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 triangular number are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55.
Examples:
Input: N = 21
Output:6
Explanation:
Since 15 is a 6th Triangular Number.
Input: N = 12
Output:-1
Explanation:
Since 12 is not a Triangular Number
Approach:
- Since triangular numbers are the sum of natural numbers so can be generalized as a quadratic equation.
C++
// 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 triangular 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 numberimport 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 numberimport mathN = 21A = math.sqrt(2 * N + 0.25)-0.5B = int(A)# if N is not tringular numberif B != A: print(-1)else: print(B) |
C#
// C# code to print sequence // number of a triangular numberusing 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
<script>// 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 </script> |
6
Time Complexity: O(logN) as sqrt function is being used
Auxiliary Space: O(1)
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