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

apps/docs/content/(02-nodal-grid)/hybrid-structures/(problems)/146_lru-cache.mdx

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+---
+title: '146. LRU Cache'
+description: Design a data structure that follows the constraints of a Least Recently Used (LRU) cache
+icon: dot
+topics:
+  - { name: "Hash Table", slug: "hash-table" }
+  - { name: "Linked List", slug: "linked-list" }
+  - { name: "Design", slug: "design" }
+  - { name: "Doubly-Linked List", slug: "doubly-linked-list" }
+video: "7ABFKPK2hD4"
+issue: "https://github.com/prdlk/leetcode/issues/87"
+sidebar:
+  label: 'LRU Cache'
+  badge: 'Medium'
+---
+
+### Example 1:
+- Input: ``
+- Output: ``
+- Explanation: Input ["LRUCache", "put", "put", "get", "put", "get", "put", "get", "get", "get"] `[[2]`, [1, 1], [2, 2], `[1]`, [3, 3], `[2]`, [4, 4], `[1]`, `[3]`, [4]] Output [null, null, null, `1`, null, `-1`, null, `-1`, `3`, 4] Explanation LRUCache lRUCache = new LRUCache(2); lRUCache.put(1, `1`); // cache is {1=1} lRUCache.put(2, `2`); // cache is {1=1, 2=2} lRUCache.get(1);    // return `1` lRUCache.put(3, `3`); // LRU `key` was `2`, evicts `key 2`, cache is {1=1, 3=3} lRUCache.get(2);    // returns `-1` (not found) lRUCache.put(4, `4`); // LRU `key` was `1`, evicts `key 1`, cache is {4=4, 3=3} lRUCache.get(1);    // return `-1` (not found) lRUCache.get(3);    // return `3` lRUCache.get(4);    // return `4`
+
+### Constraints:
+
+- `1 <= capacity <= 3000`
+- `0 <= key <= 10^4`
+- `0 <= value <= 10^5`
+- At most 2 * 10^5 calls will be made to get and put.
+
+## Approach
+
+```mermaid
+flowchart TD
+  subgraph state["state — dict for O(1) lookup, doubly linked list for O(1) reorder"]
+    H["head — least recent"] --- N["... nodes ..."] --- T["tail — most recent"]
+  end
+  subgraph get["get(key)"]
+    G1{"key in cache?"} -- no --> G2(["return -1"])
+    G1 -- yes --> G3["_remove_node then _add_node — move it beside the tail"]
+    G3 --> G4(["return node.value"])
+  end
+  subgraph put["put(key, value)"]
+    P1{"key in cache?"} -- yes --> P2["update value, _remove_node then _add_node"]
+    P1 -- no --> P3["new Node, cache[key] = node, _add_node"]
+    P3 --> P4{"len(cache) > capacity?"}
+    P4 -- yes --> P5["evict head.next — the least recent — and del cache[lru.key]"]
+    P4 -- no --> P6(["done"])
+    P2 --> P6
+    P5 --> P6
+  end
+  state --> get
+  state --> put
+```
+
+## Solution
+
+```py
+class Node:
+    def __init__(self, key=0, value=0):
+        self.key = key
+        self.value = value
+        self.prev = None
+        self.next = None
+
+
+class LRUCache:
+    def __init__(self, capacity: int):
+        self.capacity = capacity
+        self.cache = {}
+        self.head = Node()
+        self.tail = Node()
+        self.head.next = self.tail  # pyright: ignore[reportAttributeAccessIssue]
+        self.tail.prev = self.head  # pyright: ignore[reportAttributeAccessIssue]
+
+    def _remove_node(self, node):
+        prev_node = node.prev
+        next_node = node.next
+        prev_node.next = next_node
+        next_node.prev = prev_node
+
+    def _add_node(self, node):
+        # Insert just before the tail (most recent at end)
+        node.next = self.tail
+        node.prev = self.tail.prev
+        self.tail.prev.next = node  # pyright: ignore[reportAttributeAccessIssue]
+        self.tail.prev = node
+
+    def get(self, key: int) -> int:
+        if key not in self.cache:
+            return -1
+
+        node = self.cache[key]
+        self._remove_node(node)
+        self._add_node(node)
+        return node.value
+
+    def put(self, key: int, value: int) -> None:
+        if key in self.cache:
+            node = self.cache[key]
+            node.value = value
+            self._remove_node(node)
+            self._add_node(node)
+        else:
+            new_node = Node(key, value)
+            self.cache[key] = new_node
+            self._add_node(new_node)
+
+            if len(self.cache) > self.capacity:
+                lru = self.head.next  # Oldest node is next to the head
+                self._remove_node(lru)
+                del self.cache[lru.key]  # pyright: ignore[reportAttributeAccessIssue]
+
+
+# Your LRUCache object will be instantiated and called as such:
+# obj = LRUCache(capacity)
+# param_1 = obj.get(key)
+# obj.put(key,value)
+```

apps/docs/content/(02-nodal-grid)/hybrid-structures/(problems)/2_add-two-numbers.mdx

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+---
+title: '2. Add Two Numbers'
+description: You are given two non-empty linked lists representing two non-negative integers. The digits are stored in reverse order, and each of their nodes contains a single digit. Add the two numbers and return the sum as a linked list
+icon: dot
+topics:
+  - { name: "Linked List", slug: "linked-list" }
+  - { name: "Math", slug: "math" }
+  - { name: "Recursion", slug: "recursion" }
+video: "wgFPrzTjm7s"
+issue: "https://github.com/prdlk/leetcode/issues/88"
+sidebar:
+  label: 'Add Two Numbers'
+  badge: 'Medium'
+---
+
+### Example 1:
+- Input: `l1 = [2,4,3], l2 = [5,6,4]`
+- Output: `[7,0,8]`
+- Explanation: `342 + 465 = 807`.
+
+### Example 2:
+- Input: `l1 = [0], l2 = [0]`
+- Output: `[0]`
+
+### Example 3:
+- Input: `l1 = [9,9,9,9,9,9,9], l2 = [9,9,9,9]`
+- Output: `[8,9,9,9,0,0,0,1]`
+
+### Constraints:
+
+- The number of nodes in each linked list is in the range [1, 100].
+- `0 <= Node.val <= 9`
+- It is guaranteed that the list represents a number that does not have leading zeros.
+
+## Approach
+
+```mermaid
+flowchart TD
+  S(["addTwoNumbers(l1, l2)"]) --> I["dummy = ListNode(), carry = 0, curr = dummy — dummy.next will be the head"]
+  I --> W{"l1 or l2 or carry?"}
+  W -- no --> E(["return dummy.next"])
+  W -- yes --> A["s = (l1.val if l1 else 0) + (l2.val if l2 else 0) + carry — a missing digit counts as 0"]
+  A --> D["carry, val = divmod(s, 10)"]
+  D --> N["curr.next = ListNode(val), curr = curr.next"]
+  N --> V["l1 = l1.next if l1 else None, l2 = l2.next if l2 else None"]
+  V --> W
+```
+
+## Solution
+
+```py
+# Definition for singly-linked list.
+# class ListNode:
+#     def __init__(self, val=0, next=None):
+#         self.val = val
+#         self.next = next
+class Solution:
+    def addTwoNumbers(
+        self, l1: Optional[ListNode], l2: Optional[ListNode]
+    ) -> Optional[ListNode]:
+
+        dummy = ListNode()
+        carry = 0
+        curr = dummy
+        while l1 or l2 or carry:
+            s = (l1.val if l1 else 0) + (l2.val if l2 else 0) + carry
+            carry, val = divmod(s, 10)
+
+            curr.next = ListNode(val)
+            curr = curr.next
+
+            l1 = l1.next if l1 else None
+            l2 = l2.next if l2 else None
+
+        return dummy.next
+```