Binary Triangle in C, C++, Java & Python – Code with Explanation & Examples in Short and Simple

   

C Program

#include <stdio.h>
int main() {
    int n=5;
    for(int i=1;i<=n;i++){
        for(int j=1;j<=i;j++) printf("%d ",(i+j)%2);
        printf("\n");
    }
}

C Output

Input:
5
Output:
0
1 0
0 1 0
1 0 1 0
0 1 0 1 0

C++ Program

#include <iostream>
using namespace std;
int main() {
    int n=6;
    for(int i=1;i<=n;i++){
        for(int j=1;j<=i;j++) cout<<((i+j)%2)<<" ";
        cout<<"\n";
    }
}

C++ Output

Input:
6
Output:
0
1 0
0 1 0
1 0 1 0
0 1 0 1 0
1 0 1 0 1 0

JAVA Program

class Main {
    public static void main(String[] args) {
        int n=4;
        for(int i=1;i<=n;i++){
            for(int j=1;j<=i;j++)
                System.out.print((i+j)%2+" ");
            System.out.println();
        }
    }
}

JAVA Output

Input:
4
Output:
0
1 0
0 1 0
1 0 1 0

Python Program

n=3
for i in range(1,n+1):
    for j in range(1,i+1):
        print((i+j)%2,end=" ")
    print()

Python Output

Input:
3
Output:
0
1 0
0 1 0

Deep-Dive, Extended Explanation

Understanding the Pattern

The binary triangle is an alternating triangular number pattern of 0s and 1s. The catch is that each is calculated based on the formula (i+j) % 2, where the row number i and column number j are used. This makes the sequence alternation work properly in both the horizontal and vertical directions without having to keep track of the previous number manually.

Example

Suppose we have n = 5:

Row 1 → (1+1) % 2 = 0 → 0

Row 2 → (2+1) % 2 = 1, (2+2) % 2 = 0 → 1 0

Row 3 → (3+1) % 2 = 0, (3+2) % 2 = 1, (3+3) % 2 = 0 → 0 1 0

…and so on.

The pattern increases downwards as a standard triangle but with a strict 0-1 alternation depending on the sum of coordinates.

Real-Life Analogy

Think of a checkerboard, but you just use the top-left triangular half. Each square is alternating color, as the binary triangle alternates between 0 and 1. This type of alternation shows up in fabric, flooring patterns, and even in packet switching network systems.

Why It Matters

This is not just a pattern—it illustrates modulus arithmetic in a loop, something that's paramount in:

Cryptography (alternating bit patterns)

Digital circuit design (clock signals)

Data encoding (binary toggling)

Algorithm optimization (avoid extra condition checks by using %)

Learning Insights

When solving problems like this:

You don’t need to store previous values to alternate; math can do it for you.

% 2 is one of the most powerful tools for toggling between two states.

This pattern introduces beginners to loop-based formula-driven outputs rather than manual logic.

In Interviews

An interviewer may ask:

"Print a binary triangle" to find out whether you can use math within loops.

"Alternate pattern without if-else" — the modulus trick is the most elegant solution.

"Optimize memory" — you don't keep anything, you simply calculate immediately.

SEO-Friendly Closing

The binary triangle pattern is a easy-to-learn but very instructive programming problem that demonstrates the application of nested loops, modulus math, and elegant logic in producing alternating binary values. Whether done in C, C++, Java, or Python, solving this pattern enhances knowledge of mathematical operations within loops, a capability frequently assessed in coding interviews and practical purposes in alternating sequence, binary data representation, and pattern creation.