feat(content): add new problem pages, reorganize docs into (problems) subfolders, and update meta display to page

apps/docs/content/(05-decision-space)/backtracking/(problems)/46_permutations.mdx

@@ -0,0 +1,55 @@
+---
+title: '46. Permutations'
+description: Given an array nums of distinct integers, return all the possible permutations. You can return the answer in any order
+icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Backtracking", slug: "backtracking" }
+issue: "https://github.com/prdlk/leetcode/issues/151"
+sidebar:
+  label: 'Permutations'
+  badge: 'Medium'
+---
+
+### Example 1:
+- Input: `nums = [1,2,3]`
+- Output: `[[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]`
+
+### Example 2:
+- Input: `nums = [0,1]`
+- Output: `[[0,1],[1,0]]`
+
+### Example 3:
+- Input: `nums = [1]`
+- Output: `[[1]]`
+
+### Constraints:
+
+- `1 <= nums.length <= 6`
+- `-10 <= nums[i] <= 10`
+- All the integers of `nums` are unique.
+
+## Solution
+
+```py
+class Solution:
+    def permute(self, nums: list[int]) -> list[list[int]]:
+        result, path = [], []
+        used = [False] * len(nums)
+
+        def backtrack():
+            if len(path) == len(nums):
+                result.append(path[:])
+                return
+            for i in range(len(nums)):
+                if used[i]:
+                    continue
+                used[i] = True
+                path.append(nums[i])
+                backtrack()
+                path.pop()
+                used[i] = False
+
+        backtrack()
+        return result
+```