居中立方体编号
给定一个数 n，求第 n 个中心立方体数。 中心立方体编号计算由第 I 层的正方形面上的 i 2 点在 3D 中被同心立方体层包围的点形成的点数。来源【WIKI】。请参见这张图，看得更清楚。 前几个居中的立方体编号是: 1、9、35、91、189、341、559、855、1241、172………………………… 示例:****
Input : n = 1
Output : 9
Input : n = 7
Output : 855
*第 n 个*中心立方数的数学公式由: 给出
n-th Centered Cube Number = (2n + 1)(n<sup>2</sup> + n + 1)
下面是上述公式的基本实现:
C++
// Program to find nth Centered cube
// number
#include <bits/stdc++.h>
using namespace std;
// Function to find
// Centered cube number
int centered_cube(int n)
{
// Formula to calculate nth
// Centered cube number &
// return it into main function.
return (2 * n + 1) * ( n * n + n + 1);
}
// Driver Code
int main()
{
int n = 3;
cout << n << "th Centered cube number: ";
cout << centered_cube(n);
cout << endl;
n = 10;
cout << n << "th Centered cube number: ";
cout << centered_cube(n);
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java Program to find nth Centered
// cube number
import java.io.*;
class GFG {
// Function to find
// Centered cube number
static int centered_cube(int n)
{
// Formula to calculate nth
// Centered cube number &
// return it into main function.
return (2 * n + 1) * ( n * n + n + 1);
}
// Driver code
public static void main (String[] args)
{
int n = 3;
System.out.print (n + "th Centered"
+ " cube number: ");
System.out.println (centered_cube(n));
n = 10;
System.out.print ( n + "th Centered"
+ " cube number: ");
System.out.println (centered_cube(n));
}
}
// This code is contributed by m_kit.
Python 3
# Python 3 Program to find
# nth Centered cube number
# Centered cube
# number function
def centered_cube(n) :
# Formula to calculate
# nth Centered cube
# number return it
# into main function.
return (2 * n + 1) * (
n * n + n + 1)
# Driver Code
if __name__ == '__main__' :
n = 3
print(n,"th Centered cube " +
"number : " ,
centered_cube(n))
n = 10
print(n,"th Centered cube " +
"number : " ,
centered_cube(n))
# This code is contributed by ajit
C#
// C# Program to find nth
// Centered cube number
using System;
class GFG
{
// Function to find
// Centered cube number
static int centered_cube(int n)
{
// Formula to calculate
// nth Centered cube
// number & return it
// into main function.
return (2 * n + 1) *
(n * n + n + 1);
}
// Driver code
static public void Main ()
{
int n = 3;
Console.Write(n + "th Centered" +
" cube number: ");
Console.WriteLine (centered_cube(n));
n = 10;
Console.Write( n + "th Centered" +
" cube number: ");
Console.WriteLine(centered_cube(n));
}
}
// This code is contributed by aj_36
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// Program to find nth
// Centered cube number
// Function to find
// Centered cube number
function centered_cube($n)
{
// Formula to calculate nth
// Centered cube number &
// return it into main function.
return (2 * $n + 1) *
($n * $n + $n + 1);
}
// Driver Code
$n = 3;
echo $n , "th Centered cube number: ";
echo centered_cube($n);
echo "\n";
$n = 10;
echo $n , "th Centered cube number: ";
echo centered_cube($n);
// This code is contributed by m_kit
?>
java 描述语言
<script>
// Program to find nth Centered cube
// number
// Function to find
// Centered cube number
function centered_cube(n)
{
// Formula to calculate nth
// Centered cube number &
// return it into main function.
return (2 * n + 1) * ( n * n + n + 1);
}
// Driver Code
let n = 3;
document.write(n + "th Centered cube number: ");
document.write(centered_cube(n));
document.write("<br>");
n = 10;
document.write(n + "th Centered cube number: ");
document.write(centered_cube(n));
// This code is contributed by rishavmahato348.
</script>
*输出:*
3th Centered cube number: 91
10th Centered cube number: 2331
*时间复杂度:*O(1) T3】辅助空间: O(1)
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