五边形金字塔数字
原文:https://www.geeksforgeeks.org/pentagonal-pyramidal-number/
给定一个数 n，求第 n 个五边形金字塔数。 A 五边形棱锥数 属于具象数类。它是以五边形为底的金字塔中物体的数量。第 n 个五边形金字塔数等于前 n 个五边形数之和。 举例:
Input : n = 3
Output : 18
Input : n = 7
Output : 196
方法一:(天真的方法): 这个方法很简单。它说把所有的五边形数加起来到 n(通过运行循环)得到第 n 个五边形金字塔数。
以下是该方法的实现:
C++
// CPP Program to get nth Pentagonal
// pyramidal number.
#include <bits/stdc++.h>
using namespace std;
// function to get nth Pentagonal
// pyramidal number.
int pentagon_pyramidal(int n)
{
int sum = 0;
// Running loop from 1 to n
for (int i = 1; i <= n; i++) {
// get nth pentagonal number
int p = (3 * i * i - i) / 2;
// add to sum
sum = sum + p;
}
return sum;
}
// Driver Program
int main()
{
int n = 4;
cout << pentagon_pyramidal(n) << endl;
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java Program to get nth
// Pentagonal pyramidal number.
import java.io.*;
class GFG
{
// function to get nth
// Pentagonal pyramidal number.
static int pentagon_pyramidal(int n)
{
int sum = 0;
// Running loop from 1 to n
for (int i = 1; i <= n; i++)
{
// get nth pentagonal number
int p = (3 * i * i - i) / 2;
// add to sum
sum = sum + p;
}
return sum;
}
// Driver Code
public static void main (String[] args)
{
int n = 4;
System.out.println(pentagon_pyramidal(n));
}
}
// This code is contributed by anuj_67.
Python 3
# Python3 Program to get nth Pentagonal
# pyramidal number.
# function to get nth Pentagonal
# pyramidal number.
def pentagon_pyramidal(n):
sum = 0
# Running loop from 1 to n
for i in range(1, n + 1):
# get nth pentagonal number
p = ( 3 * i * i - i ) / 2
# add to sum
sum = sum + p
return sum
# Driver Program
n = 4
print(int(pentagon_pyramidal(n)))
C
// C# Program to get nth
// Pentagonal pyramidal number.
using System;
class GFG
{
// function to get nth
// Pentagonal pyramidal number.
static int pentagon_pyramidal(int n)
{
int sum = 0;
// Running loop from 1 to n
for (int i = 1; i <= n; i++)
{
// get nth pentagonal number
int p = (3 * i *
i - i) / 2;
// add to sum
sum = sum + p;
}
return sum;
}
// Driver Code
static public void Main ()
{
int n = 4;
Console.WriteLine(pentagon_pyramidal(n));
}
}
// This code is contributed by ajit.
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP Program to get nth
// Pentagonal pyramidal number.
// function to get nth
// Pentagonal pyramidal number.
function pentagon_pyramidal($n)
{
$sum = 0;
// Running loop from 1 to n
for ($i = 1; $i <= $n; $i++)
{
// get nth pentagonal number
$p = (3 * $i *
$i - $i) / 2;
// add to sum
$sum = $sum + $p;
}
return $sum;
}
// Driver Code
$n = 4;
echo pentagon_pyramidal($n);
// This code is contributed by m_kit
?>
java 描述语言
<script>
// javascript Program to get nth
// Pentagonal pyramidal number.
// function to get nth
// Pentagonal pyramidal number.
function pentagon_pyramidal(n)
{
var sum = 0;
// Running loop from 1 to n
for (i = 1; i <= n; i++)
{
// get nth pentagonal number
var p = (3 * i * i - i) / 2;
// add to sum
sum = sum + p;
}
return sum;
}
// Driver Code
var n = 4;
document.write(pentagon_pyramidal(n));
// This code is contributed by Amit Katiyar
</script>
输出:
40
时间复杂度: O(n)
方法二:(高效方法): 在这种方法中，我们用公式得到 O(1)时间内的第 n 个五边形金字塔数。
第 n 个五边形金字塔数= n 2 (n + 1) / 2 下面是这种方法的实现:
C++
// CPP Program to get nth Pentagonal
// pyramidal number.
#include <bits/stdc++.h>
using namespace std;
// function to get nth Pentagonal
// pyramidal number.
int pentagon_pyramidal(int n)
{
return n * n * (n + 1) / 2;
}
// Driver Program
int main()
{
int n = 4;
cout << pentagon_pyramidal(n) << endl;
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java Program to get nth
// Pentagonal pyramidal number.
import java.io.*;
class GFG
{
// function to get nth
// Pentagonal pyramidal number.
static int pentagon_pyramidal(int n)
{
return n * n *
(n + 1) / 2;
}
// Driver Code
public static void main (String[] args)
{
int n = 4;
System.out.println(pentagon_pyramidal(n));
}
}
// This code is contributed by ajit
Python 3
# Python3 Program to get nth Pentagonal
# pyramidal number.
# function to get nth Pentagonal
# pyramidal number.
def pentagon_pyramidal(n):
return n * n * (n + 1) / 2
# Driver Program
n = 4
print(int(pentagon_pyramidal(n)))
C
// C# Program to get nth
// Pentagonal pyramidal number.
using System;
class GFG
{
// function to get nth
// Pentagonal pyramidal number.
static int pentagon_pyramidal(int n)
{
return n * n *
(n + 1) / 2;
}
// Driver Code
static public void Main ()
{
int n = 4;
Console.WriteLine(
pentagon_pyramidal(n));
}
}
// This code is contributed
// by ajit
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP Program to get
// nth Pentagonal
// pyramidal number.
// function to get
// nth Pentagonal
// pyramidal number.
function pentagon_pyramidal($n)
{
return $n * $n *
($n + 1) / 2;
}
// Driver Code
$n = 4;
echo pentagon_pyramidal($n);
// This code is contributed
// by akt_mit
?>
java 描述语言
<script>
// javascript Program to get nth
// Pentagonal pyramidal number.
// function to get nth
// Pentagonal pyramidal number.
function pentagon_pyramidal(n)
{
return n * n *
(n + 1) / 2;
}
// Driver Code
var n = 4;
document.write(pentagon_pyramidal(n));
// This code is contributed by Princi Singh
</script>
输出:
40
时间复杂度: O(1)
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