程序检查N是否为三角角

给定数字N ，任务是检查数字是否为三角角数字。

A Triacontagonal number is a class of figurate number. It has 30 – sided polygon called triacontagon. The N-th triacontagonal number count’s the 30 number of dots and all other dots are surrounding with a common sharing corner and make a pattern. The first few triacontagonol numbers are 1, 30, 87, 172 … 
 

例子：

Input: N = 30 
Output: Yes 
Explanation: 
Second triacontagonal number is 30.
Input: 32 
Output: No 
 

方法：

1. 三角对角数的第K^个项为：

$K^{th} Term = \frac{28*K^{2} - 26*K}{2}$

1. 因为我们必须检查给定的数字是否可以表示为三角八角形数字。可以检查如下：

=> 

$N = \frac{28*K^{2} - 26*K}{2}$
 

=> 

$K = \frac{26 + \sqrt{224*N + 676}}{56}$
 

 

 

2. 最后，检查使用此公式计算的值是否为整数，这意味着N为三对角线数。

下面是上述方法的实现：

C++

// C++ program to check whether a
// number is an triacontagonal
// number or not
#include 
using namespace std;
 
// Function to check whether a
// number is an triacontagonal
// number or not
bool istriacontagonal(int N)
{
    float n
        = (26 + sqrt(224 * N + 676))
          / 56;
 
    // Condition to check whether a
    // number is an triacontagonal
    // number or not
    return (n - (int)n) == 0;
}
 
// Driver Code
int main()
{
     
    // Given number
    int i = 30;
 
    // Function call
    if (istriacontagonal(i)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

Java

// Java program to check whether a
// number is an triacontagonal
// number or not
class GFG{
 
// Function to check whether a
// number is an triacontagonal
// number or not
static boolean istriacontagonal(int N)
{
    float n = (float) ((26 + Math.sqrt(224 * N +
                                       676)) / 56);
     
    // Condition to check whether a
    // number is an triacontagonal
    // number or not
    return (n - (int)n) == 0;
}
 
// Driver code
public static void main(String[] args)
{
     
    // Given number
    int N = 30;
     
    // Function call
    if (istriacontagonal(N))
    {
        System.out.print("Yes");
    }
    else
    {
        System.out.print("No");
    }
}
}
 
// This code is contributed by shubham

Python3

# Python3 program to check whether a
# number is an triacontagonal
# number or not
import math;
 
# Function to check whether a
# number is an triacontagonal
# number or not
def istriacontagonal(N):
 
    n = (26 + math.sqrt(224 * N + 676)) // 56;
 
    # Condition to check whether a
    # number is an triacontagonal
    # number or not
    return (n - int(n)) == 0;
 
# Driver Code
 
# Given number
i = 30;
 
# Function call
if (istriacontagonal(i)):
    print("Yes");
else:
    print("No");
 
# This code is contributed by Code_Mech

C#

// C# program to check whether a
// number is an triacontagonal
// number or not
using System;
class GFG{
 
// Function to check whether a
// number is an triacontagonal
// number or not
static bool istriacontagonal(int N)
{
    float n = (float)((26 + Math.Sqrt(224 * N +
                                      676)) / 56);
     
    // Condition to check whether a
    // number is an triacontagonal
    // number or not
    return (n - (int)n) == 0;
}
 
// Driver code
public static void Main(String[] args)
{
     
    // Given number
    int N = 30;
     
    // Function call
    if (istriacontagonal(N))
    {
        Console.Write("Yes");
    }
    else
    {
        Console.Write("No");
    }
}
}
 
// This code is contributed by sapnasingh4991

Javascript

// javascript  program to check whether a
// number is an triacontagonal
// number or not
 
// Function to check whether a
// number is an triacontagonal
// number or not
function istriacontagonal( N)
{
    let n = ((26 + Math.sqrt(224 * N +
                                       676)) / 56);
     
    // Condition to check whether a
    // number is an triacontagonal
    // number or not
    return (n - parseInt(n)) == 0;
}
 
// Driver code
 
    // Given number
    let N = 30;
     
    // Function call
    if (istriacontagonal(N))
    {
          document.write("Yes");
    }
    else
    {
         document.write("No");
    }
 
    // This code is contributed by aashish1995

输出：
是的