An alternating zigzag number triangle shrinks from rows to 1. Odd lengths print 1..i; even lengths print i..1.
Remember
Rule: for i = n..1, if i odd print 1..i else print i..1
12345
4321
123
21
1 ← 5 rows
In PHP you solve it with a descending outer loop plus if/else on $i % 2: digits use echo $j, then echo PHP_EOL ends the row. Program 12 repeats one digit per row; this pattern prints a sequence and flips direction.
Approach
How to Solve It
Outer loop counts down from $rows to 1. If $i is odd, print 1..$i; if even, print $i..1. End each row with echo PHP_EOL.
Method
Idea
Best for
if / else loops
Parity picks ascending or descending inner loop
Learning, interviews, exams
start / end / step
One inner loop driven by three bounds
Leaner demos once parity clicks
Pseudocode
Pseudocode
for i from rows down to 1:
if i is even:
for j from i down to 1: print j
else:
for j from 1 to i: print j
print newline
Cheat sheet
Goal
Pattern
Shrink row length
for ($i = $rows; $i >= 1; $i--)
Odd length (ascend)
for ($j = 1; $j <= $i; $j++) echo $j;
Even length (descend)
for ($j = $i; $j >= 1; $j--) echo $j;
Pick direction
if ($i % 2 === 0) { ... } else { ... }
End the row
echo PHP_EOL;
Printing Numbers vs Starting a New Line
API
Effect
Use for
echo $j
Stays on the same line
Each digit in the sequence
echo PHP_EOL
Ends the current line
After the inner loop
Print all digits without a newline, then end the row once.
Try it
Live Preview
Change the row count and the zigzag triangle updates instantly — capped at 9 so every digit stays a single character.
Whole numbers from 1 to 9 (single digits). Tap a chip or type a value — the preview redraws as you go.
Live result5 rows · 15 digits
12345
4321
123
21
1
Trace
Worked Walkthrough
Trace $rows = 5 — each row length $i, its parity, the inner range, and the printed row.
$i
Parity
Inner $j
Printed row
5
odd
1..5
12345
4
even
4..1
4321
3
odd
1..3
123
2
even
2..1
21
1
odd
1..1
1
Row length is always $i; only the travel direction of $j changes with parity. Total digits: n(n+1)/2.
Code
PHP Programs
Three complete programs: fixed height, CLI input, and a start/end/step one-loop form. Use View Output for sample results.
Example 1 — Fixed $rows = 5
Outer loop shrinks the length; if/else picks ascending or descending digits.
1. Same zigzag rule. Odd lengths still climb; even lengths still fall.
2. Bounds replace the branch.$start, $end, and $step encode the two if/else loops in one place.
3. Learn the branch first. Prefer Examples 1–2 in class; use this form once the parity rule is clear.
Edge Cases & Pitfalls
Check these before calling the solution done.
echo $i
echo $i instead of echo $j
That repeats the row length. This pattern prints the sequence value of $j.
swapped parity
Odd descends / even ascends
Swapping the branches flips the zigzag and no longer matches 12345 / 4321.
PHP_EOL inside
echo PHP_EOL inside the inner loop
That puts each digit on its own line. Print digits without a newline; call echo PHP_EOL only after the row finishes.
rows = 1
Single digit
Output is just 1 — a good sanity check.
rows ≤ 0
Empty output
The outer loop never runs. Validate and prompt again for clearer UX.
multi-digit
$rows > 9
echo 10 prints two characters. Labs usually stick to 1–9 for a clean single-digit look.
Analysis
Time and Space Complexity
Program
Time
Extra space
if / else loops (Examples 1–2)
O(n²)
O(1)
start / end / step (Example 3)
O(n²)
O(1)
There are n rows printing n+(n-1)+…+1 digits, so total work is n(n+1)/2.
Remember
Key Takeaways
Rule: for $i = n..1, odd lengths print 1..i; even lengths print i..1.
Print $j: the sequence value lives in the inner counter, not the row length.
echo vs PHP_EOL: digits stay on the line; echo PHP_EOL advances after each row.
Next step: Program 14 keeps only odd-length rows of ascending sequences.
One line: shrink $i from n to 1; use $i % 2 to print 1..i or i..1 with echo $j, then echo PHP_EOL.
Frequently Asked Questions
The program checks whether i is even or odd. For odd i it prints 1..i ascending; for even i it prints i..1 descending, creating a zigzag direction.
The second row from the top has length i = 4, which is even. The even branch runs for ($j = i; $j >= 1; $j--) and prints 4, 3, 2, 1.
echo stays on the same line. echo PHP_EOL ends the current line. Digits use echo $j; the row break uses echo PHP_EOL after the inner loop.
Program 12 repeats the row digit with for ($j = $i; $j <= $rows; $j++) (11111, 2222, 333, 44, 5). Program 13 prints sequential digits 1..i or i..1 and alternates direction using i % 2.
O(n²) where n is the number of rows. Total echo calls equal n+(n-1)+…+1 = n(n+1)/2.
Yes. Swap the if and else branches so odd rows descend and even rows ascend — the zigzag still works, just mirrored.
Use trim(fgets(STDIN)) and check is_numeric($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?
Odd row length i prints 1..i; even row length prints i..1. The outer loop shrinks from rows to 1, and i % 2 flips direction — still O(n²) total digit prints.
