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apps/docs/content/(02-nodal-grid)/matrix-index-math/54-spiral-matrix.mdx

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+---
+title: '54. Spiral Matrix'
+description: Given an m x n matrix, return all elements of the matrix in spiral order
+sidebar:
+  label: 'Spiral Matrix'
+  badge: 'Medium'
+---
+
+<Badge variant="accent">Array</Badge>
+
+### Example 1:
+- Input: `matrix = [[1,2,3],[4,5,6],[7,8,9]]`
+- Output: `[1,2,3,6,9,8,7,4,5]`
+
+### Example 2:
+- Input: `matrix = [[1,2,3,4],[5,6,7,8],[9,10,11,12]]`
+- Output: `[1,2,3,4,8,12,11,10,9,5,6,7]`
+
+### Constraints:
+
+- `m == matrix.length`
+- `n == matrix[i].length`
+- `1 <= m, n <= 10`
+- `-100 <= matrix[i][j] <= 100`
+
+## Approach
+
+```mermaid
+flowchart TD
+  S(["spiralOrder(matrix)"]) --> I["res = [], top = 0, bottom = len(matrix) - 1, left = 0, right = len(matrix[0]) - 1"]
+  I --> W{"top <= bottom and left <= right?"}
+  W -- no --> E(["return res"])
+  W -- yes --> T["append matrix[top][c] for c in left..right, then top += 1 — top row, shrink from above"]
+  T --> R["append matrix[r][right] for r in top..bottom, then right -= 1 — right column"]
+  R --> B{"top <= bottom?"}
+  B -- yes --> C["append matrix[bottom][c] for c in right down to left, then bottom -= 1 — bottom row"]
+  C --> L{"left <= right?"}
+  B -- no --> L
+  L -- yes --> D["append matrix[r][left] for r in bottom down to top, then left += 1 — left column"]
+  D --> W
+  L -- no --> W
+```
+
+## Solution
+
+```py
+class Solution:
+    def spiralOrder(self, matrix: List[List[int]]) -> List[int]:
+        res = []
+        top, bottom = 0, len(matrix) - 1
+        left, right = 0, len(matrix[0]) - 1
+
+        while top <= bottom and left <= right:
+            # 1. Top Row
+            for c in range(left, right + 1):
+                res.append(matrix[top][c])
+            top += 1
+
+            # 2. Right Column
+            for r in range(top, bottom + 1):
+                res.append(matrix[r][right])
+            right -= 1
+
+            # 3. Bottom Row
+            if top <= bottom:
+                for c in range(right, left - 1, -1):
+                    res.append(matrix[bottom][c])
+                bottom -= 1
+
+            # 4. Left Column
+            if left <= right:
+                for r in range(bottom, top - 1, -1):
+                    res.append(matrix[r][left])
+                left += 1
+
+        return res
+```
+
+## Explanation
+
+<YouTube id="BJnMZNwUk1M" title="Spiral Matrix - Microsoft Interview Question - Leetcode 54" />