An alternating binary number triangle grows one digit per row, printing 0 or 1 from $j % 2 as the inner index counts down.
Rule: outer i = 1..rows; inner j = i..1; print j % 2
1
01
101
0101
10101 ← rows = 5In PHP you solve it with an ascending outer loop and a descending inner loop: echo $j % 2 prints each bit, then echo PHP_EOL ends the row. Program 16 flips the inner direction (1..i) for a related shape.
Outer loop from 1 to $rows. Inner loop from current $i down to 1, printing $j % 2. End each row with echo PHP_EOL.
| Method | Idea | Best for |
|---|---|---|
Descending + $j % 2 | Count j down; print parity as the bit | Learning, interviews, exams |
| Flip bits | Print 1 - ($j % 2) | Complementary triangle labs |
for i from 1 to rows:
for j from i down to 1:
print j % 2 (no newline)
print newline| Goal | Pattern |
|---|---|
| Grow row length | for ($i = 1; $i <= $rows; $i++) |
| Print binary digit | for ($j = $i; $j >= 1; $j--) echo $j % 2; |
| End the row | echo PHP_EOL; |
| Flip every bit | echo 1 - ($j % 2); |
| Program 16 twin | for ($j = 1; $j <= $i; $j++) echo $j % 2; |
| API | Effect | Use for |
|---|---|---|
echo $j % 2 | Stays on the same line | Each binary digit |
echo PHP_EOL | Ends the current line | After the inner loop |
Print all bits without a newline, then end the row once.
Change the row count and the binary triangle updates instantly.
Trace three outer values when $rows = 5 — watch $j % 2 flip as $j counts down.
$i | Inner $j | $j % 2 | Printed row |
|---|---|---|---|
1 | 1 | 1 | 1 |
2 | 2, 1 | 0, 1 | 01 |
3 | 3, 2, 1 | 1, 0, 1 | 101 |
5 | 5..1 | 1,0,1,0,1 | 10101 |
Total digits are 1+2+3+4+5 = 15 — the triangular number n(n+1)/2.
Three complete programs: fixed height, flipped bits, and CLI input. Use View Output for sample results.
$rows = 5Outer grows, inner counts down, print $j % 2.
<?php
$rows = 5;
for ($i = 1; $i <= $rows; $i++) {
for ($j = $i; $j >= 1; $j--) {
echo $j % 2;
}
echo PHP_EOL;
}
?>1. Outer grows the length. $i runs from 1 to $rows — that is how many bits each row gets.
2. Inner prints parity. $j counts down from $i to 1; $j % 2 is the bit.
3. End the row. Call echo PHP_EOL; only after the inner loop finishes.
1 - ($j % 2)Invert every bit so the first row starts with 0 instead of 1.
<?php
$rows = 5;
for ($i = 1; $i <= $rows; $i++) {
for ($j = $i; $j >= 1; $j--) {
echo 1 - ($j % 2);
}
echo PHP_EOL;
}
?>1. Same loop bounds. Outer and inner ranges match Example 1.
2. Flip the bit. 1 - ($j % 2) turns 1 into 0 and 0 into 1.
3. First row becomes 0. Useful when a lab asks for the complementary binary triangle.
Read the row count from the CLI. Prefer is_numeric in real apps (shown in the tip below).
<?php
echo "Enter the number of rows: ";
$rows = (int) trim(fgets(STDIN));
for ($i = 1; $i <= $rows; $i++) {
for ($j = $i; $j >= 1; $j--) {
echo $j % 2;
}
echo PHP_EOL;
}
?>1. Same loop core. Only the source of $rows changes from a literal to CLI input.
2. Entering 4 stops early. You get four binary rows ending at 0101.
3. Safer input tip. Bare (int) casts turn letters into 0. Prefer:
echo "Enter the number of rows: ";
$input = trim(fgets(STDIN));
if (!is_numeric($input) || (int) $input < 1) {
echo "Enter a positive whole number." . PHP_EOL;
exit(1);
}
$rows = (int) $input;Check these before calling the solution done.
for ($j = 1; $j <= $i; $j++)That is Program 16 (1, 10, 101). Keep counting down for this pattern.
echo $j instead of echo $j % 2That prints the countdown numbers. This pattern needs the parity bit only.
echo PHP_EOL inside the inner loopThat puts each bit on its own line. Print bits 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.
The classic sample is concatenated (10101), not spaced (1 0 1 0 1).
| Program | Time | Extra space |
|---|---|---|
| Fixed / flip / input (Examples 1–3) | O(n²) | O(1) |
There are n rows printing 1+2+…+n bits, so total work is n(n+1)/2.
$i, print $j % 2 while $j counts from $i down to 1.$j → 0; odd $j → 1.echo PHP_EOL advances after each row.1, 10, 101…One line: for each row length i, print $j % 2 from i down to 1 with echo, then echo PHP_EOL.
Each row prints alternating 0 and 1 using $j % 2. The inner loop counts down from $i to 1, so row length grows each line — still O(n²) total prints.
Continue with the ascending-inner twin that starts each row with 1.
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