A reverse-starting-letter alphabet triangle grows leftward: each row begins one letter earlier, but letters along the row still run forward to a fixed top.
Remember
Rule: start letter moves top→A; print forward to top
E
DE
CDE
BCDE
ABCDE ← top = 'E' (5 rows)
Mixes Program 1 (forward run) with Program 2 (moving start). The right edge stays fixed at $top on every row.
Approach
How to Solve It
Two ways to emit the same shape — nested letter loops, or a growing suffix of a fixed alphabet string.
Method
Idea
Best for
Nested letter loops
Outer = start letter; inner = start up to $top
Learning, interviews, exams
Alphabet suffix
Slice the last $r letters of "ABC…top"
Shorter demos once loops click
Pseudocode
Pseudocode
$top = chr(ord('A') + $rows - 1)
for $start from $top down to 'A':
for $ch from $start up to $top:
echo $ch
echo PHP_EOL
1. Outer loop moves the start.$i runs from 'E' down to 'A' — one start letter per row.
2. Inner loop prints forward. For each row, $j runs from $i up to 'E'. When $i = 'C', that prints CDE.
3. Break the line.echo PHP_EOL after the inner loop ends the row.
4. Full last row. When $i = 'A', the inner loop prints the full forward run ABCDE.
Example 2 — Row Count Input
Read the number of rows and compute $top = chr(ord('A') + $rows - 1). Prefer validating with is_numeric in real apps.
PHP
<?php
echo "Enter the number of rows: ";
$rows = (int) trim(fgets(STDIN));
$top = chr(ord('A') + $rows - 1);
for ($i = $top; $i >= 'A'; $i--) {
for ($j = $i; $j <= $top; $j++) {
echo $j;
}
echo PHP_EOL;
}
Output (when user enters 4)
Enter the number of rows: 4
D
CD
BCD
ABCD
How It Works
1. Scale the top. For 4 rows, $top becomes 'D'. Cap $rows at 26 so $top stays within A–Z.
2. Same core loops. Only the stop letter changes; the start-moves-backward rule is unchanged.
3. Safer input tip. Prefer:
Safer input
$raw = trim(fgets(STDIN));
if (!is_numeric($raw)) {
echo "Enter a whole number from 1 to 26." . PHP_EOL;
exit;
}
$rows = (int) $raw;
if ($rows < 1 || $rows > 26) {
echo "Enter a whole number from 1 to 26." . PHP_EOL;
exit;
}
Example 3 — Spaced Letters
Print a trailing space after each letter so columns are easier to scan.
1. Same bounds. Loop limits are unchanged — only the printed unit becomes $j . " ".
2. Optional trim. Trim trailing spaces later if you need a compact line for grading scripts.
Edge Cases & Pitfalls
Check these before calling the solution done.
Inner j--
Wrong direction on the row
If the inner loop counts down, you get Program 2 (E, ED, EDC). Keep $j++ from $i to $top.
Outer ++
Growing from A instead
If the outer loop runs A..$top with the same inner rule, you print Program 1 upside-down. Start at $top and go down to A.
PHP_EOL inside
Column of letters
If echo PHP_EOL is inside the inner loop, each letter lands on its own line. Use echo for letters; end the row only after the inner loop.
rows = 1
Single A
When $top = 'A', you print one row: A. A good sanity check.
rows > 26
Beyond Z
Cap at 26 (or reject) so $top stays within A–Z.
Bad input
Check is_numeric
Casting non-numeric text to int becomes 0. Prefer is_numeric and a clear message.
Analysis
Time and Space Complexity
Program
Time
Extra space
Nested loops (Examples 1–2)
O(n²)
O(1)
Spaced letters (Example 3)
O(n²)
O(1)
For $n rows, total letters are 1 + 2 + … + n = n(n + 1)/2 — still quadratic in n.
Remember
Key Takeaways
Rule: start letter moves $top → A; print forward to $top.
Fixed right edge: every row ends at the same top letter.
Break the row: call echo PHP_EOL only after the inner loop.
Complexity:O(n²) time; O(1) extra space.
One line: for each start from $top down to A, print that letter forward up to $top.
Frequently Asked Questions
The outer loop moves the starting letter from E down to A. The inner loop always prints forward from that start letter up to E (or top), so the last character remains E on every row.
Program 2 prints letters descending along the row (E, ED, EDC). This program prints forward along the row (E, DE, CDE) while only the row’s first letter moves backward.
Program 1 always starts at A and grows the end letter (A, AB, ABC). This pattern grows the start letter backward while keeping the right edge fixed at top.
Yes. Read rows from the CLI and set $top = chr(ord('A') + $rows - 1). Then loop $i from $top down to 'A' and echo $j from $i up to $top.
O(n²) for n rows, because the total printed letters are 1+2+...+n = n(n+1)/2.
Use trim(fgets(STDIN)) and check is_numeric($input) before casting to int, require n ≥ 1, and cap at 26 so the top letter stays within A–Z.
echo stays on the same line. echo PHP_EOL ends the current line. Letters use echo; the row break uses echo PHP_EOL after the inner loop.
Yes. Use 'a' as the base: $top = chr(ord('a') + $rows - 1), then loop the same way with $j++ up to $top.
🤔
Did you know?
This triangle changes only the starting letter of each row (E, D, C, …), while letters along the row still increase forward. In the 5-row example, every row ends at E, producing E, DE, CDE, BCDE, ABCDE.
