Dado un número n, encuentre la suma de los cuadrados de los primeros n números naturales impares.
Ejemplos:
Input : 3 Output : 35 12 + 32 + 52 = 35 Input : 8 Output : 680 12 + 32 + 52 + 72 + 92 + 112 + 132 + 152
Una solución simple es atravesar n números impares y encontrar la suma de los cuadrados.
A continuación se muestra la implementación del enfoque.
C++
// Simple C++ method to find sum of square of // first n odd numbers. #include <iostream> using namespace std; int squareSum(int n) { int sum = 0; for (int i = 1; i <= n; i++) sum += (2*i - 1) * (2*i - 1); return sum; } int main() { cout << squareSum(8); return 0; }
Java
// Simple Java method to // find sum of square of // first n odd numbers. import java.io.*; class GFG { static int squareSum(int n) { int sum = 0; for (int i = 1; i <= n; i++) sum += (2*i - 1) * (2*i - 1); return sum; } //Driver Code public static void main(String args[]) { System.out.println(squareSum(8)); } } // This code is contributed by // Nikita tiwari.
Python3
# Simple Python method # to find sum of square # of first n odd numbers. def squareSum(n): sm = 0 for i in range(1, n + 1): sm += (2 * i - 1) * (2 * i - 1) return sm # Driver Code n=8 print(squareSum(n)) # This code is contributed by Ansu Kumari
C#
// Simple C# method to find // sum of square of first // n odd numbers. using System; class GFG { static int squareSum(int n) { int sum = 0; for (int i = 1; i <= n; i++) sum += (2*i - 1) * (2*i - 1); return sum; } // Driver Code public static void Main() { Console.Write(squareSum(8)); } } // This code is contributed by // vt_m.
PHP
<?php // Simple PHP method to find sum // of square of first n odd numbers. function squareSum( $n) { $sum = 0; for ($i = 1; $i <= $n; $i++) $sum += (2*$i - 1) * (2*$i - 1); return $sum; } echo squareSum(8); // This code is contributed by Vt_m. ?>
Javascript
<script> // Simple Javascript method to find // sum of square of first n odd numbers. function squareSum(n) { let sum = 0; for(let i = 1; i <= n; i++) sum += (2 * i - 1) * (2 * i - 1); return sum; } // Driver code document.write(squareSum(8)); // This code is contributed by souravmahato348 </script>
Producción :
680
Complejidad de tiempo: O(n), donde n representa el entero dado.
Espacio auxiliar: O(1), no se requiere espacio adicional, por lo que es una constante.
Una solución eficiente es aplicar la siguiente fórmula.
sum = n * (4n2 - 1) / 3 How does it work? Please refer sum of squares of even and odd numbers for proof.
C++
// Efficient C++ method to find sum of // square of first n odd numbers. #include <iostream> using namespace std; int squareSum(int n) { return n*(4*n*n - 1)/3; } int main() { cout << squareSum(8); return 0; }
Java
// Efficient Java method // to find sum of // square of first n odd numbers. import java.io.*; class GFG { static int squareSum(int n) { return n*(4*n*n - 1)/3; } public static void main(String args[]) { System.out.println(squareSum(8)); } } // This code is contributed by // Nikita tiwari.
Python3
# Python3 code to find sum # of square of first n odd numbers def squareSum( n ): return int(n * ( 4 * n * n - 1) / 3) # driver code ans = squareSum(8) print (ans) # This code is contributed by Saloni Gupta
C#
// Efficient C# method to // find sum of square of // first n odd numbers. using System; class GFG { static int squareSum(int n) { return n * (4 * n * n - 1)/3; } // driver code public static void Main() { Console.Write(squareSum(8)); } } // This code is contributed by // Vt_m.
PHP
<?php // Efficient PHP method to find sum of // square of first n odd numbers. function squareSum($n) { return $n * (4 * $n * $n - 1) / 3; } echo squareSum(8); // This code is contributed by Vt_m. ?>
Javascript
<script> // JavaScript program to find sum of // square of first n odd numbers. function squareSum(n) { return n*(4*n*n - 1)/3; } // Driver code document.write(squareSum(8)); </script>
Producción :
680
Complejidad de tiempo: O(1), el código se ejecutará en un tiempo constante.
Espacio auxiliar: O(1), no se requiere espacio adicional, por lo que es una constante.
Publicación traducida automáticamente
Artículo escrito por Dharmendra_Kumar y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA