PHP Concentric Number Square Pattern

Beginner
5 min read
Updated: Sep 2026
3 programs
Live preview
Concentric number square pattern 5 down to 1 and back out in PHP programming
Definition

What Is This Pattern?

A concentric number square prints layers from $k down to 1: outer values stay large, the center is 1, and each row mirrors left-to-right.

Remember
Rule: print max(i, j) style via (j > i ? j : i); left k..1, right 2..k

5 5 5 5 5 5 5 5 5
5 4 4 4 4 4 4 4 5
5 4 3 3 3 3 3 4 5
5 4 3 2 2 2 3 4 5
5 4 3 2 1 2 3 4 5   ← k = 5

In PHP outer loop $i from $k down to 1. Per row: left half $j = $k..1, right half $j = 2..$k, value $j > $i ? $j : $i.

Approach

How to Solve It

One outer layer loop, then left and right halves with the same cell rule.

MethodIdeaBest for
Two-half rowLeft $k..1, right 2..$k, value $j > $i ? $j : $iLearning, interviews, exams
Input $kSame logic with a user-chosen peakPractice / demos

Pseudocode

Pseudocode
for i from k down to 1:
    for j from k down to 1:
        print (j if j > i else i) and a space
    for j from 2 to k:
        print (j if j > i else i) and a space
    print newline

Cheat sheet

GoalPattern
Layer loopfor ($i = $k; $i >= 1; $i--)
Left halffor ($j = $k; $j >= 1; $j--)
Right halffor ($j = 2; $j <= $k; $j++)
Cell valueecho ($j > $i ? $j : $i) . " ";
End the rowecho PHP_EOL;

Printing Numbers vs Starting a New Line

APIEffectUse for
echo ($j > $i ? $j : $i) . " "Stays on the same lineEach number plus a trailing space
echo PHP_EOLEnds the current lineAfter both half-loops finish a row

Print numbers without a newline, then end the row once.

Try it

Live Preview

Change $k and the concentric square updates instantly.

Whole numbers from 1 to 9. Width = 2k - 1. Tap a chip or type a value — the preview redraws as you go.

Live result k = 5 · 5 × 9
5 5 5 5 5 5 5 5 5 
5 4 4 4 4 4 4 4 5 
5 4 3 3 3 3 3 4 5 
5 4 3 2 2 2 3 4 5 
5 4 3 2 1 2 3 4 5
Trace

Worked Walkthrough — $k = 3

Trace each layer: left half, then mirrored right half.

$iLeft $j=3..1Right $j=2..3Printed row
33 3 33 33 3 3 3 3
23 2 22 33 2 2 2 3
13 2 12 33 2 1 2 3

Rows = $k, columns = 2*$k - 1. Total cells for $k = 5 = 5 × 9 = 45.

Code

PHP Programs

Three complete programs: fixed $k = 5, user-input $k, and a compact $k = 3 demo. Use View Output for sample results.

Example 1 — Fixed $k = 5

If-else cell rule with explicit left and right half-loops.

PHP
<?php
$k = 5;

for ($i = $k; $i >= 1; $i--) {
    for ($j = $k; $j >= 1; $j--) {
        if ($j > $i)
            echo $j . " ";
        else
            echo $i . " ";
    }

    for ($j = 2; $j <= $k; $j++) {
        if ($j > $i)
            echo $j . " ";
        else
            echo $i . " ";
    }

    echo PHP_EOL;
}

How It Works

1. Layers. $i runs from 5 down to 1 — each value is one concentric row.

2. Left half. $j runs $k..1; print $j when $j > $i, else print $i.

3. Right half. $j runs 2..$k with the same rule so the row mirrors without doubling the center.

Example 2 — User Input ($k)

Read $k and use a ternary for the cell value.

PHP
<?php
echo "Enter k: ";
$input = trim(fgets(STDIN));
if (!is_numeric($input) || (int) $input < 1) {
    echo "Please enter a positive whole number." . PHP_EOL;
    exit(1);
}

$k = (int) $input;

for ($i = $k; $i >= 1; $i--) {
    for ($j = $k; $j >= 1; $j--)
        echo ($j > $i ? $j : $i) . " ";

    for ($j = 2; $j <= $k; $j++)
        echo ($j > $i ? $j : $i) . " ";

    echo PHP_EOL;
}

How It Works

1. Validate k. Check is_numeric; require $k >= 1.

2. Same square. Only the peak value changes; width becomes 2*$k - 1.

Example 3 — Compact $k = 3

A smaller fixed demo — easy to trace before scaling to 5.

PHP
<?php
$k = 3;

for ($i = $k; $i >= 1; $i--) {
    for ($j = $k; $j >= 1; $j--)
        echo ($j > $i ? $j : $i) . " ";

    for ($j = 2; $j <= $k; $j++)
        echo ($j > $i ? $j : $i) . " ";

    echo PHP_EOL;
}

How It Works

1. Same rules. Layer down; left then right; ternary picks $j or $i.

2. Quick check. Three rows, five columns; center of the last row is 1.

Edge Cases & Pitfalls

Check these before calling the solution done.

j = 1..k

Right half starts at $j = 1

The center digit prints twice. Start the mirror loop at $j = 2.

i++

Outer loop goes 1..$k

You get the inverted order (center first). Keep $i from $k down to 1.

j < i

Flip the comparison

Using $j < $i inverts layers. Stay with $j > $i ? $j : $i.

k = 1

Single cell

Output is just 1 — the right half loop never runs.

PHP_EOL

echo PHP_EOL inside a half-loop

That breaks the row. Call echo PHP_EOL only after both inner loops.

Bad input

Casting without checks

Prefer is_numeric after trim(fgets(STDIN)) so non-numeric input does not silently become 0.

Analysis

Time and Space Complexity

ProgramTimeExtra space
Fixed / compact (Examples 1, 3)O($k²)O(1)
User input (Example 2)O($k²)O(1)

There are $k rows and 2*$k - 1 cells per row, so total prints are about 2*$k² — quadratic in $k.

Remember

Key Takeaways

  • Rule: layers $k..1; cell value is $j > $i ? $j : $i.
  • Shape: left $k..1, right 2..$k — width 2*$k - 1.
  • echo vs PHP_EOL: numbers stay on the line; echo PHP_EOL advances after both halves.
  • Next step: Program 47 extends this into a full concentric number diamond.

One line: for each layer, print a mirrored row using $j > $i ? $j : $i.

Frequently Asked Questions

A concentric number square: the outer layer is k (e.g. 5), values decrease toward the center to 1, then mirror back out on each row.
Each row prints a left half ($j = $k..1) and a right half ($j = 2..$k) with the same $j > $i rule, mirroring around the center.
When column $j is still outside the current row layer $i, print $j. Otherwise print $i (the current layer value).
The first builds the left descending half; the second mirrors columns 2..k on the right without repeating the center digit.
Change $k (or read it from input). Total width becomes 2*$k - 1 — see Example 2.
O(k²) because each of k rows prints about 2k - 1 cells.
Program 45 prints a star-and-zero X on a fixed grid. Program 46 prints decreasing/increasing numbers in a concentric square.
Each row has 2*$k - 1 numbers. For $k = 5, width is 9 columns.
Use trim(fgets(STDIN)) and check is_numeric($input) before casting to int — see Example 2.

Did you know?

Each cell prints $j when $j > $i, else $i. Row $i runs from $k down to 1; grid width = 2k - 1 columns per row.

Next: Concentric Number Diamond

Mirror this square top and bottom into a full diamond (5..1..5).

Program 47 tutorial →

About the author

Mari Selvan M P
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 45 — X Pattern with Stars and Zeros PHP Number Pattern 47 — Concentric Number Diamond