A rotating number pattern keeps every row the same length while the start value shifts right and wraps with a descending tail.
Remember
Rule: for i from 1 to rows,
print i..rows, then print (i-1)..1
12345
23451
34521
45321
54321 ← rows = 5
Unlike Program 38 (shrinking sequential triangle), here every row has exactly rows digits.
Approach
How to Solve It
Walk i from 1 to rows; print i..rows, then append i-1..1.
Method
Idea
Best for
Dual inner loops
Ascending run i..rows, then descending wrap i-1..1
Learning, interviews, exams
Spaced digits
Same loops; print each value with a trailing space
Readable output when rows > 9
Pseudocode
Pseudocode
for i from 1 to rows:
for j from i to rows:
print j
for k from i down to 2:
print (k - 1)
print newline
Cheat sheet
Goal
Pattern
Walk rows
for (int i = 1; i <= rows; i++)
Main run
for (int j = i; j <= rows; j++) print(j)
Wrap tail
for (int k = i; k > 1; k--) print(k - 1)
End the row
System.out.println();
Digits per row
Always rows
Printing Numbers vs Starting a New Line
API
Effect
Use for
System.out.print
Stays on the same line
Each digit in both inner loops
System.out.println
Ends the current line
After both inner loops finish
Print values without a newline, then end the row once.
Try it
Live Preview
Change the row count and the rotating pattern updates instantly.
Whole numbers from 3 to 9. Tap a chip or type a value — the preview redraws as you go.
Live resultrows = 5 · 25 digits
12345
23451
34521
45321
54321
Trace
Worked Walkthrough — rows = 5
Trace the main run (i..rows) and the wrap tail (i-1..1) for each row.
i
Main run
Wrap tail
Printed row
1
1..5
(empty)
12345
2
2..5
1
23451
3
3..5
2, 1
34521
4
4..5
3, 2, 1
45321
5
5
4 … 1
54321
Each row has exactly 5 digits — total 5 × 5 = 25.
Code
Java Programs
Three complete programs: fixed rows = 5, Scanner input, and spaced digits. Use View Output to reveal sample results.
Example 1 — Fixed rows = 5
Hard-coded size — dual inner loops with compact digits.
Java
public class RotatingNumberPattern {
public static void main(String[] args) {
int rows = 5;
for (int i = 1; i <= rows; i++) {
for (int j = i; j <= rows; j++)
System.out.print(j);
for (int k = i; k > 1; k--)
System.out.print(k - 1);
System.out.println();
}
}
}
Output
12345
23451
34521
45321
54321
How It Works
1. Outer loop.i is the start of the main run for that row.
2. Main run.j prints from i up to rows.
3. Wrap tail.k runs from i down to 2 and prints k - 1.
When i = 1: only the main run — 12345. When i = 3: 345 + 21 → 34521.
Example 2 — Rows Input
Read rows at runtime. Same dual-loop core.
Java
import java.util.Scanner;
public class RotatingNumberPatternInput {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
System.out.print("Enter the number of rows: ");
int rows = sc.nextInt();
if (rows < 1) return;
for (int i = 1; i <= rows; i++) {
for (int j = i; j <= rows; j++)
System.out.print(j);
for (int k = i; k > 1; k--)
System.out.print(k - 1);
System.out.println();
}
sc.close();
}
}
Output (when user enters 5)
Enter the number of rows: 5
12345
23451
34521
45321
54321
How It Works
1. Prompt and guard. Read rows; exit early if it is less than 1.
2. Same core. Only the source of rows changes from a literal to user input.
3. Safer input tip. Prefer:
Safer input
if (!sc.hasNextInt()) {
System.out.println("Enter a positive integer.");
return;
}
int rows = sc.nextInt();
if (rows < 1) {
System.out.println("Enter a positive integer.");
return;
}
Example 3 — Spaced Output
Same dual loops — each value printed with a trailing space for readability.
Java
public class RotatingSpacedOutput {
public static void main(String[] args) {
int rows = 5;
for (int i = 1; i <= rows; i++) {
for (int j = i; j <= rows; j++)
System.out.print(j + " ");
for (int k = i; k > 1; k--)
System.out.print((k - 1) + " ");
System.out.println();
}
}
}
Output
1 2 3 4 5
2 3 4 5 1
3 4 5 2 1
4 5 3 2 1
5 4 3 2 1
How It Works
1. Same structure. Dual loops unchanged — only the print adds a space.
2. Why space? Digits stay readable when values reach two digits.
3. Width tip. For larger rows, prefer format("%2d ", value) for aligned columns.
Edge Cases & Pitfalls
Check these before calling the solution done.
println inside
Column of digits
If println is inside either inner loop, each digit lands on its own line. Use print for digits; println only after both loops.
Skip wrap
No rotation
Omitting the second loop prints only i..rows and loses the wrap-around tail.
Wrong wrap
34512 vs 34521
Appending 1..i-1 ascending gives a pure rotation. This pattern uses descending i-1..1.
No println
One long line
Forgetting println() after the row glues every digit onto one endless line.
rows = 1
Single digit
Output is just 1 on one line — the wrap loop never runs.
Bad input
Use hasNextInt
nextInt() throws on letters — prefer hasNextInt() and require a positive integer.
Analysis
Time and Space Complexity
Program
Time
Extra space
Rotating pattern (Examples 1–3)
O(n²)
O(1)
Each of n rows prints n digits — total n². Only loop counters are stored.
Remember
Key Takeaways
Rule: row i prints i..rows then i-1..1.
Fixed width: every row has exactly rows digits.
Break the row: call println only after both inner loops.
Complexity:O(n²) time; O(1) extra space.
One line: for each row, print i..rows then i-1..1 with print, then println().
Frequently Asked Questions
When i=5 and rows=5, the first loop prints 5, then the second loop appends 4, 3, 2, 1 — giving 54321.
The first loop prints the ascending run from i to rows. The second appends the wrap-around tail from i-1 down to 1.
Program 38 prints one continuous sequence with shrinking row widths. Program 39 keeps every row at rows digits by wrapping back to smaller numbers.
No. A pure rotation would give 34512 on row 3. This pattern prints i..rows then (i-1)..1, so row 3 is 34521.
Yes. Print j + " " and (k-1) + " " in the loops — see Example 3.
O(n²) where n is rows. Each of n rows prints n digits.
Use sc.hasNextInt() before sc.nextInt() so bad input does not throw InputMismatchException.
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 prints i..rows then i-1..1 — two inner loops that create the rotation. Every row has exactly rows digits, so total output is n² for n rows.
