PHP Sequential Number Triangle Pattern (Narrowing)

Beginner

5 min read

Updated: Sep 2026

3 programs

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Decreasing row length continuous number triangle in PHP programming

Definition

What Is This Pattern?

A decreasing continuous number triangle prints values from a shared counter $k that never resets, while each row prints one fewer number than the row above.

Remember

Rule: row i prints (rows - i + 1) values of k++

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

In PHP the inner loop runs from $rows down to $i, so the first row is the longest. Use printf("%3d", $k++) to keep columns aligned past single digits.

Approach

How to Solve It

One nested-loop idea with a shared counter and format width.

Method	Idea	Best for
Counter + shrink	Print `$k++` while row length shrinks	Learning, interviews, exams
User-input rows	Same logic with a variable height	Practice / demos

Pseudocode

k = 1
for i from 1 to rows:
    for j from rows down to i:
        print k (width 3), then k = k + 1
    print newline

Cheat sheet

Goal	Pattern
Shrink each row	`for ($i = 1; $i <= $rows; $i++)`
Row length	`for ($j = $rows; $j >= $i; $j--)`
Next number	`printf("%3d", $k++);`
End the row	`echo PHP_EOL;`

Printing Numbers vs Starting a New Line

API	Effect	Use for
`printf("%3d", $k++)`	Stays on the same line	Each formatted number
`echo PHP_EOL`	Ends the current line	After the inner loop

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

Try it

Live Preview

Change the row count and the shrinking continuous triangle updates instantly.

Trace

Worked Walkthrough — `$rows = 4`

Trace how many values each row takes from counter $k.

`$i`	Count / values	Printed row
`1`	4 / `1..4`	`1 2 3 4`
`2`	3 / `5..7`	`5 6 7`
`3`	2 / `8 9`	`8 9`
`4`	1 / `10`	`10`

Row length is $rows - $i + 1. Counter $k ends at n(n+1)/2.

Code

PHP Programs

Three complete programs: fixed height, CLI input, and a compact 3-row demo. Use View Output for sample results.

Example 1 — Fixed `$rows = 5`

Shrinking inner loop prints continuous $k++ values with width-3 formatting.

PHP

<?php
$rows = 5;
$k = 1;

for ($i = 1; $i <= $rows; $i++) {
    for ($j = $rows; $j >= $i; $j--)
        printf("%3d", $k++);

    echo PHP_EOL;
}

How It Works

1. Outer loop. $i grows from 1 to 5 — each pass shortens the row by one.

2. Inner loop. $j runs from $rows down to $i, so row 1 prints 5 values and row 5 prints 1.

3. Continuous $k. $k lives outside the loops and climbs from 1 to 15 without resetting.

Example 2 — User Input

Read the row count from STDIN; the inner loop uses $rows as the starting width.

PHP

<?php
echo "Enter rows: ";
$input = trim(fgets(STDIN));

if (!is_numeric($input) || (int) $input < 1) {
    echo "Please enter a positive whole number." . PHP_EOL;
    exit(1);
}

$rows = (int) $input;
$k = 1;

for ($i = 1; $i <= $rows; $i++) {
    for ($j = $rows; $j >= $i; $j--)
        printf("%3d", $k++);

    echo PHP_EOL;
}

How It Works

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

2. Same counter. Three rows print values 1 through 6 with shrinking width.

Example 3 — Compact `$rows = 3`

A smaller fixed demo — same continuous counter, easier to trace by hand.

PHP

<?php
$rows = 3;
$k = 1;

for ($i = 1; $i <= $rows; $i++) {
    for ($j = $rows; $j >= $i; $j--)
        printf("%3d", $k++);

    echo PHP_EOL;
}

How It Works

1. Same rules. Inner loop length is $rows - $i + 1; each cell prints the next $k.

2. Quick check. The last row is a single formatted 6.

Edge Cases & Pitfalls

Check these before calling the solution done.

reset $k

Reset `$k = 1` each row

That restarts the sequence every line. Keep $k outside both loops.

wrong bound

Loop `$j` down to 1 instead of `$i`

Every row would print the same length. Stop at $j >= $i.

no format

Use `echo $k++` without width

Columns drift once values hit 10+. Prefer printf("%3d", $k++).

rows = 1

Single `1`

Output is just the formatted 1.

rows ≤ 0

Empty output

The outer loop never runs. Validate and prompt again for clearer UX.

Bad input

`(int)` alone is not enough

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

Analysis

Time and Space Complexity

Program	Time	Extra space
Fixed / compact (Examples 1, 3)	`O(n²)`	`O(1)`
User input (Example 2)	`O(n²)`	`O(1)`

Total printed values are n + (n-1) + … + 1 = n(n+1)/2, which is quadratic in n.

Remember

Key Takeaways

Rule: print continuous $k++; row $i has length $rows - $i + 1.
Inner bound: for ($j = $rows; $j >= $i; $j--) shrinks the row each time.
printf vs PHP_EOL: numbers stay on the line; echo PHP_EOL advances after each row.
Next step: Program 39 prints a rotating number pattern (12345, 23451, …).

One line: for each row, print the next values from a shared counter while the row length shrinks by one.

Frequently Asked Questions

What pattern does this program print?

Continuous numbers starting from 1, but each row has one fewer number: 5 on row 1, then 4, 3, 2, and 1 — totaling 15 numbers for 5 rows.

Why do numbers continue instead of resetting?

Counter $k starts at 1 before the loops and increments with $k++ each time a number prints — it is never reset inside the outer loop.

How many numbers does row i print?

Row i prints rows - i + 1 numbers — the inner loop runs from $j = $rows down to $i.

Why use %3d in printf?

The format specifier reserves 3 columns per number, keeping columns aligned when values become two digits.

How is this different from Program 35?

Program 35 is right-aligned with leading spaces. Program 38 is left-aligned with decreasing row width and the same continuous counter.

How do I change the number of rows?

Replace 5 with $rows in the outer loop bound — see Example 2.

What is the time complexity?

O(n²) for n rows because total prints are 1 + 2 + ... + n = n(n+1)/2.

How should I read rows safely?

Use trim(fgets(STDIN)) and check is_numeric($input) before casting to int — see Example 2.

What happens when rows is 1?

Only one row prints — a single number 1.

Did you know?

A counter $k starts at 1 and increments every time a number prints. Row $i prints $rows - $i + 1 numbers with printf("%3d", $k++) — total prints = n(n+1)/2.

Next: Rotating Number Pattern

Rotate the digit sequence on each row (12345, 23451, 34512…).

Program 39 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 37 — Palindrome Number Triangle PHP Number Pattern 39 — Rotating Number Pattern

PHP Sequential Number Triangle Pattern (Narrowing)

What Is This Pattern?

How to Solve It

Pseudocode

Cheat sheet

Printing Numbers vs Starting a New Line

Live Preview

Worked Walkthrough — $rows = 4

PHP Programs

Example 1 — Fixed $rows = 5

How It Works

Example 2 — User Input

How It Works

Example 3 — Compact $rows = 3

How It Works

Edge Cases & Pitfalls

Reset $k = 1 each row

Loop $j down to 1 instead of $i

Use echo $k++ without width

Single 1

Empty output

(int) alone is not enough

Time and Space Complexity

Key Takeaways

Frequently Asked Questions

Did you know?

Related Topics

Number Patterns Hub

Program 37

Program 39

Same Pattern in C#

Next: Rotating Number Pattern

About the author

Worked Walkthrough — `$rows = 4`

Example 1 — Fixed `$rows = 5`

Example 3 — Compact `$rows = 3`

Reset `$k = 1` each row

Loop `$j` down to 1 instead of `$i`

Use `echo $k++` without width

Single `1`

`(int)` alone is not enough