feat(patterns): pattern taxonomy + is_optimal

backend/data/patterns/linkedlist-reversal.yaml

@@ -1,6 +1,8 @@
 name: LinkedList In-Place Reversal
 slug: linkedlist-reversal
 difficulty_level: 2
+pattern_type: technique
+display_order: 14
 
 description: >
   Reverse linked list nodes in-place by manipulating pointers without allocating
@@ -277,3 +279,130 @@ related_patterns:
   - two-pointers
 
 prerequisite_patterns: []
+
+visualization_examples:
+  - id: reverse-linked-list
+    title: Reverse Entire Linked List
+    input:
+      list: [1, 2, 3, 4]
+    code: |
+      def reverse_list(head):
+          prev = None
+          curr = head
+
+          while curr:
+              next_node = curr.next
+              curr.next = prev
+              prev = curr
+              curr = next_node
+
+          return prev
+    steps:
+      - id: step-1
+        description: "Initialize prev=None, curr=head (node 1)."
+        structures:
+          list:
+            type: linkedlist
+            nodes:
+              - { value: 1, state: active }
+              - { value: 2, state: default }
+              - { value: 3, state: default }
+              - { value: 4, state: default }
+            pointers:
+              curr: 0
+        variables:
+          prev: "null"
+        codeHighlight:
+          startLine: 2
+          endLine: 3
+
+      - id: step-2
+        description: "Save next=2, reverse link: 1→null. Move pointers forward."
+        structures:
+          list:
+            type: linkedlist
+            nodes:
+              - { value: 1, state: visited, annotations: ["→null"] }
+              - { value: 2, state: active }
+              - { value: 3, state: default }
+              - { value: 4, state: default }
+            pointers:
+              prev: 0
+              curr: 1
+        variables:
+          next_node: 2
+        codeHighlight:
+          startLine: 6
+          endLine: 9
+
+      - id: step-3
+        description: "Save next=3, reverse link: 2→1. Move pointers forward."
+        structures:
+          list:
+            type: linkedlist
+            nodes:
+              - { value: 1, state: visited, annotations: ["→null"] }
+              - { value: 2, state: visited, annotations: ["→1"] }
+              - { value: 3, state: active }
+              - { value: 4, state: default }
+            pointers:
+              prev: 1
+              curr: 2
+        variables:
+          next_node: 3
+        codeHighlight:
+          startLine: 6
+          endLine: 9
+
+      - id: step-4
+        description: "Save next=4, reverse link: 3→2. Move pointers forward."
+        structures:
+          list:
+            type: linkedlist
+            nodes:
+              - { value: 1, state: visited, annotations: ["→null"] }
+              - { value: 2, state: visited, annotations: ["→1"] }
+              - { value: 3, state: visited, annotations: ["→2"] }
+              - { value: 4, state: active }
+            pointers:
+              prev: 2
+              curr: 3
+        variables:
+          next_node: 4
+        codeHighlight:
+          startLine: 6
+          endLine: 9
+
+      - id: step-5
+        description: "Save next=null, reverse link: 4→3. curr becomes null, loop ends."
+        structures:
+          list:
+            type: linkedlist
+            nodes:
+              - { value: 1, state: visited, annotations: ["→null"] }
+              - { value: 2, state: visited, annotations: ["→1"] }
+              - { value: 3, state: visited, annotations: ["→2"] }
+              - { value: 4, state: found, annotations: ["→3", "new head"] }
+            pointers:
+              prev: 3
+        variables:
+          next_node: "null"
+        codeHighlight:
+          startLine: 11
+          endLine: 11
+
+      - id: step-6
+        description: "Return prev (node 4). Reversed list: 4→3→2→1→null"
+        structures:
+          reversed:
+            type: linkedlist
+            nodes:
+              - { value: 4, state: found, annotations: ["head"] }
+              - { value: 3, state: default }
+              - { value: 2, state: default }
+              - { value: 1, state: default }
+        variables:
+          result: "4→3→2→1→null"
+        codeHighlight:
+          startLine: 11
+          endLine: 11