A hollow square of 1s prints a border of ones with empty space inside — top and bottom rows are full; middle rows have ones only at the edges.
Remember
Rule: for each cell (i, j),
print "1 " on the border, " " inside
1 1 1 1 1
1 1
1 1
1 1
1 1 1 1 1 ← rows = 5
Unlike Program 41 (square number pyramid), here every cell is either a border 1 or an inner space.
Approach
How to Solve It
Visit every cell in an n × n grid; print "1 " on the border and " " inside.
Method
Idea
Best for
Boundary check
i==1 || i==rows || j==1 || j==rows → print 1
Learning, interviews, exams
Filled square
Skip the if; always print "1 "
When you want a solid block of ones
Pseudocode
Pseudocode
for i from 1 to rows:
for j from 1 to rows:
if i is 1 or i is rows or j is 1 or j is rows:
print "1 "
else:
print " "
print newline
Cheat sheet
Goal
Pattern
Walk rows
for (int i = 1; i <= rows; i++)
Walk columns
for (int j = 1; j <= rows; j++)
Border test
i == 1 || i == rows || j == 1 || j == rows
Print cell
System.out.print("1 "); or " "
End the row
System.out.println();
Printing Numbers vs Starting a New Line
API
Effect
Use for
System.out.print
Stays on the same line
Each cell ("1 " or " ")
System.out.println
Ends the current line
After the column loop finishes
Print values without a newline, then end the row once.
Try it
Live Preview
Change the size and the hollow square updates instantly.
Whole numbers from 3 to 9. Tap a chip or type a value — the preview redraws as you go.
Live resultsize = 5 · 25 cells
1 1 1 1 1
1 1
1 1
1 1
1 1 1 1 1
Trace
Worked Walkthrough — rows = 5, row i = 3
Trace one middle row to see which cells are border ones vs inner spaces.
j
Border?
Printed
1
Yes (j == 1)
1
2
No
3
No
4
No
5
Yes (j == rows)
1
Row 3 becomes 1 1. Top and bottom rows print 1 for every column.
Code
Java Programs
Three complete programs: fixed rows = 5, Scanner input, and a filled square. Use View Output to reveal sample results.
Example 1 — Fixed rows = 5
Hard-coded size — border check decides each cell.
Java
public class HollowSquareOfOnes {
public static void main(String[] args) {
int rows = 5;
for (int i = 1; i <= rows; i++) {
for (int j = 1; j <= rows; j++) {
if (i == 1 || i == rows || j == 1 || j == rows)
System.out.print("1 ");
else
System.out.print(" ");
}
System.out.println();
}
}
}
Output
1 1 1 1 1
1 1
1 1
1 1
1 1 1 1 1
How It Works
1. Grid loops. Outer i is the row; inner j is the column.
2. Border test. Top, bottom, left, or right → print "1 ".
3. Inner cells. Everything else prints " " to keep columns aligned.
When i = 1: five ones. When i = 3: ones only at j = 1 and j = 5.
Example 2 — Size Input
Read rows at runtime. Same border-check core.
Java
import java.util.Scanner;
public class HollowSquareOfOnesInput {
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 = 1; j <= rows; j++) {
if (i == 1 || i == rows || j == 1 || j == rows)
System.out.print("1 ");
else
System.out.print(" ");
}
System.out.println();
}
sc.close();
}
}
Output (when user enters 5)
Enter the number of rows: 5
1 1 1 1 1
1 1
1 1
1 1
1 1 1 1 1
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 — Filled Square
Drop the border check — every cell prints "1 ".
Java
public class HollowSquareFilled {
public static void main(String[] args) {
int rows = 5;
for (int i = 1; i <= rows; i++) {
for (int j = 1; j <= rows; j++)
System.out.print("1 ");
System.out.println();
}
}
}
Output
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
How It Works
1. Same grid. Still n × n nested loops.
2. No if. Every cell is "1 " — a solid block.
3. Compare tip. Put Examples 1 and 3 side by side to see what the border check changes.
Edge Cases & Pitfalls
Check these before calling the solution done.
println inside
Column of cells
If println is inside the column loop, each cell lands on its own line. Use print for cells; println only after the row.
Wrong spaces
Broken columns
Inner cells must use " " (two spaces) to match the width of "1 ".
Miss a side
Open border
Forgetting j == 1 or j == rows leaves the left or right edge empty.
No println
One long line
Forgetting println() after the row glues every cell onto one endless line.
rows = 1
Single cell
Output is just 1 — a 1×1 border square.
Bad input
Use hasNextInt
nextInt() throws on letters — prefer hasNextInt() and require a positive integer.
Analysis
Time and Space Complexity
Program
Time
Extra space
Hollow / filled square (Examples 1–3)
O(n²)
O(1)
Both loops visit all n × n cells once. Only loop counters are stored.
Remember
Key Takeaways
Rule: print "1 " on the border; print " " inside.
Border test:i==1 || i==rows || j==1 || j==rows.
Break the row: call println only after the column loop.
Complexity:O(n²) time; O(1) extra space.
One line: for each cell, print "1 " if it is on the border, else " ", then println() after each row.
Frequently Asked Questions
Only border positions print 1. All inner positions print spaces, so the center stays blank.
It checks i==1 or i==rows (top/bottom) or j==1 or j==rows (left/right). If any is true, it prints 1.
Each cell uses a fixed width so columns align. Border cells use "1 " and inner cells use " ".
Yes. Replace the fixed 5 with a rows variable and read it with Scanner — see Example 2.
Remove the if condition and always print "1 " in the inner loop — see Example 3.
O(n²) for an n×n square because both loops visit every cell once.
Use sc.hasNextInt() before sc.nextInt() so bad input does not throw InputMismatchException.
You get a single "1 " on one line — technically a 1×1 border square.
🤔
Did you know?
Only border cells print 1 — when i is the first or last row, or j is the first or last column. Inner cells print spaces, which creates the hollow look.
