Compruebe si el punto dado se encuentra dentro del alcance de cualquiera de las torres dadas

Dada una array 2D arr[][] que consta de N filas de la forma {X _i , Y _i , R _i } tal que (X _i , Y _i ) representa la posición de una torre y R _i representa el rango de red de esa torre. Dados dos enteros X e Y , la tarea es verificar si el punto (X, Y) se encuentra en el rango de la red de las torres o no.

Ejemplos:

Entrada: arr[][] = { {1, 1, 3}, {10, 10, 5}, {15, 15, 15} }, X = 5, Y = 5 
Salida: Verdadero 
Explicación: 
Distancia del punto ( 5, 5) de (arr[0][0], arr[0][1]) = 5,65685 y el rango de la primera torre es 3. Por lo tanto, el punto (X, Y) no se encuentra en el rango de la red de la primera torre. 
Distancia del punto (5, 5) desde (arr[1][0], arr[1][1]) = 7.07107 y el rango de la segunda torre es 5. Por lo tanto, el punto (X, Y) no se encuentra en el rango de red de la segunda torre. 
Distancia del punto (5, 5) desde (arr[2][0], arr[2][1]) = 14,1421 y el rango de la tercera torre es 15. Por lo tanto, el punto (X, Y) se encuentra en la red -alcance de la tercera torre. 
Dado que el punto (X, Y) se encuentra en el rango de la tercera torre. Por lo tanto, la salida requerida es True. 

Entrada: arr[][] = { {1, 1, 3}, {10, 10, 3}, {15, 15, 3} }, X = 5, Y = 5 
Salida: Falso

Enfoque: siga los pasos que se indican a continuación para resolver el problema:

• Recorra la array y para cada fila (torre) recorrida, compruebe si el valor de sqrt((arr[i][0] – x) ² + (arr[i][1] – Y) ² ) es mayor que arr[ i][2] o no. Si se encuentra que es verdadero, imprima Verdadero .
• De lo contrario, imprime Falso .

// C++ program to implement
// the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to check if the point (X, Y)
// exists in the towers network-range or not
bool checkPointRange(int arr[][3], int X,
                     int Y, int N)
{
 
    // Traverse the array arr[]
    for (int i = 0; i < N; i++) {
 
        // Stores distance of the
        // point (X, Y) from i-th tower
        double dist
            = sqrt((arr[i][0] - X) * (arr[i][0] - X)
                   + (arr[i][1] - Y) * (arr[i][1] - Y));
 
        // If dist lies within the
        // range of the i-th tower
        if (dist <= arr[i][2]) {
            return true;
        }
    }
 
    // If the point (X, Y) does not lie
    // in the range of any of the towers
    return false;
}
 
// Driver Code
int main()
{
 
    int arr[][3] = { { 1, 1, 3 },
                     { 10, 10, 3 },
                     { 15, 15, 15 } };
    int X = 5, Y = 5;
 
    int N = sizeof(arr) / sizeof(arr[0]);
 
    // If point (X, Y) lies in the
    // range of any of the towers
    if (checkPointRange(arr, X, Y, N)) {
        cout << "True";
    }
    // Otherwise
    else {
        cout << "False";
    }
}

// Java program to implement
// the above approach
import java.util.*;
 
class GFG{
  
// Function to check if the point (X, Y)
// exists in the towers network-range or not
static boolean checkPointRange(int arr[][], int X,
                               int Y, int N)
{
     
    // Traverse the array arr[]
    for(int i = 0; i < N; i++)
    {
         
        // Stores distance of the
        // point (X, Y) from i-th tower
        double dist = Math.sqrt((arr[i][0] - X) *
                                (arr[i][0] - X) +
                                (arr[i][1] - Y) *
                                (arr[i][1] - Y));
  
        // If dist lies within the
        // range of the i-th tower
        if (dist <= arr[i][2])
        {
            return true;
        }
    }
  
    // If the point (X, Y) does not lie
    // in the range of any of the towers
    return false;
}
  
// Driver Code
public static void main(String[] args)
{
    int arr[][] = { { 1, 1, 3 },
                    { 10, 10, 3 },
                    { 15, 15, 15 } };
    int X = 5, Y = 5;
  
    int N = arr.length;
  
    // If point (X, Y) lies in the
    // range of any of the towers
    if (checkPointRange(arr, X, Y, N))
    {
        System.out.print("True");
    }
     
    // Otherwise
    else
    {
        System.out.print("False");
    }
}
}
 
// This code is contributed by code_hunt

# Python3 program to implement
# the above approach
from math import sqrt
 
# Function to check if the point (X, Y)
# exists in the towers network-range or not
def checkPointRange(arr, X, Y, N):
     
    # Traverse the array arr[]
    for i in range(N):
         
        # Stores distance of the
        # point (X, Y) from i-th tower
        dist = sqrt((arr[i][0] - X) *
                    (arr[i][0] - X) +
                    (arr[i][1] - Y) *
                    (arr[i][1] - Y))
 
        # If dist lies within the
        # range of the i-th tower
        if (dist <= arr[i][2]):
            return True
 
    # If the point (X, Y) does not lie
    # in the range of any of the towers
    return False
 
# Driver Code
if __name__ == '__main__':
     
    arr = [ [ 1, 1, 3 ],
            [ 10, 10, 3 ],
            [ 15, 15, 15 ] ]
    X = 5
    Y = 5
 
    N =  len(arr)
 
    # If point (X, Y) lies in the
    # range of any of the towers
    if (checkPointRange(arr, X, Y, N)):
        print("True")
         
    # Otherwise
    else:
        print("False")
 
# This code is contributed by bgangwar59

// C# program to implement
// the above approach 
using System;
   
class GFG{
   
// Function to check if the point (X, Y)
// exists in the towers network-range or not
static bool checkPointRange(int[,] arr, int X,
                            int Y, int N)
{
     
    // Traverse the array arr[]
    for(int i = 0; i < N; i++)
    {
         
        // Stores distance of the
        // point (X, Y) from i-th tower
        double dist = Math.Sqrt((arr[i, 0] - X) *
                                (arr[i, 0] - X) +
                                (arr[i, 1] - Y) *
                                (arr[i, 1] - Y));
   
        // If dist lies within the
        // range of the i-th tower
        if (dist <= arr[i, 2])
        {
            return true;
        }
    }
   
    // If the point (X, Y) does not lie
    // in the range of any of the towers
    return false;
}
   
// Driver Code
public static void Main()
{
    int[,] arr = { { 1, 1, 3 },
                   { 10, 10, 3 },
                   { 15, 15, 15 } };
                     
    int X = 5, Y = 5;
   
    int N = arr.Length;
   
    // If point (X, Y) lies in the
    // range of any of the towers
    if (checkPointRange(arr, X, Y, N))
    {
        Console.Write("True");
    }
      
    // Otherwise
    else
    {
        Console.Write("False");
    }
}
}
   
// This code is contributed by susmitakundugoaldanga

<script>
 
// JavaScript program to implement
// the above approach
 
// Function to check if the point (X, Y)
// exists in the towers network-range or not
function checkPointRange(arr, X, Y, N)
{
      
    // Traverse the array arr[]
    for(let i = 0; i < N; i++)
    {
          
        // Stores distance of the
        // point (X, Y) from i-th tower
        let dist = Math.sqrt((arr[i][0] - X) *
                                (arr[i][0] - X) +
                                (arr[i][1] - Y) *
                                (arr[i][1] - Y));
   
        // If dist lies within the
        // range of the i-th tower
        if (dist <= arr[i][2])
        {
            return true;
        }
    }
   
    // If the point (X, Y) does not lie
    // in the range of any of the towers
    return false;
}
 
// Driver Code
 
    let arr = [[ 1, 1, 3 ],
               [ 10, 10, 3 ],
              [ 15, 15, 15 ]];
    let X = 5, Y = 5;
   
    let N = arr.length;
   
    // If point (X, Y) lies in the
    // range of any of the towers
    if (checkPointRange(arr, X, Y, N))
    {
        document.write("True");
    }
      
    // Otherwise
    else
    {
        document.write("False");
    }
           
</script>

True

Complejidad temporal: O(N)
Espacio auxiliar: O(1)