Spiral Matrix II

LeetCode 59 | Difficulty: Medium

Medium

Problem Description

Given a positive integer n, generate an n x n matrix filled with elements from 1 to n^2 in spiral order.

Example 1:

Input: n = 3
Output: [[1,2,3],[8,9,4],[7,6,5]]

Example 2:

Input: n = 1
Output: [[1]]

Constraints:

- `1 <= n <= 20`

Topics: Array, Matrix, Simulation

---

Approach

Matrix

Treat the matrix as a 2D grid. Common techniques: directional arrays (dx, dy) for movement, BFS/DFS for connected regions, in-place marking for visited cells, boundary traversal for spiral patterns.

When to use

Grid traversal, island problems, path finding, rotating/transforming matrices.

---

Solutions

Solution 1: C# (Best: 40 ms)

Metric	Value
Runtime	40 ms
Memory	N/A
Date	2018-04-08

Solution

public class Solution {
    public int[,] GenerateMatrix(int n) {
        int[,] result = new int[n, n];
    int k = 0, l = 0, last_row = n-1, last_col = n - 1;
    int currentValue = 1;

    while (k <= last_row && l <= last_col)
    {
        for (int i = l; i <= last_col; i++)
        {
            result[k, i] = currentValue++;
        }
        k++;
        for (int i = k; i <= last_row; i++)
        {
            result[i, last_col] = currentValue++;
        }
        last_col--;
        if (k <= last_row)
        {
            for (int i = last_col; i >= l; i--)
            {
                result[last_row, i] =  currentValue++;
            }
        }
        last_row--;
        if (l <= last_col)
        {
            for (int i = last_row; i >= k; i--)
            {
                result[i, l] = currentValue++;
            }
        }
        l++;

    }

    return result;
    }
}

---

Complexity Analysis

Approach	Time	Space
Solution	$O(n)$	$O(1) to O(n)$

---

Interview Tips

Key Points

• Discuss the brute force approach first, then optimize. Explain your thought process.