斜角数

给定数N ，任务是找到^第N^个对角线数。

A chiliagon number is class of figurate number. It has 1000 – sided polygon called chiliagon. The N-th chiliagon number count’s the 1000 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few chiliagonol numbers are 1, 1000, 2997, 5992 …

例子：

Input: N = 2 
Output: 1000 
Explanation: 
The second chiliagonol number is 1000. 
Input: N = 3 
Output: 2997

方法：第N个对角线数由下式给出：

• 侧多边形的第N个项= $\frac{((s-2)n^2 - (s-4)n)}{2}$
• 因此，第1000个面多边形的第N个项是

$Tn =\frac{((1000-2)n^2 - (1000-4)n)}{2} =\frac{(998n^2 - 996n)}{2}$

下面是上述方法的实现：

C++

// C++ program for above approach
#include 
using namespace std;
 
// Finding the nth chiliagon Number
int chiliagonNum(int n)
{
    return (998 * n * n - 996 * n) / 2;
}
 
// Driver Code
int main()
{
    int n = 3;
    cout <<"3rd chiliagon Number is = "
         << chiliagonNum(n);
 
    return 0;
}
 
// This code is contributed by shivanisinghss2110

C

// C program for above approach
#include 
#include 
 
// Finding the nth chiliagon Number
int chiliagonNum(int n)
{
    return (998 * n * n - 996 * n) / 2;
}
 
// Driver program to test above function
int main()
{
    int n = 3;
    printf("3rd chiliagon Number is = %d",
           chiliagonNum(n));
 
    return 0;
}

Java

// Java program for the above approach
class GFG{
 
// Finding the nth chiliagon number
static int chiliagonNum(int n)
{
    return (998 * n * n - 996 * n) / 2;
}
 
// Driver code
public static void main(String[] args)
{
    int n = 3;
    System.out.println("3rd chiliagon Number is = " +
                                    chiliagonNum(n));
}
}
 
// This code is contributed by rutvik_56

Python3

# Python3 program for above approach
 
# Finding the nth chiliagon Number
def chiliagonNum(n):
 
    return (998 * n * n - 996 * n) // 2;
 
# Driver Code
n = 3;
print("3rd chiliagon Number is = ",
                  chiliagonNum(n));
 
# This code is contributed by Akanksha_Rai

C#

// C# program for the above approach
using System;
class GFG{
 
// Finding the nth chiliagon number
static int chiliagonNum(int n)
{
    return (998 * n * n - 996 * n) / 2;
}
 
// Driver code
public static void Main()
{
    int n = 3;
    Console.Write("3rd chiliagon Number is = " +
                               chiliagonNum(n));
}
}
 
// This code is contributed by Akanksha_Rai

Javascript

 
// javascript program for above approach
 
 
// Finding the nth chiliagon Number
function chiliagonNum( n)
{
    return (998 * n * n - 996 * n) / 2;
}
 
// Driver code
let n = 3;
document.write("3rd chiliagon Number is "
+ chiliagonNum(n));
 
// This code contributed by gauravrajput1
 

输出：

3rd chiliagon Number is = 2997

时间复杂度： O(1)

辅助空间： O(1)

参考： https ： //en.wikipedia.org/wiki/Chiliagon