Find the sequence number of a triangular number

Given an integer N print the sequence number of the given Triangular Number. If the number is not a triangular number then print -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.

Examples:

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



Approach:

  1. Since tringular numbers are sum of natural numbers so can be generalise as quadratic equation.
  2. (X*(X+1))/2 = N
    X = (-1 + (1 + 8*N) ) /2
    X = -0.5 + (0.25 + 2*N)^1/2

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ code to print sequence 
// number of a triangular number
#include<bits/stdc++.h>
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

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# 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)         

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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

chevron_right


Output:

6

Time Complexity: O(1)
Auxiliary Space: O(1)

competitive-programming-img




My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.