<p>You are given two integers <code>m</code> and <code>n</code>, which represent the dimensions of a matrix.</p>

<p>You are also given the <code>head</code> of a linked list of integers.</p>

<p>Generate an <code>m x n</code> matrix that contains the integers in the linked list presented in <strong>spiral</strong> order <strong>(clockwise)</strong>, starting from the <strong>top-left</strong> of the matrix. If there are remaining empty spaces, fill them with <code>-1</code>.</p>

<p>Return <em>the generated matrix</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/05/09/ex1new.jpg" style="width: 240px; height: 150px;" />
<pre>
<strong>Input:</strong> m = 3, n = 5, head = [3,0,2,6,8,1,7,9,4,2,5,5,0]
<strong>Output:</strong> [[3,0,2,6,8],[5,0,-1,-1,1],[5,2,4,9,7]]
<strong>Explanation:</strong> The diagram above shows how the values are printed in the matrix.
Note that the remaining spaces in the matrix are filled with -1.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/05/11/ex2.jpg" style="width: 221px; height: 60px;" />
<pre>
<strong>Input:</strong> m = 1, n = 4, head = [0,1,2]
<strong>Output:</strong> [[0,1,2,-1]]
<strong>Explanation:</strong> The diagram above shows how the values are printed from left to right in the matrix.
The last space in the matrix is set to -1.</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= m, n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= m * n &lt;= 10<sup>5</sup></code></li>
	<li>The number of nodes in the list is in the range <code>[1, m * n]</code>.</li>
	<li><code>0 &lt;= Node.val &lt;= 1000</code></li>
</ul>

# Definition for singly-linked list.
# class ListNode:
#     def __init__(self, val=0, next=None):
#         self.val = val
#         self.next = next
import numpy as np

class Solution:
    def spiralMatrix(self, m: int, n: int, head: Optional[ListNode]) -> List[List[int]]:
        # array = [[-1]*n]*m
        array = [[-1 for _ in range(n)] for _ in range(m)]
        # print(len(array), len(array[0]))
        # print(array)
        i,j =0,0
        
        # Define direction vectors for right, down, left, and up
        directions = [(0, 1), (1, 0), (0, -1), (-1, 0)]
        direction = 0  # Start by moving to the right

        # Boundaries
        top, bottom, left, right = 0, m - 1, 0, n - 1
        
        # Start from the top-left corner
        r, c = 0, 0
        # print(f"-> change dir to {directions[direction]}")
        # print(f"next margins: rows={top}:{bottom}, cols={left}:{right}")
        while head:
            array[r][c] = head.val
            # print(f"array[{r},{c}]-> {array}")
            head = head.next
            

            # next in the current direction
            nr, nc = r + directions[direction][0], c + directions[direction][1]

            # print(f"\t next: {nr}, {nc}")
            # Check if the new position is out of bounds or already visited
            if not (top <= nr <= bottom and left <= nc <= right):

                # Adjust the boundary after completing a row/column
                if direction == 0:  # moving right
                    top += 1
                elif direction == 1:  # moving down
                    right -= 1
                elif direction == 2:  # moving left
                    bottom -= 1
                elif direction == 3:  # moving up
                    left += 1

                # Change direction when hitting boundaries
                direction = (direction + 1) % 4
                # print(f"-> change dir to {directions[direction]}")

                nr, nc = r + directions[direction][0], c + directions[direction][1]

                # print(f"next margins: rows={top}:{bottom}, cols={left}:{right}")

            r, c = nr, nc
            
        return array
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