Spiral Matrix II

Spiral Matrix II

What is this problem about?

Following the success of the first version, the Spiral Matrix II interview question asks you to do the reverse: given an integer $n$, generate an $n \times n$ square matrix filled with elements from 1 to $n^2$ in spiral order. It is an "output generation" problem rather than a "traversal" problem, but the underlying logic remains very similar.

Why is this asked in interviews?

This Spiral Matrix II coding problem is often asked by Uber, Goldman Sachs, and Adobe. It tests the same boundary management skills as the first version but adds the requirement of constructing and returning a 2D array. It's a great way for interviewers to see if you can take a logic you've learned (spiral traversal) and adapt it to a slightly different goal (matrix construction).

Algorithmic pattern used

The Matrix Simulation pattern is used here as well. You initialize an empty $n \times n$ matrix and maintain your four boundaries (top, bottom, left, right). Instead of reading values, you write an incrementing counter into the matrix as you follow the spiral path. The logic for turning and shrinking the boundaries is identical to the original Spiral Matrix problem.

Example explanation

If $n = 3$:

1. Initialize a 3x3 matrix.
2. Fill top row (left to right): [1, 2, 3]
3. Fill right column (top to bottom): [4, 5] at (1,2) and (2,2)
4. Fill bottom row (right to left): [6, 7] at (2,1) and (2,0)
5. Fill left column (bottom to top): [8] at (1,0)
6. Fill center: [9] at (1,1) The matrix is now complete.

Common mistakes candidates make

• Wrong Matrix Initialization: Not correctly creating a 2D array in their chosen language (e.g., in Python, [[0]*n]*n is a common trap).
• Hardcoding $n=3$: Writing logic that works for small $n$ but fails to generalize.
• Counter Errors: Forgetting to increment the counter or starting it at the wrong value.
• Directional Confusion: Swapping the order of row/column fill, resulting in a non-spiral pattern.

Interview preparation tip

Practice initializing 2D arrays efficiently in your language of choice. For this specific problem, remember that the number of elements is always $n^2$. You can use a single for loop from 1 to $n^2$ and update your $(r, c)$ coordinates, but the "four boundaries" method remains the most intuitive and least error-prone way to handle the spiral logic.