将N分成三元组以形成三角形的方法数量

给定整数N ，任务是找到将N分解为可以一起形成三角形的有序三胞胎的方法数量。

例子：

Input: N = 15
Output: Total number of triangles possible are 28

Input: N = 9
Output: Total number of triangles possible is 10

方法：为了解决该问题，需要进行以下观察：

If N is split into 3 integers a, b and c, then the following conditions need to be satisfied for a, b and c to form a triangle:

a + b > c

a + c > b

b + c > a

因此，使用嵌套循环在[1，N]范围内进行迭代以生成三元组，并针对每个三元组检查是否形成三角形。

下面是上述方法的实现：

C++

// C++ Program to implement
// the above approach
#include 
using namespace std;
  
// Function to return the
// required number of ways
int Numberofways(int n)
{
    int count = 0;
  
    for (int a = 1; a < n; a++) {
  
        for (int b = 1; b < n; b++) {
  
            int c = n - (a + b);
  
            // Check if a, b and c can
            // form a triangle
            if (a + b > c && a + c > b
                && b + c > a) {
                count++;
            }
        }
    }
  
    // Return number of ways
    return count;
}
  
// Driver Code
int main()
{
    int n = 15;
  
    cout << Numberofways(n) << endl;
  
    return 0;
}

Java

// Java Program to implement
// the above approach
import java.io.*;
  
class GFG {
  
    // Function to return the
    // required number of ways
    static int Numberofways(int n)
    {
        int count = 0;
  
        for (int a = 1; a < n; a++) {
  
            for (int b = 0; b < n; b++) {
  
                int c = n - (a + b);
  
                // Check if a, b, c can
                // form a traingle
                if (a + b > c && a + c > b
                    && b + c > a) {
                    count++;
                }
            }
        }
  
        return count;
    }
  
    // Driver Code
    public static void main(String[] args)
    {
        int n = 15;
  
        System.out.println(Numberofways(n));
    }
}

Python3

# Python Program to implement
# the above approach
  
# Function to return the
# required number of ways
def Numberofways(n):
    count = 0
    for a in range(1, n):
        for b in range(1, n):
  
            c = n - (a + b)
  
            # Check if a, b, c can form a triangle
            if(a < b + c and b < a + c and c < a + b):
                count += 1
  
    return count
  
  
# Driver code
n = 15
print(Numberofways(n))

C#

// C# Program to implement
// the above approach
  
using System;
  
class GFG {
  
    // Function to return the
    // required number of ways
    static int Numberofways(int n)
    {
        int count = 0;
        for (int a = 1; a < n; a++) {
            for (int b = 1; b < n; b++) {
                int c = n - (a + b);
  
                // Check if a, b, c can form
                // a triangle or not
                if (a + b > c && a + c > b
                    && b + c > a) {
                    count++;
                }
            }
        }
  
        // Return number of ways
        return count;
    }
  
    // Driver Code
    static public void Main()
    {
        int n = 15;
  
        Console.WriteLine(Numberofways(n));
    }
}

输出：

28

时间复杂度： O(N ² )
辅助空间： O(N)