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feat(patterns): pattern taxonomy + is_optimal

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This commit is contained in:
Kai Chappell
2025-09-08 16:03:14 +01:00
parent 5b768f6a21
commit 13bab63618
28 changed files with 1434 additions and 26 deletions
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171
backend/data/patterns/binary-search.yaml
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@@ -1,6 +1,8 @@
name: Binary Search
slug: binary-search
difficulty_level: 2
pattern_type: algorithm
display_order: 4
description: >
Efficiently search sorted data by repeatedly dividing the search space in half.
@@ -200,3 +202,172 @@ related_patterns:
- two-pointers
prerequisite_patterns: []
visualization_examples:
- id: binary-search-find-target
title: Find Target in Sorted Array
input:
nums: [1, 3, 5, 7, 9, 11, 13]
target: 9
code: |
def binary_search(nums, target):
left, right = 0, len(nums) - 1
while left <= right:
mid = left + (right - left) // 2
if nums[mid] == target:
return mid
elif nums[mid] < target:
left = mid + 1
else:
right = mid - 1
return -1
steps:
- id: step-1
description: "Initialize pointers: left=0, right=6. Search space is entire array."
structures:
nums:
type: array
values:
- { value: 1, state: default }
- { value: 3, state: default }
- { value: 5, state: default }
- { value: 7, state: default }
- { value: 9, state: default }
- { value: 11, state: default }
- { value: 13, state: default }
pointers:
left: 0
right: 6
variables:
target: 9
left: 0
right: 6
codeHighlight:
startLine: 2
endLine: 2
- id: step-2
description: "Calculate mid=3. nums[3]=7 < target=9, so search right half."
structures:
nums:
type: array
values:
- { value: 1, state: visited }
- { value: 3, state: visited }
- { value: 5, state: visited }
- { value: 7, state: comparing }
- { value: 9, state: default }
- { value: 11, state: default }
- { value: 13, state: default }
pointers:
left: 0
mid: 3
right: 6
variables:
target: 9
left: 0
right: 6
mid: 3
codeHighlight:
startLine: 9
endLine: 10
- id: step-3
description: "Update left=4. New search space is indices 4-6."
structures:
nums:
type: array
values:
- { value: 1, state: visited }
- { value: 3, state: visited }
- { value: 5, state: visited }
- { value: 7, state: visited }
- { value: 9, state: default }
- { value: 11, state: default }
- { value: 13, state: default }
pointers:
left: 4
right: 6
variables:
target: 9
left: 4
right: 6
codeHighlight:
startLine: 4
endLine: 4
- id: step-4
description: "Calculate mid=5. nums[5]=11 > target=9, so search left half."
structures:
nums:
type: array
values:
- { value: 1, state: visited }
- { value: 3, state: visited }
- { value: 5, state: visited }
- { value: 7, state: visited }
- { value: 9, state: default }
- { value: 11, state: comparing }
- { value: 13, state: visited }
pointers:
left: 4
mid: 5
right: 6
variables:
target: 9
left: 4
right: 6
mid: 5
codeHighlight:
startLine: 11
endLine: 12
- id: step-5
description: "Update right=4. Search space narrowed to index 4 only."
structures:
nums:
type: array
values:
- { value: 1, state: visited }
- { value: 3, state: visited }
- { value: 5, state: visited }
- { value: 7, state: visited }
- { value: 9, state: active }
- { value: 11, state: visited }
- { value: 13, state: visited }
pointers:
left: 4
right: 4
variables:
target: 9
left: 4
right: 4
codeHighlight:
startLine: 4
endLine: 4
- id: step-6
description: "Calculate mid=4. nums[4]=9 == target=9. Found at index 4!"
structures:
nums:
type: array
values:
- { value: 1, state: visited }
- { value: 3, state: visited }
- { value: 5, state: visited }
- { value: 7, state: visited }
- { value: 9, state: found }
- { value: 11, state: visited }
- { value: 13, state: visited }
pointers:
mid: 4
variables:
target: 9
mid: 4
result: 4
codeHighlight:
startLine: 7
endLine: 8