10Triangular
- Build-up
- 1 + 2 + 3 + 4 = 10
Check Triangular Number in Java
What you’ll learn
- What a triangular number means: adding
1 + 2 + 3 + ... + k. - How to check a number using a simple loop-based running sum in Java.
- Two complete programs: test one number and print triangular numbers from 1 to 50.
- Live preview, edge cases, and interview-friendly complexity notes.
Overview
A triangular number is the total after adding consecutive counting numbers. This page focuses on the clean Java loop approach used in interviews and beginner classes.
Simple running-sum logic
Add 1, then 2, then 3, until you hit or pass the target.
Live preview
Try values quickly and see whether Java-style logic returns triangular or not.
Range example
Generate all triangular numbers from 1 to 50 in one pass.
Prerequisites
You only need basic Java control flow and integer variables.
if,while/for, and integer arithmetic in Java.- Understanding of positive whole numbers and sums like
1 + 2 + 3 + 4 = 10.
What is a triangular number?
A number is triangular if it equals 1 + 2 + 3 + ... + k for some positive integer k.
Example: 10 = 1 + 2 + 3 + 4, so 10 is triangular. But 7 is not, because the totals jump from 6 to 10.
Quick examples
7Not triangular
- Build-up
- 1 + 2 + 3 = 6, next is 10
Live preview
Enter a whole number and apply the same running-sum logic as the Java function.
Algorithm
Goal: decide whether n can be written as 1 + 2 + ... + k.
Reject invalid input
If n < 1, return false.
Initialize
Set sum = 0 and k = 1.
Grow total
While sum < n, do sum += k, then k++.
Decide
If sum == n, triangular; otherwise not triangular.
📜 Pseudocode
Pseudocode
function isTriangular(n):
if n < 1:
return false
sum = 0
k = 1
while sum < n:
sum = sum + k
k = k + 1
return (sum == n)1
Check a single number (loop method)
This program checks whether 10 is triangular.
java
public class Main {
static boolean isTriangular(int n) {
if (n < 1) return false;
int sum = 0;
int k = 1;
while (sum < n) {
sum += k;
k++;
}
return sum == n;
}
public static void main(String[] args) {
int number = 10;
if (isTriangular(number)) {
System.out.println(number + " is a triangular number.");
} else {
System.out.println(number + " is not a triangular number.");
}
}
}2
Triangular numbers from 1 to 50
This prints triangular numbers in the range 1 to 50.
java
public class Main {
static boolean isTriangular(int n) {
if (n < 1) return false;
int sum = 0;
int k = 1;
while (sum < n) {
sum += k;
k++;
}
return sum == n;
}
public static void main(String[] args) {
System.out.println("Triangular numbers from 1 to 50:");
for (int i = 1; i <= 50; i++) {
if (isTriangular(i)) {
System.out.print(i + " ");
}
}
}
}Notes and optional shortcuts
Loop first. The additive loop is easiest to explain in interviews and debugging rounds.
Formula option. Triangular numbers satisfy Tk = k * (k + 1) / 2 if you need constant-time math checks.
❓ FAQ
A number is triangular if it can be written as 1 + 2 + 3 + ... + k for some positive integer k.
Yes. 10 = 1 + 2 + 3 + 4.
No. Triangular totals around 7 are 6 and 10, so 7 is not triangular.
Keep adding 1, then 2, then 3, and stop when sum reaches or exceeds n. If sum equals n, it is triangular.
O(sqrt(n)) for one check using the additive loop.
🔄 Input / output examples
| Input | Output verdict |
|---|---|
10 | triangular |
7 | not triangular |
Edge cases
n = 1
Smallest positive triangular number.
n < 1
Treat as non-triangular in this tutorial.
⏱️ Time and space complexity
| Task | Time | Extra space |
|---|---|---|
| Check one number (additive loop) | O(√n) | O(1) |
Summary
- Idea: triangular numbers are totals of consecutive counting numbers.
- Approach: keep adding next integers until you match or pass the target.
- Interview tip: the loop method is easy to explain and code correctly.
Did you know?
Triangular numbers are totals of counting numbers: 1, 3, 6, 10, 15, 21, ... They represent dots arranged in triangle rows.
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