An alternating odd/even number triangle grows by one number each row, but switches between odd-only and even-only sequences based on the row’s parity.
Remember
Rule: odd rows start at 1; even rows start at 2;
then print i numbers with k += 2
1
2 4
1 3 5
2 4 6 8
1 3 5 7 9 ← rows = 5
In PHP you pick start value $k with $i % 2, print $k with a trailing space, update $k += 2, then echo PHP_EOL ends the row. Program 17 was odd-only with a left shift; this pattern flips parity per row.
Approach
How to Solve It
Pick the start with row parity, then print a growing odd or even stream with $k += 2.
Method
Idea
Best for
if / else start
Odd → $k = 1; even → $k = 2
Learning, interviews, exams
Ternary start
$k = ($i % 2 === 0) ? 2 : 1
Shorter demos once parity clicks
Pseudocode
Pseudocode
for i from 1 to rows:
if i is even:
k = 2
else:
k = 1
for j from 1 to i:
print k and a space
k = k + 2
print newline
Cheat sheet
Goal
Pattern
Grow row length
for ($i = 1; $i <= $rows; $i++)
Pick start
$k = ($i % 2 === 0) ? 2 : 1;
Print + step
echo $k . " "; $k += 2;
End the row
echo PHP_EOL;
Flip parity
$k = ($i % 2 === 0) ? 1 : 2;
Printing Numbers vs Starting a New Line
API
Effect
Use for
echo $k . " "
Stays on the same line
Each number in the row
echo PHP_EOL
Ends the current line
After the inner loop
Print all numbers without a newline, then end the row once.
Try it
Live Preview
Change the height and the odd/even triangle updates instantly.
Whole numbers from 1 to 12. Tap a chip or type a value — the preview redraws as you go.
Live result5 rows · 15 numbers
1
2 4
1 3 5
2 4 6 8
1 3 5 7 9
Trace
Worked Walkthrough
Trace four outer values when $rows = 5 — watch parity pick the start and $k += 2 keep the sequence.
$i
Parity
Start $k
Printed row
1
odd
1
1
2
even
2
2 4
3
odd
1
1 3 5
4
even
2
2 4 6 8
Total numbers are 1+2+3+4+5 = 15 — the triangular number n(n+1)/2.
Code
PHP Programs
Three complete programs: fixed height, CLI input with a ternary start, and flipped parity. Use View Output for sample results.
Example 1 — Fixed $rows = 5
Hard-coded height — if/else picks the start; the inner loop prints and steps by 2.
1. Swap the start map. Even $i → $k = 1; odd $i → $k = 2.
2. Same print + step. Inner loop and $k += 2 are unchanged.
3. Same triangle shape. Only which sequence lands on odd vs even rows flips.
Edge Cases & Pitfalls
Check these before calling the solution done.
wrong step
Use $k += 2, not $k++
If you use $k++, rows mix odds and evens. Keep the step at 2.
fixed start
All odds or all evens
Forgetting the parity check makes every row start at 1 (or 2). Use $i % 2 to switch.
PHP_EOL inside
echo PHP_EOL inside the inner loop
That puts each number on its own line. Print numbers without a newline; call echo PHP_EOL only after the row finishes.
rows = 1
Single number
Output is just 1 — a good sanity check for the odd-start path.
rows ≤ 0
Empty output
The outer loop never runs. Validate and prompt again for clearer UX.
spaces
Keep the trailing space
The classic sample uses echo $k . " " so numbers stay spaced and readable.
Analysis
Time and Space Complexity
Program
Time
Extra space
Fixed / input / flipped (Examples 1–3)
O(n²)
O(1)
There are n rows printing 1+2+…+n numbers, so total work is n(n+1)/2.
Remember
Key Takeaways
Rule: odd rows start at 1; even rows start at 2; then step by 2.
Width: row $i prints exactly $i numbers.
echo vs PHP_EOL: numbers stay on the line; echo PHP_EOL advances after each row.
Next step: Program 19 fills a triangle with the constant digit 5.
One line: set $k from row parity, print $i numbers with $k += 2, then echo PHP_EOL.
Frequently Asked Questions
We check $i % 2. If $i is odd, set $k = 1 for odd numbers; if $i is even, set $k = 2 for even numbers.
Row 2 is even, so $k starts at 2. The inner loop prints $k then adds 2 twice: 2, then 4.
echo $k . " " stays on the same line with a trailing space. echo PHP_EOL ends the current line. Numbers use echo; the row break uses echo PHP_EOL after the inner loop.
Row 3 is odd, so $k starts at 1 and increments by 2 three times: 1, 3, 5.
After printing $k, update $k += 2 so the sequence stays odd or even while increasing.
Yes. Swap the condition so even rows start at 1 and odd rows start at 2 — see Example 3.
O(n²) for n rows. Total number prints equal 1+2+…+n = n(n+1)/2.
Use trim(fgets(STDIN)) and check is_numeric($input) before casting to int so bad input does not produce unexpected results.
The outer loop never runs, so nothing is printed. Validate and prompt again if you want a clear user message.
🤔
Did you know?
Row parity picks the start value: odd rows begin at 1, even rows at 2. Then $k += 2 keeps each row odd-only or even-only — still O(n²) total prints for n rows.
