Shape Rule
Shrinking rows
Row 1 prints five 1s, row 2 prints four 2s, row 5 prints a single 1.
Bidirectional Number Triangle in PHP
Overview
What You’ll Learn
The bidirectional number triangle prints 11111, 2222, 333, 22, 1 — a natural step after the centered pyramid in Program 24. This tutorial covers shrinking rows, if/else digit mapping, a live preview, algorithm steps, worked PHP examples, edge cases, and complexity.
Outer Loop
i = 1..rows
for ($i = 1; $i <= $rows; $i++) walks each row top to bottom.
Shrinking Inner Loop
j = i..rows
for ($j = $i; $j <= $rows; $j++) prints fewer digits as i grows.
If/Else Mapping
6 - i mirror
i < 4 prints i; else prints 6 - i for rows 4 and 5.
Live Preview
3–9 rows
Pick a row count and draw the bidirectional triangle instantly in the browser.
O(n²)
Complexity
Total prints are triangular — scales as n² for n rows.
Introduction
A bidirectional number triangle prints repeated digits per row with shrinking length — digits rise then mirror down. With rows = 5, the output is 11111, 2222, 333, 22, 1.
In PHP you use an outer loop for rows, a shrinking inner loop j = i..rows, and an if/else to pick which digit to repeat.
Why it matters?
It combines shrinking inner loops with conditional mapping — a step up from Program 24’s spacing logic.
Key Highlights
Shrinking rows
j = i..rows — each row prints fewer digits.
Rising digits
i < 4 repeats 1, 2, 3.
Mirror down
6 - i produces 2 and 1 on last rows.
Series Foundation
Follow Program 24; continue to Program 26 (diagonal asterisk) next.
In short: for each i, repeat a digit (rows - i + 1) times — use i when i < rows - 1, else rows + 1 - i.
Foundation
📝 Problem & Approach
Given a positive integer rows (e.g. 5), print a shrinking triangle where each row repeats one digit — rising on early rows, mirroring down on the last rows.
PHP
// rows = 5 (conceptual shape)
// 11111
// 2222
// 333
// 22
// 1Inputs & Outputs
| Item | Type | Description |
|---|---|---|
rows | int | Number of rows — outer loop runs from 1 to rows. |
i | int | Outer loop — current row number (also the digit for early rows). |
j | int | Inner loop — j = i..rows controls shrinking row length. |
val | int | Digit to repeat — i or rows + 1 - i via if/else. |
Minimal workflow
Pseudocode
for i from 1 to rows:
if i < rows - 1:
val = i
else:
val = rows + 1 - i
for j from i to rows:
print val
print newlineApproach comparison
| Approach | Idea | Best for |
|---|---|---|
| If/else mapping | 11111, 2222, … 1 | Learning and interviews |
| User-input rows | (int) trim(fgets(STDIN)); | Flexible console programs |
| Ternary val | val = ($i < $rows - 1) ? $i : ($rows + 1 - $i) | Compact generalized version |
Cheat Sheet
⚡ Quick Reference
| Goal | Pattern |
|---|---|
| Walk rows | for ($i = 1; $i <= $rows; $i++) |
| Shrink inner loop | for ($j = $i; $j <= $rows; $j++) |
| Pick digit (fixed) | if ($i < 4) echo $i; else echo 6 - $i; |
| Pick digit (general) | val = ($i < $rows - 1) ? $i : ($rows + 1 - $i); |
| End the row | echo PHP_EOL; |
| User input | (int) trim(fgets(STDIN)); |
Compare
📋 Fixed rows vs User Input vs Spaced Output
Same bidirectional triangle — different ways to control rows and formatting.
Outer loop
i = 1..rowsOne row per outer iteration
Inner loop
j = i..rowsShrinking row length each row
Mapping
6 - iMirrors digits on last rows
Learning tip
if/elseCompute val once per row, not per column
Context
When This Pattern Shows Up
Reach for this pattern when teaching shrinking inner loops, conditional digit mapping, and bidirectional output.
Post pyramid exercise
Natural follow-up after Program 24 — introduces if/else mapping and shrinking rows.
Nested-loop warm-up
Outer/inner bound practice with an immediate visual check.
Console I/O practice
Combine loops with
fgets(STDIN)for a flexible row count.Gateway to variants
Compare Program 24 (centered pyramid) and Program 26 (diagonal asterisk) next.
Not a UI layout tool
This is a console teaching pattern — not how you build modern app screens.
Key benefit: one small program that locks in nested loops, output sequencing, and O(n²) thinking.
Interactive
🔮 Live Preview
Choose a row count between 3 and 9 and draw the bidirectional number triangle in the browser.
Hands-On
Examples Gallery
Three complete PHP programs — fixed rows, user input, and spaced output variant. Click View Output to reveal sample console results.
📚 Getting Started
Print five rows of the bidirectional triangle with if/else mapping.
Example 1 — Fixed rows = 5
Hard-coded row count — ideal for first demos and screenshots.
PHP
<?php
for ($i = 1; $i <= 5; $i++) {
for ($j = $i; $j <= 5; $j++) {
if ($i < 4) {
echo $i;
} else {
echo 6 - $i;
}
}
echo PHP_EOL;
}How It Works
When i = 1, print five 1s — output 11111. When i = 3, print three 3s — output 333. When i = 4, the else branch prints 6 - 4 = 2 twice — output 22. When i = 5, print 6 - 5 = 1 once.
📈 User Input
Read the row count with fgets(STDIN) instead of hard-coding 5.
Example 2 — User Input
Read rows with (int) trim(fgets(STDIN)); use a ternary to generalize the digit mapping.
PHP
<?php
echo "Enter rows: ";
$rows = (int) trim(fgets(STDIN));
for ($i = 1; $i <= $rows; $i++) {
$val = ($i < $rows - 1) ? $i : ($rows + 1 - $i);
for ($j = $i; $j <= $rows; $j++) {
echo $val;
}
echo PHP_EOL;
}How It Works
Same shrinking inner loop as Example 1; the ternary ($i < $rows - 1) ? $i : ($rows + 1 - $i) generalizes the if/else mapping for any row count. Non-numeric input leaves rows unset if you skip is_numeric() checks — always check it in safer labs.
⚡ Spaced Output
Add a space between repeated digits for easier reading.
Example 3 — Spaced Digits
Keep rows = 5 but print each digit followed by a space.
PHP
<?php
$rows = 5;
for ($i = 1; $i <= $rows; $i++) {
$val = ($i < $rows - 1) ? $i : ($rows + 1 - $i);
for ($j = $i; $j <= $rows; $j++) {
echo $val . " ";
}
echo PHP_EOL;
}How It Works
Only the print statement changes — echo $val . " " instead of echo $val. The shrinking loop and digit mapping stay the same.
🧠 How the Algorithm Prints Rows
1
Set up
Set $rows = 5; and use fgets(STDIN) when reading input. Set loop variables $i, $j.
Setup
2
Outer loop walks rows
for ($i = 1; $i <= $rows; $i++) — one row per iteration.
Row
3
Shrinking inner loop (j)
for ($j = $i; $j <= $rows; $j++) — row length shrinks as i grows.
Shrink
4
If/else digit mapping
if ($i < 4) prints i; else echo 6 - $i mirrors down.
Mapping
5
New line
echo PHP_EOL ends the row after the inner loop.
Break
=
Bidirectional triangle complete
Digits rise then mirror down — O(n²) time, O(1) extra memory.
Trace
🔎 Worked Walkthrough — rows = 5
Trace each outer-loop value of i, the digit chosen, inner-loop count, and row output.
i | Digit (val) | Inner loop (j) | Prints | Row output |
|---|---|---|---|---|
1 | 1 (i < 4) | 1..5 (5 times) | 5 | 11111 |
2 | 2 | 2..5 (4 times) | 4 | 2222 |
3 | 3 | 3..5 (3 times) | 3 | 333 |
4 | 2 (6 - i) | 4..5 (2 times) | 2 | 22 |
5 | 1 (6 - i) | 5..5 (1 time) | 1 | 1 |
Prints per row = rows - i + 1 — total prints = n(n+1)/2 for n rows.
Use Cases
Where this tiny pattern (and its loop structure) shows up beyond the homework prompt.
1. Teaching Nested Loops
Clearest visual proof that outer and inner bounds interact.
Example: change j = i to j = 1 and watch rows stop shrinking.
2. Pattern Series Base
Foundation for inverted, pyramid, diamond, and hollow variants.
Example: use rows + 1 - i for a fully symmetric variant.
3. Console Formatting Drills
Practice print vs row newline without complex math.
Example: put echo PHP_EOL inside the inner loop by mistake.
4. Character Substitution
Swap digits for letters or add spaces once the loop works.
Example: print val + " " for spaced repeated digits.
5. Complexity Intuition
Triangular totals make O(n²) concrete for beginners.
Example: count printed numbers for rows = 5 → 5 + 4 + 3 + 2 + 1 = 15.
6. Input Validation Labs
Pair the pattern with fgets(STDIN) return checks and positive-row checks.
Example: reject max <= 0 and re-prompt.
Pro Tip: when an interviewer asks for patterns, explain the outer/inner roles first — then write the loops. The story matters as much as the code.
Advantages
Why this pattern earns a permanent spot in beginner PHP courses.
1. Instant Visual Feedback
Wrong bounds show up immediately as a broken staircase.
2. Minimal Concepts
Only loops and console output — no arrays or math libraries.
3. Easy to Extend
Invert, center, hollow, or change the fill character with small edits.
4. O(1) Extra Memory
Streaming output needs no storage beyond loop counters.
Pro Tip: trace the shrinking inner loop on paper for rows = 3 before coding — mapping bugs hide in the 6 - i threshold.
Usage Tips
Small habits that keep number-pattern code clean.
1. Name Bounds Clearly
Do not reset
valinside the inner loop — compute it once per row.2. Prefer
is_numeric()Call
is_numeric(trim($line))so bad input does not leaverowsuninitialized.3. Keep echo PHP_EOL Outside
Only call
echo PHP_EOLafter the inner loop finishes the row.4. Trace i and val on Paper
Write each
i, digit chosen, and print count before coding.5. Dry-Run One Small n
Trace
rows = 3on paper before coding larger demos.
Pro Tip: if the output is a vertical list of single digits per line, you almost certainly put echo PHP_EOL inside the inner loop.
Common Pitfalls
Mistakes that commonly break bidirectional number triangle patterns.
1. Newline Inside the Inner Loop
Each digit lands on its own line — you get a column, not a triangle.
→ Use
echo $val;echo PHP_EOLonly after the inner loop.2. Recomputing val Inside Inner Loop
Putting the if/else inside the inner loop works but is wasteful — compute
valonce per row.→ Set
$valbefore the inner loop, then justecho $val.3. Wrong Inner Loop Bound
Using
j = 1torowsprints full-width rows — no shrinking.→ Use
for ($j = $i; $j <= $rows; $j++)so each row is shorter.4. Wrong Mirror Threshold
Using
i < rowsinstead ofi < rows - 1skips the mirror on the last row.→ For generalized code use
($i < $rows - 1) ? $i : ($rows + 1 - $i).5. Unchecked CLI input
Letters or empty input leave
rowsuninitialized.→ Call
is_numeric(trim($line))and re-prompt on failure.
Edge Cases
Check these inputs before calling the solution done.
rows = 1
Single row
Output is just 1 — one digit, one row.
rows = 0
Empty pattern
Outer loop never runs — print nothing or show a message.
Negative
rows < 0
Treat as invalid; re-prompt instead of silent empty output.
rows = 2
Smallest triangle
Two rows: 11 and 1.
Bad input
Non-numeric CLI input
Unchecked fgets(STDIN) input leaves rows unset — call is_numeric(trim($line)) first.
Large rows
Large row count
Output grows as n² characters — fine for labs, noisy for huge n.
Drill
🎯 Practice Problems
Try these variations to lock in the pattern.
1. Centered pyramid
- Continuous counter with spacing
- Review Program 24
2. Diagonal asterisk
- Descending numbers with
*on diagonal - Continue with Program 26
3. Extract a method
- Move pattern logic into
PrintTriangle(int rows) - Call from
Mainwith user input
4. Full mirror mapping
- Use
rows + 1 - ifor all rows, not just last two - Compare symmetric vs bidirectional output
Important
Notes
- Shrinking rows. Inner loop
j = i..rows— row length =rows - i + 1digits per row. echo $valrepeats the digit;echo PHP_EOLadvances — mix them carefully.- Validate
rows > 0for interactive programs;rows = 1prints a single1. - Compute
valonce per row outside the inner loop — cleaner and slightly faster.
Quick Takeaway: outer loop i = 1..rows, shrinking inner loop j = i..rows, if/else digit mapping, then echo PHP_EOL after each row.
Analysis
⏱️ Time and Space Complexity
| Program | Time | Extra space |
|---|---|---|
| Nested loops (Examples 1–2) | O(n²) | O(1) |
| Spaced output (Example 3) | O(n²) | O(1) |
🎉 Conclusion
The bidirectional number triangle is a compact lesson in shrinking loops and conditional mapping: repeat a digit per row with j = i..rows, then mirror down with 6 - i. Master the fixed-rows version, then try user input and spaced output.
Practice the three examples above, then continue to Program 26 for the descending pattern with diagonal asterisk.
Compute val once per row — validate rows when reading from the console.
Pro Tips
💡 Best Practices
✅ Do
- Use
for ($i = 1; $i <= $rows; $i++)in the outer loop - Shrink with
for ($j = $i; $j <= $rows; $j++) - Compute
valonce per row before the inner loop - Call
is_numeric(trim($line))before usingrows - State O(n²) time when asked about complexity
❌ Don’t
- Call
echo PHP_EOLinside the inner loop - Use
j = 1in the inner loop — rows won’t shrink - Hard-code
6 - iin generalized code — userows + 1 - i - Recompute the digit mapping on every inner iteration
- Ignore bad console input in user-facing demos
- Skip the
rows = 1edge case
Summary
Key Takeaways
Knowledge Unlocked
Five things to remember about this triangle pattern
Print the pattern the beginner-friendly way.
5
Core concepts 01
Rule
Shrink + repeat
Definition 02
j = i..rows
Shrinking rows
Code 03
if/else
6 - i mirror
Code 04
Bidirectional
1,2,3 then 2,1
Shape 05
Complexity
O(n²) time
Analysis❓ Frequently Asked Questions
For $i = 5, the condition $i < 4 is false, so the program prints 6 - $i which becomes 1.
Because the inner loop runs from $j = $i to $rows. As $i increases, the inner loop executes fewer times.
Digits rise (1, 2, 3) on early rows then mirror down (2, 1) on the last rows via the 6 - $i mapping.
echo $val repeats the digit on the same line. echo PHP_EOL ends the row after the inner loop finishes.
A single inner loop with a digit mapping keeps the shrinking row logic in one place.
Replace 5 with $rows and use $val = ($i < $rows - 1) ? $i : ($rows + 1 - $i) — see Example 2.
O(n²) for n rows because total prints are triangular (n + (n-1) + … + 1).
Use trim(fgets(STDIN)) and check is_numeric($input) before casting to int — see Example 2 notes.
Only one row prints — a single 1.
Did you Know? 🔊
This pattern prints repeated digits per row. The inner loop runs from $j = $i to $rows, shrinking each row. The row digit is $i for the first half, then switches to $rows + 1 - $i to produce 22 and 1.
Continue to Program 26
Move on to the descending number pattern with diagonal asterisk in the PHP number-pattern series.
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