PPractick

The problem

The last pattern in the series prints a (2n − 1) × (2n − 1) square of numbers made of concentric rings: the outermost ring is all n, the next ring inside is n − 1, and so on down to a single 1 in the centre. Building it ring by ring is awkward. The elegant solution computes each cell directly: its value depends on how far the cell is from the nearest edge. That "distance to the nearest boundary" idea shows up again in matrix and BFS problems.

Example for n = 4:

4 4 4 4 4 4 4
4 3 3 3 3 3 4
4 3 2 2 2 3 4
4 3 2 1 2 3 4
4 3 2 2 2 3 4
4 3 3 3 3 3 4
4 4 4 4 4 4 4

Function signature

vector<string> concentricSquare(int n);  // (2n - 1) rows of (2n - 1) space-separated numbers

Test cases

Input n	Output rows	Explanation
1	"1"	A 1 × 1 grid
2	"2 2 2", "2 1 2", "2 2 2"	Ring of 2s around a 1
3	"3 3 3 3 3", "3 2 2 2 3", "3 2 1 2 3", "3 2 2 2 3", "3 3 3 3 3"	Three rings
4	as in the example	7 × 7 grid

(Confirm: numbers are space-separated with no trailing space; the grid side is 2n − 1.)

How interviewers phrase it

• "Print the concentric number pattern for N."
• Considered the hardest of the standard pattern problems; sometimes used to separate strong candidates in pattern-heavy screens.

Clarifying questions to ask

1. Is the grid size 2n − 1?
2. Space-separated?
3. Print or return?

Follow-ups to expect

1. "How do you compute a cell without drawing rings?"
2. "Why the minimum of four distances?"
3. "How would you print the rings in reverse (1 on the outside)?"
4. "Complexity?"

Related questions

• Pattern 20 Medium
• Pattern 21 Medium
• Easy and Medium Easy
• Hard Easy
• Pattern 1 Easy
• Pattern 2 Easy

All 474 dsa interview questions

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