An odd-length descending number triangle prints ascending digits 1..i, but only for odd row widths — so you see 1234567, 12345, 123, 1.
Rule: for i = max..1 step -2, print 1..i
1234567
12345
123
1 ← max = 7In PHP you solve it with an outer loop that steps by 2: for ($i = $max; $i >= 1; $i -= 2), an inner loop that prints each digit with echo $j, then echo PHP_EOL ends the row. Program 13 flips direction with $i % 2; this pattern always ascends but skips even widths.
Outer loop counts down from an odd $max with step 2. Inner loop prints 1..$i. End each row with echo PHP_EOL.
| Method | Idea | Best for |
|---|---|---|
| Step by 2 | Outer $i -= 2 visits only odd widths | Learning, interviews, exams |
| Every width | Same inner loop with $i-- for comparison | Seeing what the custom step skips |
for i from max down to 1 step 2:
for j from 1 to i:
print j (no newline)
print newline| Goal | Pattern |
|---|---|
| Walk odd widths | for ($i = $max; $i >= 1; $i -= 2) |
Print 1..i | for ($j = 1; $j <= $i; $j++) echo $j; |
| End the row | echo PHP_EOL; |
| Force odd max | if ($max % 2 === 0) $max -= 1; |
| Every width (compare) | for ($i = $max; $i >= 1; $i--) |
| API | Effect | Use for |
|---|---|---|
echo $j | Stays on the same line | Each digit in 1..i |
echo PHP_EOL | Ends the current line | After the inner loop |
Print all digits without a newline, then end the row once.
Change the maximum width and the odd-length triangle updates instantly — prefer odd values so the top row matches the classic demo.
Trace $max = 7 — each outer-loop value of $i, the inner range, and the printed row.
$i | Inner $j | Length | Printed row |
|---|---|---|---|
7 | 1..7 | 7 | 1234567 |
5 | 1..5 | 5 | 12345 |
3 | 1..3 | 3 | 123 |
1 | 1..1 | 1 | 1 |
Total digits are 7+5+3+1 = 16 — for odd max n, that equals ((n+1)/2)².
Three complete programs: fixed odd max, CLI input, and an every-width comparison. Use View Output for sample results.
$max = 7Hard-coded odd maximum — outer steps by 2, inner prints 1..i.
<?php
$max = 7;
for ($i = $max; $i >= 1; $i -= 2) {
for ($j = 1; $j <= $i; $j++) {
echo $j;
}
echo PHP_EOL;
}
?>1. Outer skips even widths. $i -= 2 visits 7, 5, 3, 1 only.
2. Inner prints ascending digits. $j runs from 1 to $i with echo $j.
3. End the row. Call echo PHP_EOL; only after the inner loop finishes.
Read the maximum width from the CLI. Prefer an odd value so the top row matches the classic demo.
<?php
echo "Enter an odd maximum (e.g. 9): ";
$max = (int) trim(fgets(STDIN));
for ($i = $max; $i >= 1; $i -= 2) {
for ($j = 1; $j <= $i; $j++) {
echo $j;
}
echo PHP_EOL;
}
?>1. Same loop core. Only the source of $max changes from a literal to CLI input.
2. Entering 5 stops early. You get three odd-length rows ending at 1.
3. Safer input tip. Validate and force an odd top width:
echo "Enter an odd maximum (e.g. 9): ";
$input = trim(fgets(STDIN));
if (!is_numeric($input) || (int) $input < 1) {
echo "Enter a positive whole number." . PHP_EOL;
exit(1);
}
$max = (int) $input;
if ($max % 2 === 0) {
$max -= 1;
}$i--)Same inner loop with a normal step — includes even lengths for comparison.
<?php
$max = 7;
for ($i = $max; $i >= 1; $i--) {
for ($j = 1; $j <= $i; $j++) {
echo $j;
}
echo PHP_EOL;
}
?>1. Only the step changed. $i-- visits every width; $i -= 2 in Example 1 skips the even ones.
2. Same inner rule. Digits still print 1..i with echo $j.
3. Compare side by side. Seeing both outputs makes the custom step easy to remember.
Check these before calling the solution done.
An even start prints even lengths (6, 4, 2). Force odd with if ($max % 2 === 0) $max -= 1;.
$i -= 2, not $i--$i-- reprints the every-width triangle (see Example 3).
echo $i instead of echo $jThat repeats the row length. This pattern prints the sequence value of $j.
echo PHP_EOL inside the inner loopThat puts each digit on its own line. Print digits without a newline; call echo PHP_EOL only after the row finishes.
Output is just 1 — a good sanity check.
The outer loop never runs. Validate and prompt again for clearer UX.
| Program | Time | Extra space |
|---|---|---|
| Odd widths (Examples 1–2) | O(n²) | O(1) |
| Every width (Example 3) | O(n²) | O(1) |
For odd max n you print 1+3+…+n digits — about half of the full triangle, but still O(n²).
$i from $max down by 2, print digits 1..i.$i -= 2 is what skips even row lengths.echo PHP_EOL advances after each row.0 and 1.One line: step $i down by 2 from an odd max, print 1..i with echo $j, then echo PHP_EOL.
Only odd-length rows print. The outer loop uses $i −= 2 (7, 5, 3, 1) and the inner loop prints 1..$i — still O(n²) total digit prints for maximum width n.
Continue with rows built from alternating 0 and 1.
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