Shape Rule
Odd row lengths
Row 1 prints 1, row 2 prints 123, row 3 prints 12345, and so on — digits run together with no spaces.
Increasing Odd-Length Number Rows in C
Overview
What You’ll Learn
The increasing odd-length number rows pattern uses i += 2 in the outer loop so each row prints 1..i with lengths 1, 3, 5, 7, 9 — a natural step after the jump triangle in Program 21. This tutorial covers the shape rule, step-size logic, a live preview, algorithm steps, worked C examples, edge cases, and complexity.
Outer Loop
i += 2
for (i = 1; i <= max; i += 2) walks odd values 1, 3, 5, 7, 9 as row lengths.
Inner Loop
1..i
for (j = 1; j <= i; j++) then printf("%d", j) — no space between digits.
printf vs newline
Same line / next line
Digits use printf("%d", j); end each row with printf("\n").
Live Preview
1–15 max
Pick an odd maximum and draw the odd-length rows pattern instantly in the browser.
O(n²)
Complexity
Total prints = 1+3+5+...+max; extra memory stays O(1).
Introduction
An increasing odd-length number rows pattern prints consecutive digits 1..i on each row, with row lengths growing by 2 each time. With max = 9, the output is 1, 123, 12345, 1234567, 123456789.
In C you use for (i = 1; i <= max; i += 2) in the outer loop and printf("%d", j) in the inner loop, then printf("\n") ends each row.
Why it matters?
It introduces loop step sizes — a simple change to i += 2 creates a whole new family of patterns.
Key Highlights
Outer i += 2
Row lengths are 1, 3, 5, 7, 9 — always odd.
Inner 1..i
printf("%d", j) concatenates digits on one line.
No spaces
Digits run together — 123 not 1 2 3.
Series Foundation
Follow Program 21; continue to Program 23 (number & asterisk mirror) next.
In short: for each odd i up to max, print digits 1 through i with printf("%d", j), then call printf("\n").
Foundation
📝 Problem & Approach
Given a positive odd integer max, print increasing odd-length rows: for each odd i from 1 to max, print digits 1 through i concatenated on one line.
c
// max = 9 (conceptual shape)
// 1
// 123
// 12345
// 1234567
// 123456789Inputs & Outputs
| Item | Type | Description |
|---|---|---|
max | int | Maximum row length (typically odd, e.g. 9). |
i | int | Outer loop — odd values 1, 3, 5, … up to max. |
j | int | Inner loop — prints digits 1 through i. |
| Printed output | text | Row i has i concatenated digits — no spaces. |
Minimal workflow
Pseudocode
for i from 1 to max step 2:
for j from 1 to i:
print j (no space)
print newlineApproach comparison
| Approach | Idea | Best for |
|---|---|---|
| Outer i += 2 | 1, 123, 12345, … | Learning and interviews |
| User-input max | scanf("%d", &max); | Flexible console programs |
| Inner j += 2 | 1, 13, 135, 1357, … | Odd-only digit rows |
Cheat Sheet
⚡ Quick Reference
| Goal | Pattern |
|---|---|
| Walk odd lengths | for (i = 1; i <= max; i += 2) |
| Print digits | for (j = 1; j <= i; j++) |
| Write digit | printf("%d", j); |
| End the row | printf("\n"); |
| Odd-only variant | for (j = 1; j <= i; j += 2) |
| User input | scanf("%d", &max); |
Compare
📋 Fixed Max vs User Input vs Odd-Only Digits
Same odd-length rows — different ways to control max and inner loop step.
Outer step
i += 2Row lengths 1, 3, 5, 7, 9
Inner 1..i
printf("%d", j)Concatenate digits — no spaces
Odd digits
j += 2Print 1, 3, 5 only in Example 3
Learning tip
even maxSubtract 1 if user enters an even maximum
Context
When This Pattern Shows Up
Reach for this pattern when teaching loop step sizes and concatenated digit output inside nested loops.
Post-jump exercise
Natural follow-up after Program 21 — introduces outer loop step
i += 2.Nested-loop warm-up
Outer/inner bound practice with an immediate visual check.
Console I/O practice
Combine loops with
scanffor a flexible row count.Gateway to variants
Compare Program 21 (jump triangle) and Program 23 (number & asterisk mirror) 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 an odd maximum between 1 and 15 and draw the odd-length rows pattern in the browser.
Hands-On
Examples Gallery
Three complete C programs — fixed maximum, user input, and odd-only digits variant. Click View Output to reveal sample console results.
📚 Getting Started
Print five rows of odd-length consecutive digits with i += 2.
Example 1 — Fixed max = 9
Hard-coded maximum — ideal for first demos and screenshots.
c
#include <stdio.h>
int main() {
int i, j;
for (i = 1; i <= 9; i += 2) {
for (j = 1; j <= i; ++j)
printf("%d", j);
printf("\n");
}
return 0;
}How It Works
When i = 1, the inner loop prints 1 once. When i = 3, j runs 1, 2, 3 — output 123. When i = 9, digits 1 through 9 concatenate into 123456789. printf("\n") after the inner loop starts the next row.
📈 User Input
Read the maximum with scanf instead of hard-coding 9.
Example 2 — User Input
Read max with scanf("%d", &max); adjust to odd if the user enters an even value.
c
#include <stdio.h>
int main() {
int max;
int i, j;
printf("Enter the maximum value: ");
scanf("%d", &max);
if (max % 2 == 0) max -= 1;
for (i = 1; i <= max; i += 2) {
for (j = 1; j <= i; ++j)
printf("%d", j);
printf("\n");
}
return 0;
}How It Works
Same nested-loop core as Example 1; only the source of max changes. The if (max % 2 == 0) max -= 1 guard keeps the last row odd-length. Non-numeric input leaves max unset if you ignore scanf’s return value — always check it in safer labs.
⚡ Odd-Only Digits
Use j += 2 in the inner loop to print only odd digits.
Example 3 — Odd-Only Digits j += 2
Keep max = 9 but print 1, 3, 5, 7, 9 instead of 1..i on each row.
c
#include <stdio.h>
int main() {
int i, j;
for (i = 1; i <= 9; i += 2) {
for (j = 1; j <= i; j += 2)
printf("%d", j);
printf("\n");
}
return 0;
}How It Works
Change only the inner loop to j += 2 — the outer loop and printf("\n") logic stay the same. Each row prints odd digits up to i instead of every digit from 1 to i.
🧠 How the Algorithm Prints Rows
1
Set up
#include <stdio.h> brings in printf / scanf. Set max and loop variables i, j.
Setup
2
Outer loop + i += 2
for (i = 1; i <= max; i += 2) — row lengths are 1, 3, 5, 7, 9.
Row
3
Inner loop + printf("%d", j)
for (j = 1; j <= i; j++) then printf("%d", j) — digits concatenate with no spaces.
Digits
4
New line
printf("\n") ends the row so the next outer iteration starts fresh.
Break
=
Odd-length rows complete
Total prints grow as 1+3+5+...+max — O(n²) time, O(1) extra memory.
Trace
🔎 Worked Walkthrough — max = 9
Trace each outer-loop value of i and the digits printed on each row.
i | Inner j range | Digits printed | Row output |
|---|---|---|---|
1 | 1 | 1 | 1 |
3 | 1..3 | 1, 2, 3 | 123 |
5 | 1..5 | 1, 2, 3, 4, 5 | 12345 |
7 | 1..7 | 1..7 | 1234567 |
9 | 1..9 | 1..9 | 123456789 |
Total digit prints: 1 + 3 + 5 + 7 + 9 = 25.
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 and watch the shape change.
2. Pattern Series Base
Foundation for inverted, pyramid, diamond, and hollow variants.
Example: use (i + j) % 2 for row+column parity grids.
3. Console Formatting Drills
Practice printf vs row newline without complex math.
Example: put printf("\n") 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 still → 55.
6. Input Validation Labs
Pair the pattern with scanf 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 C 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: learn i += 2 in the outer loop first; compare with j += 2 odd-digit variant in Example 3.
Usage Tips
Small habits that keep number-pattern code clean.
1. Name Bounds Clearly
Use
printf("%d", j)without spaces — notprintf("%d ", j)unless you want gaps.2. Prefer
scanfCheck the return value so bad input does not leave
maxuninitialized.3. Keep printf("\n") Outside
Only call
printf("\n")after the inner loop finishes the row.4. Trace i and j on Paper
Write each odd
iand thejrange before coding.5. Dry-Run One Small n
Trace
max = 7on paper before coding larger demos.
Pro Tip: if the output is a vertical list of single digits per line, you almost certainly put printf("\n") inside the inner loop.
Common Pitfalls
Mistakes that commonly break odd-length row patterns.
1. Newline Inside the Inner Loop
Each digit lands on its own line — you get a column, not a triangle.
→ Use
printf("%d", j);printf("\n")only after the inner loop.2. Forgetting i += 2
Using
i++prints every length 1, 2, 3, 4 — not odd lengths only.→ Use
for (i = 1; i <= max; i += 2)for odd row lengths.3. Adding Spaces Between Digits
printf("%d ", j)produces1 2 3instead of123.→ Use
printf("%d", j)for concatenated digits.4. Forgetting the Row Break
Omitting
printf("\n")glues every number onto one endless line.→ Always end the row after the inner loop.
5. Unchecked scanf
Letters or empty input leave
maxuninitialized.→ Check
scanfreturn value and re-prompt on failure.
Edge Cases
Check these inputs before calling the solution done.
max = 1
Single digit
Output is just 1 on one line.
max = 0
Empty pattern
Outer loop never runs — print nothing or show a message.
Negative
max < 0
Treat as invalid; re-prompt instead of silent empty output.
Large n
Large width
Output grows as n² characters — fine for labs, noisy for huge n.
Bad input
Non-numeric scanf input
Unchecked scanf leaves max unset — check the return value.
Even max
User enters even
Subtract 1 to keep odd row lengths — see Example 2.
Drill
🎯 Practice Problems
Try these variations to lock in the pattern.
1. Jump number triangle
- Decreasing step variable per row
- Review Program 21
2. Number & asterisk mirror
- Mirror pattern with stars
- Continue with Program 23
3. Spaced digits
- Use
printf("%d ", j)for gaps - Compare with concatenated output
4. No trailing space
- Print space only between numbers, not after the last
- Harder follow-up after this page
Important
Notes
- Odd sum. Total prints =
1+3+5+...+max— O(n²) for maximum row lengthn. printf("%d", j)stays on the line;printf("\n")advances — mix them carefully.- Validate
max > 0for interactive programs;max = 1should print a single1. - This page is left-aligned. Centered pyramids need leading spaces — covered later in the series.
Quick Takeaway: use i += 2 in the outer loop, printf("%d", j) in the inner loop, then printf("\n") after each row.
Analysis
⏱️ Time and Space Complexity
| Program | Time | Extra space |
|---|---|---|
| Nested loops (Examples 1–2) | O(max²) | O(1) |
| Odd digits (Example 3) | O(max²) | O(1) |
🎉 Conclusion
The increasing odd-length number rows pattern is a compact lesson in loop step sizes: use i += 2 in the outer loop and printf("%d", j) in the inner loop to concatenate digits. Master the fixed-max version, then try user input and the odd-only digit variant.
Practice the three examples above, then continue to Program 23 for the number & asterisk mirror pattern.
Use i += 2 for odd lengths — validate max and adjust even input when reading from the console.
Pro Tips
💡 Best Practices
✅ Do
- Use
for (i = 1; i <= max; i += 2)in the outer loop - Use
printf("%d", j)— no space between digits - Adjust even
maxwithmax -= 1for user input - Check
scanfreturn value before usingmax - State O(n²) time when asked about complexity
❌ Don’t
- Call
printf("\n")inside the inner digit loop - Use
i++when you want odd lengths only - Add spaces unless you want separated digits
- Skip the newline after each row
- Ignore bad console input in user-facing demos
- Skip the
max = 1edge case
Summary
Key Takeaways
Knowledge Unlocked
Five things to remember about this odd-length pattern
Print the pattern the beginner-friendly way.
5
Core concepts 01
Rule
i += 2 rows
Definition 02
Inner 1..i
printf("%d", j) no space
Code 03
Odd lengths
1, 3, 5, 7, 9
Shape 04
j += 2
Odd digits variant
Variant 05
Complexity
O(n²) time
Analysis❓ Frequently Asked Questions
Because the outer loop uses i += 2, so i becomes 1, 3, 5, 7, 9 — each row prints one more odd count of digits than the previous.
printf("%d", j) prints each digit immediately after the previous one on the same line — no space character is added.
Yes. Change the inner loop to j += 2 and print j to output 1, 13, 135, 1357, 13579 (see Example 3).
printf("%d", j) stays on the same line. printf("\n") ends the current line. Digits use printf; the row break uses printf("\n") after the inner loop.
Because the outer loop condition is i <= 9. Change 9 to any odd maximum to extend the pattern.
Subtract 1 to make it odd (see Example 2) so the last row still has an odd length.
O(n²) for maximum row length n because total prints are 1+3+5+...+n.
Check scanf's return value: if (scanf("%d", &max) != 1) handle bad input. Unchecked scanf leaves max uninitialized on failure.
The outer loop never runs, so nothing is printed. Validate and prompt again if you want a clear user message.
Did you Know? 🔊
Each row length increases by 2 because the outer loop uses i += 2 (1, 3, 5, 7, 9). The inner loop prints 1..i with no spaces — total prints grow as O(n²) for maximum row length n.
Continue to Program 23
Move on to the number & asterisk mirror pattern in the C number-pattern series.
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