Shape Rule
i..1 per row
Row with outer i = 1 prints 1; row with i = 5 prints 54321 — digits grow from the right.
Reverse Row Number Triangle in Python
Overview
What You’ll Learn
Program 7 prints a reverse row number triangle: each row shows digits from the current row index down to 1 — 1, 21, 321, and so on. This tutorial covers the shape rule, ascending outer loop, inner countdown i..1, a live preview, worked Python examples, edge cases, and complexity.
Outer Loop
i = 1..rows
for i in range(1, rows + 1) — row width increases from one digit to rows digits.
Inner Loop
j = i..1
for j in range(i, 0, -1) prints digits in reverse order on each row.
print() vs end
Same line / next line
Digits use print(j, end=""); end each row with print().
Live Preview
rows = 3..9
Pick row count and draw the reverse row triangle in the browser.
O(n²)
Complexity
Total prints = 1+2+…+n = n(n+1)/2 — a triangular number.
Introduction
A reverse row number triangle grows digits from the right: each row prints numbers from the current row index down to 1. With rows = 5, you get 1, 21, 321, 4321, 54321.
In Python use an outer loop counting up from 1 to rows, an inner loop printing j from i down to 1, then print() after each row.
Why it matters?
It pairs with Program 6’s left-growing triangle — the inner loop counts down instead of up, teaching reverse iteration.
Key Highlights
Outer up
i = 1..rows — narrow row first.
Inner i..1
Countdown from i to 1.
vs Program 6
Program 6 outer down, inner i..rows; Program 7 outer up, inner i..1.
Series Step
Follow Program 6; continue to Program 8 next.
In short: outer i = 1..rows, inner j = i..1, print(j, end="") per digit, then print().
Foundation
📝 Problem & Approach
Given row count rows = 5, print a reverse row number triangle — row outer index i shows digits i..1.
Python
# rows = 5
#1
#21
#321
#4321
#54321Inputs & Outputs
| Item | Type | Description |
|---|---|---|
rows | int | Triangle height — also the widest row digit count. |
i (outer) | int | Current row index — runs 1 up to rows. |
j (inner) | int | Prints i..1 with print(j, end=""). |
| Row width | int | Row with outer i prints exactly i digits. |
| First row | int | Single digit 1 when i = 1. |
| Last row | string | Digits rows..1 when i = rows. |
Minimal workflow
Pseudocode
for i from 1 to rows:
for j from i down to 1:
print j
print newlineApproach comparison
| Approach | Idea | Best for |
|---|---|---|
| Ascending outer | for i in range(1, rows + 1) | Narrow-first row order |
| Inner i..1 | Countdown from i to 1 | Right-growing triangle |
| User-input rows | int(input()) | Flexible height |
| Compact trace | rows = 3 on paper first | Quick dry-runs |
| Spaced output | print(j, end="") | Readable columns |
Cheat Sheet
⚡ Quick Reference
| Goal | Pattern |
|---|---|
| Outer loop | for i in range(1, rows + 1) |
| Inner loop | for j in range(i, 0, -1): print(j, end="") |
| End row | print() |
| Program 6 contrast | Program 6: outer down, inner i..rows; Program 7: outer up, inner i..1 |
Compare
📋 Fixed Rows vs User Input vs Compact Trace
Same reverse row triangle — three ways to set row count and trace the logic.
Fixed rows
rows = 5Hard-coded height for demos
User input
int(input())Read row count from console
Compact trace
rows = 3Quick dry-run on paper
Outer
i = 1..rowsAscending row index
Inner
j = i..1Countdown per row
Context
When This Pattern Shows Up
Reach for this pattern when teaching ascending outer loops, inner countdown, and comparing shapes with Program 6.
Post Program 6 exercise
Natural companion to Program 6 — same triangular print count, inner loop counts down instead of up.
Reverse counting drills
Inner loop
j--fromito1— essential countdown practice.Interview warm-ups
Classic nested-loop question — explain outer up, inner countdown before coding.
Gateway to Program 8
Compare this right-growing triangle with the next pattern in the series.
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 ascending outers, inner countdown, and O(n²) thinking.
Interactive
🔮 Live Preview
Choose a row count between 3 and 9 and draw the reverse row number triangle in the browser.
Hands-On
Examples Gallery
Three complete Python programs — fixed rows, user input, and a compact trace with rows = 3. Click View Output to reveal sample console results.
📚 Getting Started
Print five rows of the reverse row number triangle with nested loops.
Example 1 — Fixed rows = 5
Hard-coded height — outer loop up, inner loop counts down each row.
Python
rows = 5
for i in range(1, rows + 1):
for j in range(i, 0, -1):
print(j, end="")
print()How It Works
Outer i runs 1 to 5 — inner j prints i down to 1 on each row.
📈 Practical Variant
Read row count from the user with validation.
Example 2 — User Input Rows
Configurable height with int(input()) and a positive-rows check.
Python
try:
rows = int(input("Enter the number of rows: "))
if rows <= 0:
raise ValueError
except ValueError:
print("Please enter a positive integer.")
else:
for i in range(1, rows + 1):
for j in range(i, 0, -1):
print(j, end="")
print()How It Works
Same nested loops — only the row count comes from console input with safe parsing.
⚡ Compact Trace
Use rows = 3 for a quick paper trace before larger triangles.
Example 3 — Compact rows = 3 Trace
Small triangle — easy to dry-run on paper before scaling up.
Python
rows = 3
for i in range(1, rows + 1):
for j in range(i, 0, -1):
print(j, end="")
print()How It Works
Three rows, six total digits — trace i and j on paper before coding rows = 5.
🧠 How the Nested Loops Build Each Row
1
Choose the row count
int rows = 5; sets how many rows to print.
Setup
2
Outer loop (row index)
for i in range(1, rows + 1) moves from row 1 to row 5.
Row control
3
Inner loop (print i..1)
for j in range(i, 0, -1) prints digits in reverse order for each row.
Reverse print
4
New line
print() moves to the next row after each line is printed.
Line break
=
Reverse row triangle complete
Total printed digits follow triangular numbers: n(n+1)/2, so time complexity is O(n²).
Trace
🔎 Worked Walkthrough — rows = 5
Trace each row — outer i sets width, inner j counts down from i to 1.
| Row (i) | Inner j values | Output line |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2, 1 | 21 |
| 3 | 3, 2, 1 | 321 |
| 4 | 4, 3, 2, 1 | 4321 |
| 5 | 5, 4, 3, 2, 1 | 54321 |
Total digits printed: 1+2+3+4+5 = 15 = 5×6/2 — the fifth triangular number.
Use Cases
Where this tiny pattern (and its countdown inner loop) shows up beyond the homework prompt.
1. Teaching Countdown Loops
Inner j-- from i to 1 — concrete reverse iteration practice.
Example: trace row 3 and watch j print 3, 2, 1.
2. Pair with Program 6
Program 6 grows digits from the left; Program 7 grows from the right — same O(n²) total.
Example: print both patterns side by side for rows = 5.
3. Output Formatting Drills
Practice print(j, end="") vs print() without complex math.
Example: put print() inside the inner loop by mistake.
4. Character Substitution
Swap digits for letters, stars, or spaced output once the loop works.
Example: print j + " " for spaced digits on each row.
5. Complexity Intuition
Triangular totals make O(n²) concrete for beginners.
Example: count printed digits for n = 10 → 55.
6. Input Validation Labs
Pair the pattern with int(input()) and positive-row checks.
Example: reject rows <= 0 and re-prompt.
Pro Tip: when an interviewer asks for patterns, explain outer up and inner countdown first — then write the loops.
Advantages
Why this pattern earns a permanent spot in beginner Python courses.
1. Instant Visual Feedback
Using
j++instead ofj--shows up immediately as wrong row order.2. Minimal Concepts
Only loops and console output — no arrays or math libraries.
3. Easy to Extend
Add spaces, right-align, or swap digits for stars with small edits.
4. O(1) Extra Memory
Streaming output needs no storage beyond loop counters.
Pro Tip: trace i and j on paper for rows = 3 before coding — watch how each row adds one digit on the right.
Usage Tips
Small habits that keep reverse-row triangle code clean.
1. Name Bounds Clearly
Use
rows(orn) and keepi/jfor row/column loops.2. Prefer try/except
Avoid crashes when the user types letters instead of a number.
3. Keep Newline Outside
Only call
print()after the inner loop finishes the row.4. Count Down on the Inner Loop
for j in range(i, 0, -1)matches “row i prints digits i..1” naturally.5. Dry-Run One Small n
Trace
rows = 3on paper before coding larger demos.
Pro Tip: if rows print ascending digits (12, 123, 1234), you used j++ instead of j--.
Common Pitfalls
Mistakes that commonly break reverse row number triangles.
1. Incrementing j Instead of Decrementing
j++prints ascending digits per row — 12, 123, 1234 instead of 21, 321, 4321.→ Use
for j in range(i, 0, -1).2. Forgetting Newline After Each Row
All digits print on one long line without a row break.
→ Call
print()after the inner loop.3. Zero or Negative Rows
Invalid input may print nothing or behave unexpectedly.
→ Validate
rows > 0before the loops.4. Blind int(input())
Letters or empty input raise
ValueErrorwhenint(input())is unchecked.→ Wrap in
try/except ValueErrorand re-prompt on failure.5. Newline Inside Inner Loop
Each digit prints on its own line — vertical output instead of a triangle.
→ Use
print(j, end="")inside,print()outside only.
Edge Cases
Check these inputs before calling the solution done.
rows = 1
Single row
Prints only 1 — inner loop runs once with j = 1.
rows = 0
Zero rows
Outer loop never runs — print nothing or show a message.
rows = 2
Minimal triangle
Output 1 then 21 — good quick test.
Negative
Negative rows
Reject with validation — outer loop condition fails silently otherwise.
Bad input
Non-numeric input
Bare int(input()) raises ValueError — use try/except.
Large n
Many rows
Still O(n²) prints — cap rows for console demos.
Drill
🎯 Practice Problems
Try these variations to lock in the pattern.
1. Compare with Program 6
- Program 6: outer down, inner i..rows
- Program 7: outer up, inner i..1
2. Add spaces between digits
- Use
print(j, end="") - Same loops, readable columns
3. Next in series
- Continue with Program 8
- Next number pattern in the series
4. Paper trace
- Dry-run
rows = 3before coding - Fill the walkthrough table by hand
Important
Notes
- Row width. Row
iprints exactlyidigits — the triangle widens from the right. - Total digits =
n(n+1)/2— a triangular number. Forrows = 5, that is 15 digits. - Program 5 prints
1..iascending; Program 7 printsi..1descending — mirror per-row logic. - The last row always shows digits from
rowsdown to1— e.g.54321whenrows = 5.
Quick Takeaway: outer i = 1..rows, inner j = i..1, print(j, end=""), then print().
Analysis
⏱️ Time and Space Complexity
| Program | Time | Extra space |
|---|---|---|
| Nested loops (Examples 1–2) | O(rows²) | O(1) |
| Compact trace (Example 3) | O(rows²) | O(1) |
🎉 Conclusion
The reverse row number triangle is a compact nested-loop exercise: outer counts up, inner counts down, and each row grows one digit wider from the right. Master the fixed rows = 5 version, then try user input with int(input()) and the compact rows = 3 trace.
Practice the three examples above, then continue to Program 8 for the next pattern in the series.
Use range(i, 0, -1) for reverse digits per row, keep print() outside the inner loop, and validate row count when reading from the console.
Pro Tips
💡 Best Practices
✅ Do
- Explain outer up and inner countdown before coding
- Use
for j in range(i, 0, -1) - Call
print()after each inner loop - Validate
rows > 0for user input - Dry-run
rows = 3on paper first - State O(n²) time when asked about complexity
❌ Don’t
- Use
range(1, i + 1)when the pattern needs countdown - Put
print()inside the inner loop - Skip input validation on console reads
- Confuse this with Program 6’s left-growing triangle
- Skip the
rows = 3dry-run before larger demos
Summary
Key Takeaways
Knowledge Unlocked
Five things to remember about this reverse row pattern
Print the reverse row number triangle the beginner-friendly way.
5
Core concepts 01
Rule
Row i prints i..1
Definition 02
Outer
i = 1..rows
Loop 03
Inner
j = i..1 countdown
Loop 04
Output
print then newline
I/O 05
Complexity
O(n²) time
Analysis❓ Frequently Asked Questions
It prints a reverse row number triangle: row 1 shows 1, row 2 shows 21, row 3 shows 321, and so on until the last row shows digits from rows down to 1.
The inner loop uses range(i, 0, -1) which prints i, i-1, ..., 1 on each row.
When i = rows (5), the inner loop prints j from 5 down to 1 — giving 54321 on the last line.
Program 6 outer counts down and prints i..rows (5, 45, 345). Program 7 outer counts up and prints i down to 1 (1, 21, 321).
Program 5 prints 1..i ascending per row. Program 7 prints i..1 descending per row — digits grow from the right instead of the left.
print(j, end="") stays on the same line for each digit. print() ends the row after the inner loop finishes.
Change rows or read it from user input with int(input()) — see Example 2.
Yes — use range(1, i + 1) in the inner loop like Program 5.
O(n²) for n rows because total prints are 1 + 2 + ... + n = n(n+1)/2.
Use try/except ValueError around int(input()). Bare int(input()) raises ValueError on bad input.
Did you Know? 🔊
Each row prints digits in reverse order — outer i runs 1..rows, inner j counts down from i to 1 — producing 1, 21, 321, and so on. Total prints grow as O(n²).
Continue to Program 8
Move on to the next pattern in the Python number-pattern series.
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