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Number Pyramid

Java coding interview problem for Pattern Printing: Number Pyramid.

The Number Pyramid Pattern is one of the most commonly asked number pattern programs in Java coding interviews.

Unlike star patterns, Number Pyramid patterns use numbers instead of stars, making them slightly more challenging because they involve both loop control and number generation.

Interviewers frequently ask Number Pyramid problems to evaluate a candidate's understanding of:

  • Nested loops
  • Pattern recognition
  • Number manipulation
  • Symmetry
  • Mathematical thinking

Learning Number Pyramid patterns also helps in solving advanced interview questions like:

  • Palindrome Number Pyramid
  • Hollow Number Pyramid
  • Pascal's Triangle
  • Floyd's Triangle
  • Continuous Number Pyramid

What is a Number Pyramid?

A Number Pyramid is a triangular arrangement of numbers where each row contains numbers arranged in a specific pattern.

The simplest Number Pyramid prints the current row number repeatedly.

Example

        1
      2 2 2
    3 3 3 3 3
  4 4 4 4 4 4 4
5 5 5 5 5 5 5 5 5

Observe:

  • Every row starts with its row number.
  • Every row prints the same number repeatedly.
  • The pyramid is centered.
  • The width increases by two positions in every row.

Types of Number Pyramid Patterns

Java interviews may ask different variations of Number Pyramid.

Some common ones include:

Pattern Example
Repeated Number Pyramid 1, 2 2 2, 3 3 3 3 3
Increasing Number Pyramid 1, 1 2 1, 1 2 3 2 1
Continuous Number Pyramid 1, 2 3 4, 5 6 7 8 9
Palindrome Number Pyramid 1, 212, 32123
Hollow Number Pyramid Numbers only on boundaries

In this article, we focus on the Repeated Number Pyramid, which serves as the foundation for all other variations.

Difference Between Star Pyramid and Number Pyramid

Star Pyramid Number Pyramid
Uses * characters. Uses numbers.
Simpler printing logic. Requires number generation.
No changing values. Numbers change based on row or position.
Focuses on alignment. Focuses on both alignment and value generation.

Star Pyramid

    *
   ***
  *****
 *******
*********

Number Pyramid

        1
      2 2 2
    3 3 3 3 3
  4 4 4 4 4 4 4
5 5 5 5 5 5 5 5 5

Why is Number Pyramid Asked in Interviews?

Interviewers ask Number Pyramid because it tests multiple programming concepts together.

They evaluate whether candidates can:

  • Control nested loops.
  • Print centered patterns.
  • Generate numbers dynamically.
  • Understand row-column relationships.
  • Apply mathematical formulas.

It also serves as the base for solving more complex number-based patterns.

Understanding Number Placement

Suppose

Rows = 5

Output

        1
      2 2 2
    3 3 3 3 3
  4 4 4 4 4 4 4
5 5 5 5 5 5 5 5 5

Observe the pattern.

Row Printed Number Occurrences
1 1 1
2 2 3
3 3 5
4 4 7
5 5 9

Notice:

  • Row number equals the printed value.
  • Number of printed values follows:
2 × Row − 1

Mathematical Pattern

Suppose

Rows = 5

Pyramid Width

For every row,

Width

=

2 × Row − 1

Example

Row 4

Width

=

2 × 4 − 1

=

7

Leading Spaces

Before printing numbers,

Rows − Current Row

spaces are printed.

Example

Row Leading Spaces
1 4
2 3
3 2
4 1
5 0

Printed Number

Every position prints

Current Row

Visual Representation

For

Rows = 5

Row 1

        1

-------------------

Row 2

      2 2 2

-------------------

Row 3

    3 3 3 3 3

-------------------

Row 4

  4 4 4 4 4 4 4

-------------------

Row 5

5 5 5 5 5 5 5 5 5

Observe:

  • Width increases by 2.
  • Leading spaces decrease by 1.
  • Every row prints the same number repeatedly.

Pattern Output

Input

Rows = 5

Output

        1
      2 2 2
    3 3 3 3 3
  4 4 4 4 4 4 4
5 5 5 5 5 5 5 5 5

Understanding the Logic

There are three main steps.

Step 1

Print leading spaces.

Example

Row 3

Spaces

2

Step 2

Print numbers.

Each row prints

2 × Row − 1

numbers.

Every printed value equals

Current Row

Step 3

Move to the next line.

Repeat until all rows are completed.

Algorithm

Step 1

Read the number of rows.

rows = 5;

Step 2

Start the outer loop.

1

↓

Rows

Each iteration prints one row.

Step 3

Print leading spaces.

Rows − Current Row

Step 4

Print numbers.

Repeat

2 × Current Row − 1

times.

Step 5

Print

Current Row

for every position.

Step 6

Move to the next line.

Repeat until the pyramid is completed.

Dry Run

Input

Rows = 4

Row 1

Spaces

3

Numbers

1

Output

   1

Row 2

Spaces

2

Numbers

2 2 2

Output

  2 2 2

Row 3

Spaces

1

Numbers

3 3 3 3 3

Output

 3 3 3 3 3

Row 4

Numbers

4 4 4 4 4 4 4

Output

4 4 4 4 4 4 4

Final Output

   1
  2 2 2
 3 3 3 3 3
4 4 4 4 4 4 4

Approach 1 — Using Nested Loops

This is the standard interview solution.

The idea is simple:

  1. Print leading spaces.
  2. Print the row number repeatedly.
  3. Increase the width for every new row.

Complete Java Program

public class NumberPyramid {

    public static void main(String[] args) {

        int rows = 5;

        for (int i = 1; i <= rows; i++) {

            // Print leading spaces
            for (int j = i; j < rows; j++) {
                System.out.print("  ");
            }

            // Print numbers
            for (int j = 1; j <= (2 * i - 1); j++) {
                System.out.print(i + " ");
            }

            System.out.println();

        }

    }

}

Output

        1
      2 2 2
    3 3 3 3 3
  4 4 4 4 4 4 4
5 5 5 5 5 5 5 5 5

Step-by-Step Code Explanation

Step 1

Declare the number of rows.

int rows = 5;

Step 2

Create the outer loop.

for (int i = 1; i <= rows; i++)

Each iteration prints one row.

Step 3

Print leading spaces.

for (int j = i; j < rows; j++)

These spaces align the pyramid at the center.

Step 4

Print numbers.

for (int j = 1; j <= (2 * i - 1); j++)

Each row contains

2 × Row − 1

numbers.

Step 5

Print the current row number.

System.out.print(i + " ");

Every value in the current row is the same.

Example Execution

Input

Rows = 3

Output

    1
  2 2 2
3 3 3 3 3

Why Does This Work?

The algorithm combines three nested operations for each row:

  1. Leading spaces center the pyramid.
  2. The inner loop determines the width using the formula 2 × row − 1.
  3. The current row number (i) is printed repeatedly for every position.

Because the number of spaces decreases while the number of printed values increases, the output forms a perfectly centered Number Pyramid.

Advantages of This Approach

  • Easy to understand.
  • Uses simple nested loops.
  • Excellent for learning number-based patterns.
  • Frequently asked in Java interviews.
  • Forms the foundation for advanced number pyramid variations.
  • Uses only O(1) extra space.

Drawbacks

Although this is the standard interview solution, interviewers often ask follow-up questions such as:

  • Can you create a reusable printNumberPyramid() method?
  • Can you print a Palindrome Number Pyramid?
  • Can you print a Hollow Number Pyramid?
  • Can you generate continuous numbers instead of repeated numbers?
  • What is the time complexity?
  • Can you replace numbers with alphabets?

In Part 2, we'll cover:

  • Optimized Approach
  • Reusable printNumberPyramid() Method
  • Palindrome Number Pyramid
  • Hollow Number Pyramid
  • Continuous Number Pyramid
  • Time & Space Complexity
  • Comparison of Approaches
  • Common Interview Mistakes
  • Interview Follow-up Questions
  • Related Pattern Problems
  • Key Takeaways
  • Interview Tips

Approach 2 — Optimized Approach

The solution shown in Part 1 is already the optimal approach.

Every number and every space in the pyramid must be printed exactly once, so the algorithm cannot be improved beyond visiting each output position.

The optimization focuses on:

  • Cleaner code
  • Better readability
  • Reusable methods
  • Easier maintenance
  • Supporting multiple Number Pyramid variations

Optimized Java Program

public class NumberPyramidOptimized {

    public static void main(String[] args) {

        int rows = 5;

        for (int row = 1; row <= rows; row++) {

            // Print leading spaces
            for (int space = 1; space <= rows - row; space++) {
                System.out.print("  ");
            }

            // Print numbers
            for (int col = 1; col <= (2 * row - 1); col++) {
                System.out.print(row + " ");
            }

            System.out.println();
        }

    }

}

Output

        1
      2 2 2
    3 3 3 3 3
  4 4 4 4 4 4 4
5 5 5 5 5 5 5 5 5

Approach 3 — Using a Reusable Method

Instead of placing all logic inside main(), create a reusable method.

Advantages:

  • Better code organization
  • Reusable in multiple programs
  • Easier testing
  • Cleaner implementation

Java Program

public class NumberPyramidMethod {

    static void printNumberPyramid(int rows) {

        for (int row = 1; row <= rows; row++) {

            // Leading Spaces
            for (int space = 1; space <= rows - row; space++) {
                System.out.print("  ");
            }

            // Numbers
            for (int col = 1; col <= (2 * row - 1); col++) {
                System.out.print(row + " ");
            }

            System.out.println();

        }

    }

    public static void main(String[] args) {

        printNumberPyramid(5);

    }

}

Pattern Variation 1 — Palindrome Number Pyramid

Instead of printing the same number repeatedly, print numbers that increase and then decrease.

Output

        1
      2 3 2
    3 4 5 4 3
  4 5 6 7 6 5 4
5 6 7 8 9 8 7 6 5

Another commonly used interview variation is:

        1
      2 1 2
    3 2 1 2 3
  4 3 2 1 2 3 4
5 4 3 2 1 2 3 4 5

These patterns test number manipulation instead of simply repeating values.

Pattern Variation 2 — Hollow Number Pyramid

Print numbers only on the boundary.

Output

        1
      2   2
    3       3
  4           4
5 5 5 5 5 5 5 5 5

Rules:

  • Print numbers on the left boundary.
  • Print numbers on the right boundary.
  • Print the last row completely.
  • Print spaces inside.

Pattern Variation 3 — Continuous Number Pyramid

Instead of repeating row numbers, continue counting.

Output

            1
         2 3 4
      5 6 7 8 9
10 11 12 13 14 15 16

This variation is frequently asked after the basic Number Pyramid.

Pattern Variation 4 — Floyd's Style Pyramid

Print consecutive numbers row by row.

Output

1
2 3
4 5 6
7 8 9 10
11 12 13 14 15

Although different from a centered pyramid, interviewers often compare it with Number Pyramid problems.

Pattern Variation 5 — User Input

Allow users to specify the pyramid height.

Scanner scanner = new Scanner(System.in);

System.out.print("Enter rows: ");

int rows = scanner.nextInt();

printNumberPyramid(rows);

Dry Run

Input

Rows = 3

Row 1

Spaces

2

Numbers

1

Output

    1

Row 2

Spaces

1

Numbers

2 2 2

Output

  2 2 2

Row 3

Spaces

0

Numbers

3 3 3 3 3

Output

3 3 3 3 3

Final Output

    1
  2 2 2
3 3 3 3 3

Time Complexity

Suppose

n

is the number of rows.

Number Pyramid

Operation Complexity
Time O(n²)
Space O(1)

Palindrome Number Pyramid

Operation Complexity
Time O(n²)
Space O(1)

Hollow Number Pyramid

Operation Complexity
Time O(n²)
Space O(1)

Continuous Number Pyramid

Operation Complexity
Time O(n²)
Space O(1)

Comparison of Approaches

Approach Time Space Recommended
Basic Number Pyramid O(n²) O(1) Best for Beginners
Reusable Method O(n²) O(1) Production Ready
Palindrome Pyramid O(n²) O(1) Interview Favorite
Hollow Number Pyramid O(n²) O(1) Advanced
Continuous Number Pyramid O(n²) O(1) Frequently Asked

Common Mistakes

Mistake 1

Printing an incorrect number of values.

Wrong

row

Correct

2 * row - 1

Mistake 2

Using the column number instead of the row number.

Wrong

System.out.print(col);

Correct

System.out.print(row);

Mistake 3

Incorrect leading spaces.

Always print

rows - row

leading spaces.

Mistake 4

Printing spaces after every row instead of before the numbers.

The alignment should always be:

  1. Leading spaces
  2. Numbers
  3. New line

Mistake 5

Forgetting to print a new line.

Always end each row with:

System.out.println();

Interview Follow-up Questions

Q1. What is a Number Pyramid?

Q2. Why do we print 2 × row − 1 numbers?

Q3. How are leading spaces calculated?

Q4. What is the difference between a Number Pyramid and a Star Pyramid?

Q5. Can you print a Hollow Number Pyramid?

Q6. Can you print a Palindrome Number Pyramid?

Q7. Can you print continuous numbers?

Q8. What is the time complexity?

Q9. Can you print the pyramid using recursion?

Q10. Can you generate the pattern using methods?

Related Pattern Problems

  • Full Pyramid
  • Hollow Pyramid
  • Diamond Pattern
  • Hollow Diamond
  • Butterfly Pattern
  • Floyd's Triangle
  • Pascal's Triangle
  • Number Diamond
  • Alphabet Pyramid

Key Takeaways

  • A Number Pyramid is a centered triangular arrangement of numbers.
  • Every row contains 2 × row − 1 values.
  • Leading spaces decrease by one with each row.
  • The simplest Number Pyramid prints the current row number repeatedly.
  • The same loop structure can be reused for Palindrome, Hollow, and Continuous Number Pyramids.
  • The algorithm runs in O(n²) time using O(1) extra space.

Frequently Asked Interview Questions

Q1. Why does every row contain 2 × row − 1 numbers?

A centered pyramid expands equally on both sides. Each new row adds one position to the left and one to the right, increasing the width by two.

Q2. Why are leading spaces required?

Leading spaces ensure the numbers remain centered. Without them, the pattern becomes left-aligned instead of pyramid-shaped.

Q3. Why does the simplest Number Pyramid print the row number repeatedly?

Using the row number demonstrates the relationship between the current row and the generated output. It is the easiest number-based variation and forms the basis for more advanced patterns.

Q4. Can this solution be extended?

Yes. The same structure can be modified to build:

  • Palindrome Number Pyramid
  • Hollow Number Pyramid
  • Continuous Number Pyramid
  • Pascal's Triangle
  • Floyd's Triangle
  • Number Diamond

Only the value-generation logic changes.

Q5. What is the biggest difference between a Number Pyramid and a Palindrome Number Pyramid?

Number Pyramid Palindrome Number Pyramid
Repeats the same number across the row. Numbers increase and then decrease symmetrically.
Simple value generation. Requires additional number calculations.
Good beginner problem. Common advanced interview question.

Interview Tip

If an interviewer asks:

"Print a Number Pyramid in Java."

Break the solution into three simple steps:

  1. Print leading spaces to center the pyramid.
  2. Print 2 × row − 1 numbers.
  3. Print the current row number for each position.

Once you solve the basic pattern, explain that the same nested loop structure can be reused for Palindrome Number Pyramid, Hollow Number Pyramid, Continuous Number Pyramid, and Pascal's Triangle by changing only the number-generation logic. This demonstrates a strong understanding of reusable algorithms rather than memorizing individual patterns.