A diagonal mirror number pattern prints digits only on the main diagonal (i == j) and the mirror diagonal (i == k). Everywhere else is a space — an X shape.
Remember
Rule: for i = 1..n
left: if i==j print j else space
mirror: if i==k print k else space (k = n-1..1)
1 1
2 2
3 3
4 4
5 ← n = 5
Unlike Program 52 (palindrome digit runs), here most cells are spaces — only the two diagonals carry values.
Approach
How to Solve It
For each row, walk the left half with i==j, then the mirror half with i==k.
Method
Idea
Best for
Fixed n
Hard-code size; i==j / i==k
Labs and demos
Scanner input
Same logic; read n at runtime
Interactive practice
Star diagonals
Print * instead of the digit
Visual X-shape practice
Pseudocode
Pseudocode
for i from 1 to n:
for j from 1 to n:
if i == j: print j
else: print space
for k from n-1 down to 1:
if i == k: print k
else: print space
new line
Cheat sheet
Goal
Pattern
Set size
int n = 5;
Main diagonal
if (i == j) print(j); else print(" ");
Mirror half
for (int k = n - 1; k >= 1; k--)
Mirror hit
if (i == k) print(k); else print(" ");
End row
System.out.println();
Printing Numbers vs Starting a New Line
API
Effect
Use for
System.out.print
Stays on the same line
Each digit or space in both halves
System.out.println
Ends the line
After both halves finish
Build the full row with print, then break once.
Try it
Live Preview
Change n and the diagonal mirror pattern updates instantly.
Whole numbers from 3 to 9. Tap a chip or type a value — the preview redraws as you go.
Live resultn = 5 · width = 9
1 1
2 2
3 3
4 4
5
Trace
Worked Walkthrough — n = 5
Trace where each digit lands on the main and mirror diagonals.
i
Main (j)
Mirror (k)
Printed row
1
j=1 → 1
k=1 → 1
1 1
2
j=2 → 2
k=2 → 2
2 2
3
j=3 → 3
k=3 → 3
3 3
4
j=4 → 4
k=4 → 4
4 4
5
j=5 → 5
(none)
5
Row 5 has no mirror hit because k only goes down to 1 from n−1 — the diagonals already meet in the left half.
Code
Java Programs
Three complete programs: fixed n = 5, Scanner input, and star diagonals. Use View Output to reveal sample results.
Example 1 — Fixed n = 5
Hard-coded size — left loop with i==j, mirror loop with i==k.
Java
public class DiagonalMirrorNumberPattern {
public static void main(String[] args) {
int n = 5;
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= n; j++) {
if (i == j) System.out.print(j);
else System.out.print(" ");
}
for (int k = n - 1; k >= 1; k--) {
if (i == k) System.out.print(k);
else System.out.print(" ");
}
System.out.println();
}
}
}
Output
1 1
2 2
3 3
4 4
5
How It Works
1. Left half. Columns j = 1..n — print j only when i == j (main diagonal).
2. Mirror half. Columns k = n−1..1 — print k only when i == k (mirror diagonal).
3. Spaces elsewhere. Every other cell is a space, so the digits form an X.
Example 2 — Scanner Input
Read n at runtime. Same diagonal conditions.
Java
import java.util.Scanner;
public class DiagonalMirrorNumberPatternInput {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
System.out.print("Enter n: ");
int n = sc.nextInt();
if (n < 1) return;
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= n; j++) {
System.out.print(i == j ? j : " ");
}
for (int k = n - 1; k >= 1; k--) {
System.out.print(i == k ? k : " ");
}
System.out.println();
}
sc.close();
}
}
Output (when user enters 5)
Enter n: 5
1 1
2 2
3 3
4 4
5
How It Works
1. Prompt and guard. Read n; exit early if it is less than 1.
2. Same logic. Ternary i == j ? j : " " is just a shorter form of the if/else in Example 1.
3. Safer input tip. Prefer:
Safer input
if (!sc.hasNextInt()) {
System.out.println("Enter a positive integer.");
return;
}
int n = sc.nextInt();
if (n < 1) {
System.out.println("Enter a positive integer.");
return;
}
Example 3 — Star Diagonals
Same X-shape — print * instead of the diagonal digit.
Java
public class DiagonalMirrorNumberPatternStar {
public static void main(String[] args) {
int n = 5;
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= n; j++) {
System.out.print(i == j ? "*" : " ");
}
for (int k = n - 1; k >= 1; k--) {
System.out.print(i == k ? "*" : " ");
}
System.out.println();
}
}
}
Output
* *
* *
* *
* *
*
How It Works
1. Same positions. Still use i == j and i == k to choose which cells light up.
2. Different glyph. Print * instead of j or k — the X shape stays the same.
3. Same width. Each row is still 2n − 1 characters.
Edge Cases & Pitfalls
Check these before calling the solution done.
k from n
Doubled center
Starting the mirror loop at k = n reprints the middle column. Always start at n − 1.
print(i)
Wrong digit
Print j or k (the column), not i, so both arms show matching numbers on each row.
Missing spaces
Collapsed X
Skipping the else print(" ") branch packs digits together and destroys the diagonal shape.
n = 1
Single digit
Output is just 1 — the mirror loop does not run.
n = 0
Empty output
The outer loop never runs. Guard interactive input with n >= 1.
Bad input
Use hasNextInt
nextInt() throws on letters — prefer hasNextInt() and require a positive integer.
Analysis
Time and Space Complexity
Program
Time
Extra space
All three examples
O(n²)
O(1)
Each of n rows prints 2n − 1 characters → about 2n² prints.
Remember
Key Takeaways
Rule: print on i==j (left) and i==k (mirror); spaces everywhere else.
Mirror start:k = n − 1 avoids duplicating the center column.
Width: each row is 2n − 1 characters.
Complexity:O(n²) for size n.
One line: light up i==j and i==k; fill the rest with spaces for an X.
Frequently Asked Questions
For i=1, i==j prints 1 on the main diagonal and i==k prints 1 on the mirror diagonal when k=1.
At i=n, both diagonals meet at the same position in the left half, so only one digit appears. The mirror loop starts at n-1 and never matches i=n.
Starting at n would duplicate the center column. k = n-1 down to 1 mirrors without repeating the middle.
Yes. Use a variable n — both inner loops run with the same diagonal conditions.
Replace the printed digit with * when i==j or i==k — see Example 3.
Each row has 2n-1 character positions — n for the left half and n-1 for the mirror half.
O(n²) for n rows. Each row checks O(n) cells in two loops.
Use sc.hasNextInt() before sc.nextInt() so bad input does not throw InputMismatchException.
🤔
Did you know?
Row i prints the number on the main diagonal (i == j) and on the mirror diagonal (i == k). All other cells are spaces — an X-shaped number pattern.
