feat(patterns): pattern taxonomy + is_optimal

backend/data/patterns/sliding-window.yaml

@@ -1,6 +1,8 @@
 name: Sliding Window
 slug: sliding-window
 difficulty_level: 2
+pattern_type: algorithm
+display_order: 2
 
 description: >
   Maintain a window of elements that slides through the data, tracking a
@@ -192,3 +194,129 @@ related_patterns:
 
 prerequisite_patterns:
   - two-pointers
+
+visualization_examples:
+  - id: max-sum-subarray
+    title: Maximum Sum Subarray of Size K
+    input:
+      nums: [2, 1, 5, 1, 3, 2]
+      k: 3
+    code: |
+      def max_sum_subarray(nums, k):
+          window_sum = sum(nums[:k])
+          max_sum = window_sum
+
+          for i in range(k, len(nums)):
+              window_sum += nums[i] - nums[i - k]
+              max_sum = max(max_sum, window_sum)
+
+          return max_sum
+    steps:
+      - id: step-1
+        description: "Initialize window with first k=3 elements: [2, 1, 5]. Sum = 8"
+        structures:
+          nums:
+            type: array
+            values:
+              - { value: 2, state: active, annotations: ["window"] }
+              - { value: 1, state: active, annotations: ["window"] }
+              - { value: 5, state: active, annotations: ["window"] }
+              - { value: 1, state: default }
+              - { value: 3, state: default }
+              - { value: 2, state: default }
+            pointers:
+              left: 0
+              right: 2
+        variables:
+          window_sum: 8
+          max_sum: 8
+        codeHighlight:
+          startLine: 2
+          endLine: 3
+
+      - id: step-2
+        description: "Slide window: remove 2, add 1. New window [1, 5, 1]. Sum = 7"
+        structures:
+          nums:
+            type: array
+            values:
+              - { value: 2, state: visited }
+              - { value: 1, state: active, annotations: ["window"] }
+              - { value: 5, state: active, annotations: ["window"] }
+              - { value: 1, state: active, annotations: ["window"] }
+              - { value: 3, state: default }
+              - { value: 2, state: default }
+            pointers:
+              left: 1
+              right: 3
+        variables:
+          window_sum: 7
+          max_sum: 8
+          i: 3
+        codeHighlight:
+          startLine: 5
+          endLine: 7
+
+      - id: step-3
+        description: "Slide window: remove 1, add 3. New window [5, 1, 3]. Sum = 9. New max!"
+        structures:
+          nums:
+            type: array
+            values:
+              - { value: 2, state: visited }
+              - { value: 1, state: visited }
+              - { value: 5, state: found, annotations: ["window"] }
+              - { value: 1, state: found, annotations: ["window"] }
+              - { value: 3, state: found, annotations: ["window"] }
+              - { value: 2, state: default }
+            pointers:
+              left: 2
+              right: 4
+        variables:
+          window_sum: 9
+          max_sum: 9
+          i: 4
+        codeHighlight:
+          startLine: 5
+          endLine: 7
+
+      - id: step-4
+        description: "Slide window: remove 5, add 2. New window [1, 3, 2]. Sum = 6"
+        structures:
+          nums:
+            type: array
+            values:
+              - { value: 2, state: visited }
+              - { value: 1, state: visited }
+              - { value: 5, state: visited }
+              - { value: 1, state: active, annotations: ["window"] }
+              - { value: 3, state: active, annotations: ["window"] }
+              - { value: 2, state: active, annotations: ["window"] }
+            pointers:
+              left: 3
+              right: 5
+        variables:
+          window_sum: 6
+          max_sum: 9
+          i: 5
+        codeHighlight:
+          startLine: 5
+          endLine: 7
+
+      - id: step-5
+        description: "Loop complete. Maximum sum found is 9 (window [5, 1, 3])"
+        structures:
+          nums:
+            type: array
+            values:
+              - { value: 2, state: visited }
+              - { value: 1, state: visited }
+              - { value: 5, state: found }
+              - { value: 1, state: found }
+              - { value: 3, state: found }
+              - { value: 2, state: visited }
+        variables:
+          max_sum: 9
+        codeHighlight:
+          startLine: 9
+          endLine: 9