Rotating Number Pattern in PHP

Beginner

⏱️ 8 min read

📚 Updated: Aug 2026

🎯 3 Code Examples

🚀 Live Preview

Dual Inner Loops

Rotating number pattern output (12345, 23451, 34521, 45321, 54321) in PHP

Overview

What You’ll Learn

The rotating number pattern shifts the starting digit each row while keeping fixed width. This tutorial covers the two-part row rule, dual inner loops, a live preview, algorithm steps, worked PHP examples, edge cases, and complexity.

Shape Rule

Fixed width, rotating start

Every row prints exactly $rows digits; the starting value shifts from 1 up to $rows.

Part 1 Loop

i..rows

for ($j = $i; $j <= $rows; $j++) prints the ascending run like 2345.

Part 2 Loop

Wrap-around tail

for ($k = $i; $k > 1; $k--) appends $k-1 to complete the row.

Outer Loop

Row start i

for ($i = 1; $i <= $rows; $i++) shifts the rotation each line.

Live Preview

1–20 rows

Pick a row count and draw the rotating pattern instantly in the browser.

O(n²)

Complexity

Total digits = n × n; extra memory stays O(1).

Introduction

A rotating number pattern keeps every row the same length while the sequence wraps around. With $rows = 5, the output is 12345, 23451, 34521, 45321, and 54321.

In PHP you solve it with one outer loop and two inner loops per row: print $i..$rows, append $i-1..1, then call echo PHP_EOL to move to the next line.

Why it matters?

It teaches dual inner loops on the same row — a key step before wrap-around and cyclic patterns.

Key Highlights

Two Parts Per Row

Part 1: $i..$rows; Part 2: $i-1..1.

Fixed Row Width

Every row prints exactly $rows digits.

Print Then Break

echo $j and echo $k - 1 in the inner loops; echo PHP_EOL after.

Series Foundation

Follow Program 38 sequential triangle; continue to Program 40 alternating 1/0.

In short: for each row $i from 1 to $rows, print $i..$rows then $i-1..1, then call echo PHP_EOL.

Foundation

📝 Problem & Approach

Given a positive integer $rows, print a rotating number pattern: each row $i prints $i..$rows then $i-1..1 — exactly $rows digits per row.

PHP

// $rows = 5
//12345
//23451
//34521
//45321
//54321

Inputs & Outputs

Item	Type	Description
`$rows`	int	Number of rotating rows to print (typically ≥ 1).
Printed output	text	Fixed-width rows of rotating digits; row `$i` has exactly `$rows` digits.

Minimal workflow

Pseudocode

for i from 1 to rows:
    for j from i to rows: print j
    for k from i down to 2: print k-1
    print newline

Approach comparison

Approach	Idea	Best for
Dual inner loops per row	Outer row + two inner parts	Learning and interviews
Spaced / formatted output	Add spaces or `printf("%2d")` between digits	Readability for `$rows > 9`

Cheat Sheet

⚡ Quick Reference

Goal	Pattern
Walk each row	`for ($i = 1; $i <= $rows; $i++)`
Print ascending run	`for ($j = $i; $j <= $rows; $j++) echo $j;`
Append wrap-around	`for ($k = $i; $k > 1; $k--) echo $k - 1;`
End the row	`echo PHP_EOL;`
Program 38 variant	Shrinking width with global k counter instead of rotation

Compare

📋 Part 1 vs Part 2 vs Combined

Same rotating row — the two inner loops and their roles.

Part 1 (ascending)

$i..$rows

Prints 2345 when $i = 2 and $rows = 5

Part 2 (wrap)

$i-1..1

Appends 1 to complete 23451

Row length

always n

Both parts together always print $rows digits

Learning tip

trace i=2

Dry-run one row before coding the full pattern

Context

When This Pattern Shows Up

Reach for this pattern when teaching two inner loops on the same row.

First lab exercise
Most PHP pattern series start here before pyramids and diamonds.
Nested-loop warm-up
Outer/inner bound practice with an immediate visual check.
Console I/O practice
Combine loops with fgets(STDIN) for a flexible row count.
Gateway to variants
Compare Program 38 sequential triangle and Program 40 alternating 1/0 next.
Not a UI layout tool
This is a console teaching pattern — not how you build modern app screens.

Key benefit: one small program that locks in nested loops, output sequencing, and O(n²) thinking.

Interactive

🔮 Live Preview

Choose a row count between 1 and 20 and draw the rotating number pattern in the browser.

Hands-On

Examples Gallery

Three complete PHP programs — fixed row count, fgets(STDIN) input, and a spaced-output variant. Click View Output to reveal sample console results.

📚 Getting Started

Print five rows with dual inner loops per line.

Example 1 — Fixed `$rows = 5`

Hard-coded size — two inner loops build each rotating row.

PHP

<?php
$rows = 5;

for ($i = 1; $i <= $rows; $i++) {
    for ($j = $i; $j <= $rows; $j++) {
        echo $j;
    }
    for ($k = $i; $k > 1; $k--) {
        echo $k - 1;
    }
    echo PHP_EOL;
}

How It Works

When $i = 2, the first loop prints 2345 and the second appends 1, giving 23451. When $i = 5, the first loop prints 5 and the second appends 4321, giving 54321.

📈 Practical Variant

Let the user choose the height at runtime.

Example 2 — User Input Version

Read the maximum digit with trim(fgets(STDIN)) (check is_numeric() in real apps).

PHP

<?php
echo "Enter the maximum number: ";
$input = trim(fgets(STDIN));
if (!is_numeric($input)) {
    echo "Invalid input." . PHP_EOL;
    exit(1);
}
$rows = (int) $input;

for ($i = 1; $i <= $rows; $i++) {
    for ($j = $i; $j <= $rows; $j++) {
        echo $j;
    }
    for ($k = $i; $k > 1; $k--) {
        echo $k - 1;
    }
    echo PHP_EOL;
}

How It Works

Same dual-loop core as Example 1; only the source of $rows changes. Non-numeric input fails is_numeric() — validate before casting to int for safer labs.

⚡ Readability Variant

Same rotation with spaces between digits for easier reading.

Example 3 — Spaced Output

Append a space after each digit so multi-digit rows stay readable.

PHP

<?php
$rows = 5;

for ($i = 1; $i <= $rows; $i++) {
    for ($j = $i; $j <= $rows; $j++) {
        echo $j . " ";
    }
    for ($k = $i; $k > 1; $k--) {
        echo ($k - 1) . " ";
    }
    echo PHP_EOL;
}

How It Works

Same loop structure; only the print calls add + " " after each digit. Essential when $rows exceeds 9 or when demonstrating output formatting.

🧠 How the Algorithm Prints Rows

Set up

Set $rows = 5; and use fgets(STDIN) when reading input. Set loop variables $i, $j, $k.

Setup

Outer loop (rows)

for ($i = 1; $i <= $rows; $i++) picks the starting digit for each rotating row.

Row

Inner loop 1 (ascending)

for ($j = $i; $j <= $rows; $j++) prints the main run with echo $j.

Part 1

Inner loop 2 (wrap)

for ($k = $i; $k > 1; $k--) appends $k-1, then echo PHP_EOL ends the row.

Part 2

Pattern complete

Total digit prints: n × n — O(n²) time, O(1) extra memory.

Trace

🔎 Worked Walkthrough — `$rows = 4`

Trace each row: part 1 ($i..$rows) plus part 2 ($i-1..1).

`$i`	Part 1	Part 2	Full row
`1`	`1234`		`1234`
`2`	`234`	`1`	`2341`
`3`	`34`	`21`	`3421`
`4`	`4`	`321`	`4321`

Total digit prints: 4 × 4 = 16 = n².

Use Cases

Where this tiny pattern (and its loop structure) shows up beyond the homework prompt.

1. Teaching Nested Loops

Clearest visual proof that outer and inner bounds interact.

Example: change $j <= $i and watch the shape change.

2. Pattern Series Base

Foundation for inverted, pyramid, diamond, and hollow variants.

Example: change $k start to 100 for a shifted sequence.

3. Console Formatting Drills

Practice echo vs echo PHP_EOL without complex math.

Example: put echo PHP_EOL inside the inner loop by mistake.

4. Character Substitution

Swap digits for letters, stars, or spaced output once the loop works.

Example: use %4d when values exceed two digits.

5. Complexity Intuition

Square totals make O(n²) concrete for beginners.

Example: count printed digits for n = 10 → 100.

6. Input Validation Labs

Pair the pattern with fgets(STDIN) and positive-row checks.

Example: reject $rows <= 0 and re-prompt.

Pro Tip: when an interviewer asks for patterns, explain the outer/inner roles first — then write the loops. The story matters as much as the code.

Advantages

Why this pattern earns a permanent spot in beginner PHP courses.

1. Instant Visual Feedback
Wrong bounds show up immediately as a broken staircase.
2. Minimal Concepts
Only loops and console output — no arrays or math libraries.
3. Easy to Extend
Invert, center, hollow, or change the fill character with small edits.
4. O(1) Extra Memory
Streaming output needs no storage beyond loop counters.

Pro Tip: learn the two-loop row version first; then try spaced output for larger rows.

Usage Tips

Small habits that keep number-pattern code clean.

1. Name Bounds Clearly
Use $rows (or $n) and keep $i/$j/$k for loops — or rename to $row/$col.
2. Prefer fgets(STDIN)
Validate with is_numeric() when the user types letters instead of a number.
3. Keep echo PHP_EOL Outside
Only call echo PHP_EOL after the inner loop finishes the row.
4. Pick Field Width Early
Add spaces or %2d when rows exceeds 9.
5. Dry-Run One Small n
Trace $rows = 3 on paper before coding larger demos.

Pro Tip: if the output is a vertical list of single digits per line, you almost certainly put echo PHP_EOL inside the inner loop.

Common Pitfalls

Mistakes that commonly break rotating number patterns.

1. echo PHP_EOL Inside the Inner Loop
Each digit lands on its own line — you get a column, not a triangle.
→ Use echo $j and echo $k - 1; echo PHP_EOL only after both inner loops.
2. Wrong Inner Bound
Skipping the second inner loop leaves rows short — e.g. 2345 instead of 23451.
→ Run both loops: $j = $i..$rows then $k = $i..2 printing $k-1.
3. Forgetting the Row Break
Omitting echo PHP_EOL glues every digit onto one endless line.
→ Always end the row after the inner loop.
4. Unchecked STDIN input
Letters or empty input throw undefined rows.
→ Prefer fgets(STDIN) and re-prompt on failure.
5. Off-by-One on 0-Based Loops
Switching to i = 0 without adjusting the inner bound prints an empty first row or wrong counts.
→ If 0-based, print i with wrong inner bound (e.g. j <= i + 1).

Edge Cases

Check these inputs before calling the solution done.

$rows = 1

Single digit

Output is just 1 on one line.

$rows = 0

Empty pattern

Outer loop never runs — print nothing or show a message.

Negative

`$rows < 0`

Treat as invalid; re-prompt instead of silent empty output.

Large n

Many rows

Output grows as n² characters — fine for labs, noisy for huge n.

Bad input

Non-numeric STDIN input

Unchecked fgets(STDIN) leaves $rows unset — call is_numeric($input) first.

Fill char

Alphabet rotation

Try alphabet rotation (A..E) using the same two-loop structure.

Drill

🎯 Practice Problems

Try these variations to lock in the pattern.

1. Sequential decreasing triangle

Global $k counter with shrinking rows
Review Program 38

2. Alternating 1/0 pattern

Odd rows print 1, even rows print 0
Continue with Program 40

3. Reverse rotation

Start outer loop from $rows down to 1
Watch how the starting digit shifts backward

4. Spaced output

Add spaces between digits for rows > 9
See Example 3 on this page

Important

Notes

Square count. Total digit prints for n rows is n² — every row has n digits.
echo stays on the line; echo PHP_EOL advances — mix them carefully.
Validate $rows > 0 for interactive programs; $rows = 1 should print a single 1.
This page is left-aligned. Centered pyramids need leading spaces — covered later in the series.

Quick Takeaway: outer loop picks start $i, two inner loops build the row, then break the line.

Analysis

⏱️ Time and Space Complexity

Program	Time	Extra space
Nested loops (Examples 1–2)	`O(rows²)`	`O(1)`
Spaced output (Example 3)	`O(rows²)`	`O(1)`

Wrap Up

🎉 Conclusion

The rotating number pattern combines one outer loop with two inner loops per row — a natural step after sequential triangles. Master the compact digit output first, then optionally add spaces for readability.

Practice the three examples above, then continue to Program 40 for the alternating 1/0 pattern.

Row $i prints $i..$rows then $i-1..1 — keep echo PHP_EOL only after both inner loops finish.

View Examples Gallery Continue to Program 40

Pro Tips

💡 Best Practices

✅ Do

Explain part 1 ($i..$rows) and part 2 ($i-1..1) before coding
Use echo $j and echo $k - 1 in the inner loops and echo PHP_EOL after each row
Validate $rows ≥ 1 for interactive programs
Check is_numeric($input) before using $rows
State O(n²) time when asked about complexity

❌ Don’t

Call echo PHP_EOL inside the inner digit loop
Skip the second inner loop (rows come out too short)
Skip the newline after each row
Ignore bad console input in user-facing demos
Skip the $rows = 1 edge case

Summary

Key Takeaways

Knowledge Unlocked

Five things to remember about this rotating pattern

Print the pattern the beginner-friendly way.

Core concepts

△ 01

Rule

Row $i: $i..$rows then $i-1..1

Definition

↻ 02

Outer loop

Controls each row

Code

2 03

Two inner loops

Part 1 + Part 2 per row

Logic

n 04

Fixed width

n digits every row

I/O

O 05

Complexity

O(n²) time

Analysis

❓ Frequently Asked Questions

Why does the last row become 54321?

When $i=5 and $rows=5, the first loop prints 5, then the second loop appends 4, 3, 2, 1 — giving 54321.

Why use two inner loops per row?

The first loop prints the ascending run from $i to $rows. The second appends the wrap-around tail from $i-1 down to 1.

How is this different from Program 38?

Program 38 prints one continuous sequence with shrinking row widths. Program 39 keeps every row at $rows digits by wrapping back to smaller numbers.

Can I add spaces between digits?

Yes. Use echo $j . " " and echo ($k - 1) . " " in the loops, or build each row with string concatenation.

Does this work for rows greater than 9?

Yes, but digits run together without separators. Use spaces or printf("%2d") formatting for readability.

What is the time complexity?

O(n²) where n is rows. Each of n rows prints n digits.

How should I read the row count safely?

Use trim(fgets(STDIN)) and check is_numeric($input) before casting to int.

What happens if rows is 0 or negative?

The outer loop never runs, so nothing is printed. Validate and prompt again if you want a clear user message.

Did you Know? 🔊

Each row prints $i..$rows then $i-1..1 — two inner loops that create the rotation. Every row has exactly $rows digits, so total output is n² for n rows.

Continue to Program 40

Move on to the alternating 1/0 pattern in the PHP number-pattern series.

Program 40 tutorial →

About the author

Mari Selvan M P 🔗

Developer, cloud engineer, and technical writer

Experience 12 years building web and cloud systems
Focus Full Stack Development, AWS, and Developer Education

I write practical tutorials so students and working developers can learn by doing—from databases and APIs to deployment on AWS.

AWS Certified Developer – Associate (Credly)

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PHP Number Pattern 38 — Sequential Triangle Decreasing Width PHP Number Pattern 40 — Alternating 1/0

Rotating Number Pattern in PHP

What You’ll Learn

Shape Rule

Part 1 Loop

Part 2 Loop

Outer Loop

Live Preview

O(n²)

Introduction

Why it matters?

Two Parts Per Row

Fixed Row Width

Print Then Break

Series Foundation

📝 Problem & Approach

Inputs & Outputs

Minimal workflow

Approach comparison

⚡ Quick Reference

📋 Part 1 vs Part 2 vs Combined

When This Pattern Shows Up

First lab exercise

Nested-loop warm-up

Console I/O practice

Gateway to variants

Not a UI layout tool

🔮 Live Preview

Examples Gallery

📚 Getting Started

Example 1 — Fixed $rows = 5

How It Works

📈 Practical Variant

Example 2 — User Input Version

How It Works

⚡ Readability Variant

Example 3 — Spaced Output

How It Works

🧠 How the Algorithm Prints Rows

Set up

Outer loop (rows)

Inner loop 1 (ascending)

Inner loop 2 (wrap)

Pattern complete

🔎 Worked Walkthrough — $rows = 4

Use Cases

1. Teaching Nested Loops

2. Pattern Series Base

3. Console Formatting Drills

4. Character Substitution

5. Complexity Intuition

6. Input Validation Labs

Advantages

1. Instant Visual Feedback

2. Minimal Concepts

3. Easy to Extend

4. O(1) Extra Memory

Usage Tips

1. Name Bounds Clearly

2. Prefer fgets(STDIN)

3. Keep echo PHP_EOL Outside

4. Pick Field Width Early

5. Dry-Run One Small n

Common Pitfalls

1. echo PHP_EOL Inside the Inner Loop

2. Wrong Inner Bound

3. Forgetting the Row Break

4. Unchecked STDIN input

5. Off-by-One on 0-Based Loops

Edge Cases

Single digit

Empty pattern

$rows < 0

Many rows

Non-numeric STDIN input

Alphabet rotation

🎯 Practice Problems

1. Sequential decreasing triangle

2. Alternating 1/0 pattern

3. Reverse rotation

4. Spaced output

Example 1 — Fixed `$rows = 5`

🔎 Worked Walkthrough — `$rows = 4`

2. Prefer `fgets(STDIN)`

`$rows < 0`