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easyBasicsSometimes asked

Number Triangle

Basics · 6 min

Given n, return a triangle where row i contains the numbers 1..i, e.g. row 3 is 123. Rows separated by newlines.

In plain English

Nested loop where the inner loop prints 1..i.

Examples

Example 1

Input: n = 3
Output: "1\n12\n123"
Note: Increasing per row.

Example 2

Input: n = 1
Output: "1"
Note: Single.

Example 3

Input: n = 4
Output: "1\n12\n123\n1234"
Note: Four rows.

Constraints

1 ≤ n ≤ 9

Clarifying questions1First question: Single-digit assumption?Explore questions

Q1.Single-digit assumption?
Yes, n ≤ 9 keeps columns aligned.

Quick interview revision

Understand

30-second explanation

Build the interview-ready mental model before comparing implementations.

Outer row 1..n; inner loop appends j for j = 1..i; newline between rows.

Interview contextWhat is testedWhere candidates slipHow to stand outExplore interview context

What's being tested

Whether you reuse the nested-loop skeleton with a different cell value.

Where candidates slip

Emitting the row index instead of the column index.

How to stand out

Articulate that pattern problems share one skeleton.

Choose

Compare the available approaches

Use constraints and trade-offs to select the route you can defend in an interview.

Learn & trace

Build each solution step by step

Move from the core idea to a visual trace, implementation, proof, and edge cases.

03.1

Approach 1 of 1 · Optimal

Nested numeric loop

TimeO(n²)SpaceO(n²)

This is the standard, expected solution — lead with it.

Stuck? Progressive hintsReveal one at a time

1Hint 1Explore hint

Start from the star triangle — what single thing changes?

2Hint 2Explore hint

Print the inner loop variable j, not a star.

3Hint 3Explore hint

Why is n capped at 9?

A · Core idea

Same nested structure as the star triangle, but the inner loop emits the running number j (1..i) instead of a fixed star — so row 3 is 123.

The one change from the star version. Replace the constant '*' with the inner loop variable j. Everything else — outer row loop, inner bound i, newlines between rows — is identical. Recognising that a pattern problem is 'the same skeleton with a different cell value' is the transferable insight.

Why n ≤ 9. Capping n at 9 keeps each printed number a single digit, so the columns line up; beyond 9 the multi-digit numbers would misalign.

Print j, not i. Emitting the outer index i (a fixed value per row) instead of the inner j is the common slip.

B · Visual dry run

Interactive dry run

Select a frame to connect the decision with its visual state.

n = 3

row 1

State"1"

Final result"1\n12\n123"

C · Code with teaching comments

solution.javaJava

Nested numeric loop — optimal

1
public String numberTriangle(int n) {
2
    StringBuilder sb = new StringBuilder();
3
    for (int i = 1; i <= n; i++) {
4
        for (int j = 1; j <= i; j++) sb.append(j);
5
        if (i < n) sb.append('\n');
6
    }
7
    return sb.toString();
8
}

D · Why it works and complexityO(n²) timeO(n²) spaceOpen the invariant and proofExplore the proof

ComplexityO(n²) time, O(n²) space — row i emits i digits; total is O(n²).

E · Edge cases and pitfalls4n = 1 — "1".Explore edge cases

Edge cases handled

n = 1"1".
n = 4"1\n12\n123\n1234".

Pitfalls

Printing i instead of the running j.
Off-by-one in the inner bound.

Practice

Try the solution yourself

Edit the optimal implementation, test another input, and observe the result.

Editable code previewpublic String numberTriangle(int n) { StringBuilder sb = new StringBuilder(); for (int i = 1; i <= n; i++) { for (int j = 1; j <= i; j++) sb.append(j); if (i < n) sb.append('\n');Explore the playground

Try it — Java· run a complete program; method snippets need a driver

Avoid mistakes

Recognize the interview traps

Understand why common attempts fail before reviewing the corrected implementation.

Printing i instead of the running j.
Off-by-one in the inner bound.

Revise

Carry the pattern into the interview

Quick interview revision

Pattern to remember

Nested numeric loop

Code pattern to memorize

for i in 1..n: for j in 1..i: print(j)

Rules to remember

1Outer = rows.
2Inner prints 1..i.
3Newlines between rows.

Use this pattern when

Index-valued patterns

Interview takeaway

Swap the star for the loop variable to print numbers.

Continue

Transfer the pattern to another problem

Use a direct variation or pattern sibling to prove the idea is reusable.

Transferable patternA core fresher pattern: Nested numeric loop. Master it on small inputs and it transfers to harder problems.

Practice queueDirect variations and pattern siblings

Direct follow-ups

Right Triangle Star
The star version of the same skeleton.

easyBasicsSometimes asked

Number Triangle

Basics · 6 min

Given n, return a triangle where row i contains the numbers 1..i, e.g. row 3 is 123. Rows separated by newlines.

In plain English

Nested loop where the inner loop prints 1..i.

Examples

Example 1

Input: n = 3
Output: "1\n12\n123"
Note: Increasing per row.

Example 2

Input: n = 1
Output: "1"
Note: Single.

Example 3

Input: n = 4
Output: "1\n12\n123\n1234"
Note: Four rows.

Constraints

1 ≤ n ≤ 9

Clarifying questions1First question: Single-digit assumption?Explore questions

Q1.Single-digit assumption?
Yes, n ≤ 9 keeps columns aligned.

Quick interview revision

Understand

30-second explanation

Build the interview-ready mental model before comparing implementations.

Outer row 1..n; inner loop appends j for j = 1..i; newline between rows.

Interview contextWhat is testedWhere candidates slipHow to stand outExplore interview context

What's being tested

Whether you reuse the nested-loop skeleton with a different cell value.

Where candidates slip

Emitting the row index instead of the column index.

How to stand out

Articulate that pattern problems share one skeleton.

Choose

Compare the available approaches

Use constraints and trade-offs to select the route you can defend in an interview.

Learn & trace

Build each solution step by step

Move from the core idea to a visual trace, implementation, proof, and edge cases.

03.1

Approach 1 of 1 · Optimal

Nested numeric loop

TimeO(n²)SpaceO(n²)

This is the standard, expected solution — lead with it.

Stuck? Progressive hintsReveal one at a time

1Hint 1Explore hint

Start from the star triangle — what single thing changes?

2Hint 2Explore hint

Print the inner loop variable j, not a star.

3Hint 3Explore hint

Why is n capped at 9?

A · Core idea

Same nested structure as the star triangle, but the inner loop emits the running number j (1..i) instead of a fixed star — so row 3 is 123.

Why n ≤ 9. Capping n at 9 keeps each printed number a single digit, so the columns line up; beyond 9 the multi-digit numbers would misalign.

Print j, not i. Emitting the outer index i (a fixed value per row) instead of the inner j is the common slip.

B · Visual dry run

Interactive dry run

Select a frame to connect the decision with its visual state.

n = 3

row 1

State"1"

Final result"1\n12\n123"

C · Code with teaching comments

solution.javaJava

Nested numeric loop — optimal

1
public String numberTriangle(int n) {
2
    StringBuilder sb = new StringBuilder();
3
    for (int i = 1; i <= n; i++) {
4
        for (int j = 1; j <= i; j++) sb.append(j);
5
        if (i < n) sb.append('\n');
6
    }
7
    return sb.toString();
8
}

D · Why it works and complexityO(n²) timeO(n²) spaceOpen the invariant and proofExplore the proof

ComplexityO(n²) time, O(n²) space — row i emits i digits; total is O(n²).

E · Edge cases and pitfalls4n = 1 — "1".Explore edge cases

Edge cases handled

n = 1"1".
n = 4"1\n12\n123\n1234".

Pitfalls

Printing i instead of the running j.
Off-by-one in the inner bound.

Practice

Try the solution yourself

Edit the optimal implementation, test another input, and observe the result.

Try it — Java· run a complete program; method snippets need a driver

Avoid mistakes

Recognize the interview traps

Understand why common attempts fail before reviewing the corrected implementation.

Printing i instead of the running j.
Off-by-one in the inner bound.

Revise

Carry the pattern into the interview

Quick interview revision

Pattern to remember

Nested numeric loop

Code pattern to memorize

for i in 1..n: for j in 1..i: print(j)

Rules to remember

1Outer = rows.
2Inner prints 1..i.
3Newlines between rows.

Use this pattern when

Index-valued patterns

Interview takeaway

Swap the star for the loop variable to print numbers.

Continue

Transfer the pattern to another problem

Use a direct variation or pattern sibling to prove the idea is reusable.

Transferable patternA core fresher pattern: Nested numeric loop. Master it on small inputs and it transfers to harder problems.

Practice queueDirect variations and pattern siblings

Direct follow-ups

Right Triangle Star
The star version of the same skeleton.