An increasing-start alphabet triangle keeps a fixed end letter on the right and moves the start letter one step later each row — so the left edge slides inward.
Remember
Rule: for start letter $i from A to last,
print $i through last
ABCDE
BCDE
CDE
DE
E ← 5 rows (right edge fixed at E)
Same widths as Program 5 (5, 4, 3, 2, 1), but Program 5 shortens the end while restarting at A. Here the start advances and the end stays put. Compare also with Program 3, which grows into the same right edge.
Approach
How to Solve It
Two ways to emit the same shape — start with nested letter loops, then optionally shorten with substr.
Method
Idea
Best for
Nested letter loops
Outer = advancing start; inner = start..end
Learning, interviews, exams
substr($top, $i)
Drop one left letter each row from a fixed prefix
Shorter demos once loops click
Pseudocode
Pseudocode
$end = $lastLetter
for $start from 'A' to $end:
for $ch from $start to $end:
echo $ch
echo PHP_EOL
Cheat sheet
Goal
Pattern
Advance start letter
for ($i = 'A'; $i <= $end; $i++)
Print $i..$end
for ($j = $i; $j <= $end; $j++) echo $j;
End the row
echo PHP_EOL;
End letter from rows
$end = chr(ord('A') + $rows - 1);
One-line row shortcut
echo substr($top, $i) . PHP_EOL; while $i advances
1. Outer loop picks the start letter.$i runs from 'A' to 'E' — longest row first.
2. Inner loop starts at $i. For each start, $j runs from $i to 'E', so the row is $i..E.
3. Print letters, then break the line.echo $j stays on the row; echo PHP_EOL after the inner loop starts the next (shorter) row.
When $i = 'A' you get ABCDE; when $i = 'E' you get E.
Example 2 — User Input Version
Read the row count at runtime. Prefer validating with is_numeric and clamp to 26 (shown in the tip below).
PHP
<?php
echo "Enter the number of rows: ";
$rows = (int) trim(fgets(STDIN));
$end = chr(ord('A') + $rows - 1);
for ($i = 'A'; $i <= $end; $i++) {
for ($j = $i; $j <= $end; $j++) {
echo $j;
}
echo PHP_EOL;
}
Output (when user enters 4)
Enter the number of rows: 4
ABCD
BCD
CD
D
How It Works
1. Prompt and read. Ask for a row count, then cast the trimmed line to an int.
2. Map rows to an end letter.$end = chr(ord('A') + $rows - 1) — for $rows = 4, $end is 'D'.
3. Same advance core. Only the source of $end changes — the print logic matches Example 1.
4. 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 || $rows > 26) {
echo "Enter a whole number from 1 to 26." . PHP_EOL;
exit;
}
Example 3 — substr($top, $i)
Drop one left letter each row from a fixed prefix — same shape, no explicit inner letter loop.
1. Build the first row.$top = substr($letters, 0, $rows) is ABCDE when $rows = 5.
2. Slice from index $i.substr($top, 0) is the full row; substr($top, 1) drops A; and so on.
3. Learn loops first. Use Examples 1–2 when you need to show nested bounds; treat this as a polish shortcut afterward.
Edge Cases & Pitfalls
Check these before calling the solution done.
$j = 'A'
Program 5 by mistake
If the inner loop starts at 'A' instead of $i, you print ABCDE, ABCD, … Use for ($j = $i; …).
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; break the row only after the inner loop.
Wrong end
Off-by-one end letter
Use chr(ord('A') + $rows - 1). Forgetting - 1 pushes the end past the intended letter.
$rows > 26
Past Z
chr(ord('A') + $rows - 1) leaves A–Z when $rows > 26. Clamp or reject in interactive programs.
$rows = 1
Single A
Output is just A — start and end coincide. A good sanity check.
Bad input
Use is_numeric
Bare (int) fgets(STDIN) turns letters into 0 — validate before the outer loop.
Analysis
Time and Space Complexity
Program
Time
Extra space
Nested loops (Examples 1–2)
O(rows²)
O(1)
substr (Example 3)
O(rows²)
O(rows) for the prefix and temporary row strings
Total letters = n + (n - 1) + … + 1 = n(n + 1)/2 — quadratic in n. Same totals as Programs 1 and 5.
Remember
Key Takeaways
Rule: advance start letter $i; print $i through a fixed end each row.
vs Program 5: same widths — here the left edge moves; there the right edge moves.
Break the row: call echo PHP_EOL only after the inner loop.
Complexity:O(n²) time; O(1) extra space for nested loops.
One line: for $i from 'A' to the end letter, print $i through that end, then echo PHP_EOL.
Frequently Asked Questions
The outer loop picks the starting letter (A, then B, then C…). The inner loop prints from that start up to a fixed end letter. Each row drops the leftmost character and becomes shorter.
Because the inner loop always stops at the same end letter ('E'), so the last printed character is fixed on the right.
Program 5 restarts each row at A and shortens the end letter (ABCDE, ABCD, …). Program 6 shifts the start letter forward each row while keeping the same end letter (ABCDE, BCDE, …).
Program 3 grows while starting earlier (E, DE, CDE). This pattern shrinks while starting later (ABCDE, BCDE, CDE). Both keep a fixed right edge at the top letter.
echo stays on the same line. echo PHP_EOL ends the current line. Letters use echo; the row break uses echo PHP_EOL after the inner loop.
O(n²) for n rows, because total printed characters are n(n+1)/2.
Yes. Take substr($letters, 0, $rows), then echo substr($top, $i) . PHP_EOL while $i runs from 0 to $rows-1. Nested letter loops are better for learning; substr is a handy shortcut later.
Use trim(fgets(STDIN)) and check is_numeric($input) before casting to int, then clamp rows between 1 and 26 so bad input does not walk past Z.
🤔
Did you know?
Each row starts one letter later but always ends at the same letter. For 5 rows: ABCDE, BCDE, CDE, DE, E. Same widths as Program 5, but the left edge moves instead of the right.
