查找三角数的序列号

给定整数N，则打印给定三角数的序列号。如果该数字不是三角形数字，则打印-1。

A number is termed as a triangular number if we can represent it in the form of a triangular grid of points such that the points form an equilateral triangle and each row contains as many points as the row number, i.e., the first row has one point, the second row has two points, the third row has three points and so on. 
First 10 tringular number are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55. 
 

 

例子：

Input: N = 21 
Output:6 
Explanation: 
Since 15 is a 6th Tringular Number.
Input: N = 12 
Output:-1 
Explanation: 
Since 12 is not a tringular Number 
 

方法：

1. 由于奇偶数是自然数的和，因此可以概括为二次方程。

C++

// C++ code to print sequence
// number of a triangular number
#include
using namespace std;
 
int main()
{
    int N = 21;
    int A = sqrt(2 * N + 0.25) - 0.5;
    int B = A;
 
    // If N is not tringular number
    if (B != A)
        cout << "-1";
    else
        cout << B;
}
 
// This code is contributed by yatinagg

Java

// Java code to print sequence
// number of a triangular number
import java.util.*;
class GFG{
     
public static void main(String args[])
{
    int N = 21;
    int A = (int)(Math.sqrt(2 * N + 0.25) - 0.5);
    int B = A;
 
    // If N is not tringular number
    if (B != A)
        System.out.print("-1");
    else
        System.out.print(B);
}
}
 
// This code is contributed by Akanksha_Rai

Python3

# Python3 code to print sequence
# number of a triangular number
 
import math
 
N = 21
A = math.sqrt(2 * N + 0.25)-0.5
B = int(A)
 
# if N is not tringular number
if B != A:
    print(-1)
else:
    print(B)

C#

// C# code to print sequence
// number of a triangular number
using System;
class GFG{
     
public static void Main()
{
    int N = 21;
    int A = (int)(Math.Sqrt(2 * N + 0.25) - 0.5);
    int B = A;
 
    // If N is not tringular number
    if (B != A)
        Console.Write("-1");
    else
        Console.Write(B);
}
}
 
// This code is contributed by Code_Mech

Javascript

// javascript code to print sequence
// number of a triangular number
    let N = 21;
    let A = Math.sqrt(2 * N + 0.25) - 0.5;
    let B = A;
 
    // If N is not tringular number
    if (B != A)
         document.write("-1");
    else
         document.write(B);
          
// This code is contributed by Rajput-Ji
 

输出：

6

时间复杂度： O(1)
辅助空间： O(1)