编写程序以查找前n个偶数自然数的四次幂之和。
2 4 + 4 4 + 6 4 + 8 4 + 10 4 +………+ 2n 4
例子:
Input : 3
Output : 1568
24 +44 +64 = 1568
Input : 6
Output : 36400
24 + 44 + 64 + 84 + 104 + 124
天真的方法:-在这个简单的函数中,找到前n个偶数个自然数的第4次幂是从1到n次循环。第i次迭代都存储在变量中,并一直持续到(i!= n)。这需要O(N)时间复杂度。
C++
// CPP Program to find the sum of fourth powers of
// first n even natural numbers
#include
using namespace std;
// calculate the sum of fourth power of first n even
// natural numbers
long long int evenPowerSum(int n)
{
long long int sum = 0;
for (int i = 1; i <= n; i++) {
// made even number
int j = 2 * i;
sum = sum + (j * j * j * j);
}
return sum;
}
// Driven Program
int main()
{
int n = 5;
cout << evenPowerSum(n) << endl;
return 0;
}
Java
// Java Program to find the sum of fourth powers of
// first n even natural numbers
import java.io.*;
class GFG {
// calculate the sum of fourth power of first
// n even natural numbers
static long evenPowerSum(int n)
{
long sum = 0;
for (int i = 1; i <= n; i++)
{
// made even number
int j = 2 * i;
sum = sum + (j * j * j * j);
}
return sum;
}
// Driven Program
public static void main (String[] args) {
int n = 5;
System.out.println(evenPowerSum(n));
}
}
/*This code is contributed by vt_m.*/
Python3
# Python3 Program to find
# the sum of fourth powers of
# first n even natural numbers
# calculate the sum of fourth
# power of first n even
# natural numbers
def evenPowerSum(n):
sum = 0;
for i in range(1, n + 1):
# made even number
j = 2 * i;
sum = sum + (j * j * j * j);
return sum;
# Driver Code
n = 5;
print(evenPowerSum(n));
# This is contributed by mits.
C#
// C# Program to find the sum of fourth powers of
// first n even natural numbers
using System;
class GFG {
// calculate the sum of fourth power of
// first n even natural numbers
static long evenPowerSum(int n)
{
long sum = 0;
for (int i = 1; i <= n; i++) {
// made even number
int j = 2 * i;
sum = sum + (j * j * j * j);
}
return sum;
}
// Driven Program
public static void Main()
{
int n = 5;
Console.Write(evenPowerSum(n));
}
}
// This code is contributed by vt_m.
PHP
Javascript
C++
// CPP Program to find the sum of fourth powers of
// first n even natural numbers
#include
using namespace std;
// calculate the sum of fourth power of first n
// even natural numbers
long long int evenPowerSum(int n)
{
return (8 * n * (n + 1) * (2 * n + 1) *
(3 * n * n + 3 * n - 1)) / 15;
}
// Driven Program
int main()
{
int n = 4;
cout << evenPowerSum(n) << endl;
return 0;
}
Java
// JAVA Program to find the sum of fourth powers of
// first n even natural numbers
import java.io.*;
class GFG {
// calculate the sum of fourth power of first n
// even natural numbers
static long evenPowerSum(int n)
{
return (8 * n * (n + 1) * (2 * n + 1) *
(3 * n * n + 3 * n - 1)) / 15;
}
// Driven Program
public static void main (String[] args) {
int n = 4;
System.out.println(evenPowerSum(n));
}
}
/* This code is contributed by vt_m. */
Python3
# Python3 Program to find
# the sum of fourth powers
# of first n even natural
# numbers
# calculate the sum of
# fourth power of first n
# even natural numbers
def evenPowerSum(n):
return (8 * n * (n + 1) *
(2 * n + 1) * (3 *
n * n + 3 * n - 1)) / 15;
# Driver Code
n = 4;
print (int(evenPowerSum(n)));
# This code is contributed by mits
C#
// C# Program to find the sum of fourth powers of
// first n even natural numbers
using System;
class GFG {
// calculate the sum of fourth power of first n
// even natural numbers
static long evenPowerSum(int n)
{
return (8 * n * (n + 1) * (2 * n + 1) *
(3 * n * n + 3 * n - 1)) / 15;
}
// Driven Program
public static void Main()
{
int n = 4;
Console.Write(evenPowerSum(n));
}
}
/* This code is contributed by vt_m.*/
PHP
Javascript
输出:
15664
时间复杂度:O(n)
高效的方法:-高效的解决方案是使用下面得出的直接数学公式,这仅需要O(1)时间复杂度。
Sum of fourth power of first n even natural number = 8*(n*(n+1)*(2*n+1)(3*n2+3*n -1))/15
How does this formula work?
Sum of fourth power of natural numbers is = (n(n+1)(2n+1)(3n2+3n-1))/30
we need even natural number so we multiply each term 24
= 24(14 + 24 + 34 + ………… +n4)
= (24 + 44 + 64 + ………… +2n4)
= 24*(sum of fourth power natural number)
= 16*(n*(n+1)*(2*n+1)(3*n2+3*n -1))/30
= 8*(n*(n+1)*(2*n+1)(3*n2+3*n -1))/15
C++
// CPP Program to find the sum of fourth powers of
// first n even natural numbers
#include
using namespace std;
// calculate the sum of fourth power of first n
// even natural numbers
long long int evenPowerSum(int n)
{
return (8 * n * (n + 1) * (2 * n + 1) *
(3 * n * n + 3 * n - 1)) / 15;
}
// Driven Program
int main()
{
int n = 4;
cout << evenPowerSum(n) << endl;
return 0;
}
Java
// JAVA Program to find the sum of fourth powers of
// first n even natural numbers
import java.io.*;
class GFG {
// calculate the sum of fourth power of first n
// even natural numbers
static long evenPowerSum(int n)
{
return (8 * n * (n + 1) * (2 * n + 1) *
(3 * n * n + 3 * n - 1)) / 15;
}
// Driven Program
public static void main (String[] args) {
int n = 4;
System.out.println(evenPowerSum(n));
}
}
/* This code is contributed by vt_m. */
Python3
# Python3 Program to find
# the sum of fourth powers
# of first n even natural
# numbers
# calculate the sum of
# fourth power of first n
# even natural numbers
def evenPowerSum(n):
return (8 * n * (n + 1) *
(2 * n + 1) * (3 *
n * n + 3 * n - 1)) / 15;
# Driver Code
n = 4;
print (int(evenPowerSum(n)));
# This code is contributed by mits
C#
// C# Program to find the sum of fourth powers of
// first n even natural numbers
using System;
class GFG {
// calculate the sum of fourth power of first n
// even natural numbers
static long evenPowerSum(int n)
{
return (8 * n * (n + 1) * (2 * n + 1) *
(3 * n * n + 3 * n - 1)) / 15;
}
// Driven Program
public static void Main()
{
int n = 4;
Console.Write(evenPowerSum(n));
}
}
/* This code is contributed by vt_m.*/
的PHP
Java脚本
输出:
5664
时间复杂度:O(1)