居中十二面体数
原文:https://www.geeksforgeeks.org/centered-dodecahedral-number/
给定一个数 n，求第 n 个中心十二面体数。 一个中心十二面体数是一类比喻数。它由一个中心点形成，周围是连续的十二面体(多面体有 12 个平面)层。 前几个居中的十二面体数(其中 n = 0、1、2、3……)。)有: 1、33、155、427、909、1661………… 例:
Input : 5
Output : 1661
Input :1
Output :33
第 n 个中心十二面体数的数学公式如下:
以下是上述思路的基本实现:
C++
// Program to find nth centered
// dodecahedral number
#include <bits/stdc++.h>
using namespace std;
// Function to find
// centered dodecahedral number
int CenteredDodecahedral_num(long int n)
{
// Formula to calculate nth
// centered dodecahedral number
// and return it into main function.
return (2 * n + 1) * (5 * n * n + 5 * n + 1);
}
// Driver Code
int main()
{
long int n = 3;
// print result
cout << n << "th Centered Dodecahedral number : ";
cout << CenteredDodecahedral_num(n) << endl;
n = 10;
// print result
cout << n << "th Centered Dodecahedral number : ";
cout << CenteredDodecahedral_num(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 dodecahedral number
import java.io.*;
class GFG {
// Function to find centered
// dodecahedral number
static int CenteredDodecahedral_num(int n)
{
// Formula to calculate nth
// centered dodecahedral number
// and return it into main function.
return (2 * n + 1) *
(5 * n * n + 5 * n + 1);
}
// Driver Code
public static void main (String[] args)
{
int n = 3;
// print result
System.out.print( n + "th Centered "
+ "Dodecahedral number : ");
System.out.println (
CenteredDodecahedral_num(n));
n = 10;
// print result
System.out.print( n + "th Centered "
+ "Dodecahedral number : ");
System.out.println(
CenteredDodecahedral_num(n));
}
}
// This code is contributed by m_kit.
Python 3
# Program to find nth centered
# dodecahedral number
# Function to find centered
# dodecahedral number
def CenteredDodecahedral_num(n) :
# Formula to calculate nth
# centered dodecahedral number
return (2 * n + 1) * (5 * n * n + 5 * n + 1)
# Driver Code
if __name__ == '__main__' :
n = 3
print(n,"rd centered dodecahedral number: ",
CenteredDodecahedral_num(n))
n = 10
print(n,"th centered dodecahedral number : ",
CenteredDodecahedral_num(n))
# This code is contributed by aj_36
C
// C# Program to find
// nth centered
// dodecahedral number
using System;
class GFG
{
// Function to find
// nth centered
// dodecahedral number
static int CenteredDodecahedral_num(int n)
{
// Formula to calculate
// nth centered dodecahedral
// number and return it
// into main function.
return (2 * n + 1) *
(5 * n * n +
5 * n + 1);
}
// Driver Code
static public void Main ()
{
int n = 3;
// print result
Console.Write( n + "th Centered " +
"Dodecahedral number : ");
Console.WriteLine(
CenteredDodecahedral_num(n));
n = 10;
// print result
Console.Write( n + "th Centered " +
"Dodecahedral number : ");
Console.WriteLine(
CenteredDodecahedral_num(n));
}
}
// This code is contributed by ajit
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// Program to find nth centered
// dodecahedral number
// Function to find
// centered dodecahedral number
function CenteredDodecahedral_num($n)
{
// Formula to calculate nth
// centered dodecahedral number
// and return it into main function.
return (2 * $n + 1) *
(5 * $n * $n +
5 * $n + 1);
}
// Driver Code
$n = 3;
// print result
echo $n, "th Centered Dodecahedral " .
"number : ";
echo CenteredDodecahedral_num($n),"\n";
$n = 10;
// print result
echo $n, "th Centered Dodecahedral " .
"number : ";
echo CenteredDodecahedral_num($n);
// This code is contributed by akt_mit
?>
java 描述语言
<script>
// Javascript Program to find nth
// centered dodecahedral number
// Function to find centered
// dodecahedral number
function CenteredDodecahedral_num(n)
{
// Formula to calculate nth
// centered dodecahedral number
// and return it into main function.
return (2 * n + 1) *
(5 * n * n + 5 * n + 1);
}
// Driver code
var n = 3;
// print result
document.write(n + "th Centered " +
"Dodecahedral number : ");
document.write(CenteredDodecahedral_num(n) + "<br>");
n = 10;
// print result
document.write(n + "th Centered " +
"Dodecahedral number : ");
document.write(CenteredDodecahedral_num(n));
// This code is contributed by Khushboogoyal499
</script>
输出:
3th Centered Dodecahedral number : 427
10th Centered Dodecahedral number : 11571
时间复杂度:O(1) T3】辅助空间: O(1)
参考文献:T2https://en.wikipedia.org/wiki/Centered_dodecahedral_numberT5】
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