio Auxiliar: O(1)
Publicación traducida automáticamente
Artículo escrito por dangenmaster2 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA