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docs: Add DESIGN_V4.md with 2-round full discussion architecture
- Refinement mode: improve existing high-quality markmap - 2-round discussion: independent review + full discussion - Code-based consensus: majority vote (2/3), no AI Integrator - Natural language suggestions: leverage AI's strength - Scalable: 2N+1 API calls, fixed 3 sequential batches - Initial implementation: 3 experts (Architect, Professor, Engineer)
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‎docs/mindmaps/neetcode_ontology_ai_en.md‎

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---
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title: LeetCode Patterns Knowledge Graph (33 Problems) — API Kernels → Patterns → Problems 🎯
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markmap:
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colorFreezeLevel: 2
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maxWidth: 300
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---
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## 🎯 How to use this mind map (fast)
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- **Read top-down**: *API Kernel* → *Pattern* → *Problems* (linked)
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- **Practice loop**: implement template → solve 2–3 problems → refactor into reusable `solve(pattern_state_machine)` mental model
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- **Progress tracking**
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- [ ] Do all **Easy** first
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- [ ] Then **Medium** variants
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- [ ] Finally **Hard** “edge-case amplifiers”
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---
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## 🧠 API Kernels (the “engines”)
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### SubstringSlidingWindow — *1D window state machine*
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- ==Core invariant==: window `[L,R]` stays valid by **expand right** + **contract left**
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- Complexity: typically $O(n)$ time, $O(\Sigma)$ space (alphabet / distinct keys)
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<!-- markmap: fold -->
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#### Pattern cheat sheet (from docs)
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| Problem | Invariant | State | Window Size | Goal |
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|---------|-----------|-------|-------------|------|
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| [LeetCode 3 - Longest Substring Without Repeating Characters](https://github.com/lufftw/neetcode/blob/main/solutions/0003_longest_substring_without_repeating_characters.py) | All unique | last index map | Variable | Max |
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| [LeetCode 340 - Longest Substring with At Most K Distinct Characters](https://github.com/lufftw/neetcode/blob/main/solutions/0340_longest_substring_with_at_most_k_distinct.py) | ≤K distinct | freq map | Variable | Max |
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| [LeetCode 76 - Minimum Window Substring](https://github.com/lufftw/neetcode/blob/main/solutions/0076_minimum_window_substring.py) | covers `t` | need/have | Variable | Min |
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| [LeetCode 567 - Permutation in String](https://github.com/lufftw/neetcode/blob/main/solutions/0567_permutation_in_string.py) | exact freq match | freq + matches | Fixed | Exists |
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| [LeetCode 438 - Find All Anagrams in a String](https://github.com/lufftw/neetcode/blob/main/solutions/0438_find_all_anagrams_in_a_string.py) | exact freq match | freq + matches | Fixed | All |
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| [LeetCode 209 - Minimum Size Subarray Sum](https://github.com/lufftw/neetcode/blob/main/solutions/0209_minimum_size_subarray_sum.py) | sum ≥ target | integer sum | Variable | Min |
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#### Patterns
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- **sliding_window_unique** *(maximize, “jump left” optimization)*
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- 🎯 Problems
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- [ ] [LeetCode 3 - Longest Substring Without Repeating Characters](https://github.com/lufftw/neetcode/blob/main/solutions/0003_longest_substring_without_repeating_characters.py)
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- Key state: `last_seen[char]` → `L = max(L, last_seen[c]+1)`
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- **sliding_window_at_most_k_distinct** *(maximize, shrink while invalid)*
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- 🎯 Problems
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- [ ] [LeetCode 340 - Longest Substring with At Most K Distinct Characters](https://github.com/lufftw/neetcode/blob/main/solutions/0340_longest_substring_with_at_most_k_distinct.py)
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- Key invariant: `len(freq) <= k`
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- **sliding_window_freq_cover** *(cover / exact-match family)*
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- 🎯 Problems
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- [ ] [LeetCode 76 - Minimum Window Substring](https://github.com/lufftw/neetcode/blob/main/solutions/0076_minimum_window_substring.py) — *minimize while valid*
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- [ ] [LeetCode 438 - Find All Anagrams in a String](https://github.com/lufftw/neetcode/blob/main/solutions/0438_find_all_anagrams_in_a_string.py) — *fixed window, collect indices*
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- [ ] [LeetCode 567 - Permutation in String](https://github.com/lufftw/neetcode/blob/main/solutions/0567_permutation_in_string.py) — *fixed window, boolean*
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- **sliding_window_cost_bounded** *(numeric constraint)*
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- 🎯 Problems
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- [ ] [LeetCode 209 - Minimum Size Subarray Sum](https://github.com/lufftw/neetcode/blob/main/solutions/0209_minimum_size_subarray_sum.py)
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- Typical requirement: positives → monotone contraction works
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---
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### TwoPointersTraversal — *pointer choreography on sequences*
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- ==Core invariant==: pointers move deterministically; processed region is “safe”
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- Complexity: often $O(n)$ time, $O(1)$ space (except sorting step)
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#### Pattern comparison (from docs)
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| Pattern | Pointer Init | Movement | Termination | Time | Space | Key Use Case |
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|---------|--------------|----------|-------------|------|-------|--------------|
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| Opposite | `0, n-1` | toward center | `L>=R` | $O(n)$ | $O(1)$ | sorted pairs / palindrome / maximize |
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| Same-direction | `write, read` | forward | `read==n` | $O(n)$ | $O(1)$ | in-place modify |
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| Fast–Slow | `slow, fast` | 1× / 2× | meet or null | $O(n)$ | $O(1)$ | cycle / midpoint |
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| Dedup enum | `i` + `L,R` | nested | done | $O(n^2)$ | $O(1)$ | 3Sum/4Sum |
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#### Patterns
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- **two_pointer_opposite_maximize**
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- 🎯 Problems
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- [ ] [LeetCode 11 - Container With Most Water](https://github.com/lufftw/neetcode/blob/main/solutions/0011_container_with_most_water.py)
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- Insight: move the pointer at the **shorter** height
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- **two_pointer_three_sum** *(dedup enumeration)*
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- 🎯 Problems
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- [ ] [LeetCode 15 - 3Sum](https://github.com/lufftw/neetcode/blob/main/solutions/0015_3sum.py)
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- [ ] [LeetCode 16 - 3Sum Closest](https://github.com/lufftw/neetcode/blob/main/solutions/0016_3sum_closest.py)
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- Requires: sort first ($O(n\log n)$), then scan with dedup
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- **two_pointer_opposite_palindrome**
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- 🎯 Problems
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- [ ] [LeetCode 125 - Valid Palindrome](https://github.com/lufftw/neetcode/blob/main/solutions/0125_valid_palindrome.py)
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- [ ] [LeetCode 680 - Valid Palindrome II](https://github.com/lufftw/neetcode/blob/main/solutions/0680_valid_palindrome_ii.py)
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- **two_pointer_writer_dedup**
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- 🎯 Problems
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- [ ] [LeetCode 26 - Remove Duplicates from Sorted Array](https://github.com/lufftw/neetcode/blob/main/solutions/0026_remove_duplicates_from_sorted_array.py)
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- [ ] [LeetCode 80 - Remove Duplicates from Sorted Array II](https://github.com/lufftw/neetcode/blob/main/solutions/0080_remove_duplicates_from_sorted_array_ii.py)
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- **two_pointer_writer_remove**
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- 🎯 Problems
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- [ ] [LeetCode 27 - Remove Element](https://github.com/lufftw/neetcode/blob/main/solutions/0027_remove_element.py)
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- **two_pointer_writer_compact**
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- 🎯 Problems
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- [ ] [LeetCode 283 - Move Zeroes](https://github.com/lufftw/neetcode/blob/main/solutions/0283_move_zeroes.py)
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---
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### FastSlowPointers — *Floyd + midpoints + implicit sequences*
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- ==Core invariant==: if a cycle exists, `fast` meets `slow`
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- Patterns
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- **fast_slow_cycle_detect**
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- [ ] [LeetCode 141 - Linked List Cycle](https://github.com/lufftw/neetcode/blob/main/solutions/0141_linked_list_cycle.py)
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- **fast_slow_cycle_start**
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- [ ] [LeetCode 142 - Linked List Cycle II](https://github.com/lufftw/neetcode/blob/main/solutions/0142_linked_list_cycle_ii.py)
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- **fast_slow_midpoint**
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- [ ] [LeetCode 876 - Middle of the Linked List](https://github.com/lufftw/neetcode/blob/main/solutions/0876_middle_of_the_linked_list.py)
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- **fast_slow_implicit_cycle**
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- [ ] [LeetCode 202 - Happy Number](https://github.com/lufftw/neetcode/blob/main/solutions/0202_happy_number.py)
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---
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### TwoPointerPartition — *in-place partitioning “mini quicksort”*
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- ==Core invariant==: regions are partitioned by property
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- Patterns
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- **dutch_flag_partition**
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- [ ] [LeetCode 75 - Sort Colors](https://github.com/lufftw/neetcode/blob/main/solutions/0075_sort_colors.py)
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- **two_way_partition**
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- [ ] [LeetCode 905 - Sort Array By Parity](https://github.com/lufftw/neetcode/blob/main/solutions/0905_sort_array_by_parity.py)
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- [ ] [LeetCode 922 - Sort Array By Parity II](https://github.com/lufftw/neetcode/blob/main/solutions/0922_sort_array_by_parity_ii.py)
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- **quickselect_partition** *(selection via partition)*
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- [ ] [LeetCode 215 - Kth Largest Element in an Array](https://github.com/lufftw/neetcode/blob/main/solutions/0215_kth_largest_element_in_an_array.py)
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---
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### MergeSortedSequences — *merge two sorted sequences*
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- ==Core invariant==: output prefix is fully sorted
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- Patterns
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- **merge_two_sorted_lists**
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- [ ] [LeetCode 21 - Merge Two Sorted Lists](https://github.com/lufftw/neetcode/blob/main/solutions/0021_merge_two_sorted_lists.py)
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- **merge_two_sorted_arrays**
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- [ ] [LeetCode 88 - Merge Sorted Array](https://github.com/lufftw/neetcode/blob/main/solutions/0088_merge_sorted_array.py)
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- **merge_sorted_from_ends**
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- [ ] [LeetCode 977 - Squares of a Sorted Array](https://github.com/lufftw/neetcode/blob/main/solutions/0977_squares_of_a_sorted_array.py)
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---
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### KWayMerge — *merge K sorted sequences*
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- Two main implementations
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- **merge_k_sorted_heap** → $O(N\log k)$ time, $O(k)$ heap
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- **merge_k_sorted_divide** → $O(N\log k)$ time, smaller constants sometimes
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- 🎯 Problems
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- [ ] [LeetCode 23 - Merge k Sorted Lists](https://github.com/lufftw/neetcode/blob/main/solutions/0023_merge_k_sorted_lists.py)
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- Related “hybrid thinking”: [LeetCode 4 - Median of Two Sorted Arrays](https://github.com/lufftw/neetcode/blob/main/solutions/0004_median_of_two_sorted_arrays.py)
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---
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### HeapTopK — *keep best K under streaming updates*
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- Patterns
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- **heap_kth_element**
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- [ ] [LeetCode 215 - Kth Largest Element in an Array](https://github.com/lufftw/neetcode/blob/main/solutions/0215_kth_largest_element_in_an_array.py)
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---
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### LinkedListInPlaceReversal — *pointer surgery*
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- Pattern
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- **linked_list_k_group_reversal**
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- [ ] [LeetCode 25 - Reverse Nodes in k-Group](https://github.com/lufftw/neetcode/blob/main/solutions/0025_reverse_nodes_in_k_group.py)
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- Also core linked list arithmetic
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- [ ] [LeetCode 2 - Add Two Numbers](https://github.com/lufftw/neetcode/blob/main/solutions/0002_add_two_numbers.py)
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---
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### BacktrackingExploration — *search tree with pruning*
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- Pattern
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- **backtracking_n_queens**
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- [ ] [LeetCode 51 - N-Queens](https://github.com/lufftw/neetcode/blob/main/solutions/0051_n_queens.py)
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---
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### GridBFSMultiSource — *wavefront propagation on grids*
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- Pattern
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- **grid_bfs_propagation**
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- [ ] [LeetCode 994 - Rotting Oranges](https://github.com/lufftw/neetcode/blob/main/solutions/0994_rotting_oranges.py)
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- Implementation invariant: queue holds frontier of current “minute/level”
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---
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## 🧭 Roadmap slices (what to do next)
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### Sliding Window Mastery 📚
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- [ ] [LeetCode 3 - Longest Substring Without Repeating Characters](https://github.com/lufftw/neetcode/blob/main/solutions/0003_longest_substring_without_repeating_characters.py)
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- [ ] [LeetCode 340 - Longest Substring with At Most K Distinct Characters](https://github.com/lufftw/neetcode/blob/main/solutions/0340_longest_substring_with_at_most_k_distinct.py)
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- [ ] [LeetCode 209 - Minimum Size Subarray Sum](https://github.com/lufftw/neetcode/blob/main/solutions/0209_minimum_size_subarray_sum.py)
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- [ ] [LeetCode 567 - Permutation in String](https://github.com/lufftw/neetcode/blob/main/solutions/0567_permutation_in_string.py)
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- [ ] [LeetCode 438 - Find All Anagrams in a String](https://github.com/lufftw/neetcode/blob/main/solutions/0438_find_all_anagrams_in_a_string.py)
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- [ ] [LeetCode 76 - Minimum Window Substring](https://github.com/lufftw/neetcode/blob/main/solutions/0076_minimum_window_substring.py) 🔥
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### Two Pointers Mastery ⚡
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- Opposite pointers
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- [ ] [LeetCode 11 - Container With Most Water](https://github.com/lufftw/neetcode/blob/main/solutions/0011_container_with_most_water.py)
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- [ ] [LeetCode 125 - Valid Palindrome](https://github.com/lufftw/neetcode/blob/main/solutions/0125_valid_palindrome.py)
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- [ ] [LeetCode 680 - Valid Palindrome II](https://github.com/lufftw/neetcode/blob/main/solutions/0680_valid_palindrome_ii.py)
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- Writer pointers (in-place)
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- [ ] [LeetCode 26 - Remove Duplicates from Sorted Array](https://github.com/lufftw/neetcode/blob/main/solutions/0026_remove_duplicates_from_sorted_array.py)
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- [ ] [LeetCode 27 - Remove Element](https://github.com/lufftw/neetcode/blob/main/solutions/0027_remove_element.py)
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- [ ] [LeetCode 283 - Move Zeroes](https://github.com/lufftw/neetcode/blob/main/solutions/0283_move_zeroes.py)
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- [ ] [LeetCode 80 - Remove Duplicates from Sorted Array II](https://github.com/lufftw/neetcode/blob/main/solutions/0080_remove_duplicates_from_sorted_array_ii.py)
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- Fast–slow
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- [ ] [LeetCode 141 - Linked List Cycle](https://github.com/lufftw/neetcode/blob/main/solutions/0141_linked_list_cycle.py)
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- [ ] [LeetCode 142 - Linked List Cycle II](https://github.com/lufftw/neetcode/blob/main/solutions/0142_linked_list_cycle_ii.py)
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- [ ] [LeetCode 876 - Middle of the Linked List](https://github.com/lufftw/neetcode/blob/main/solutions/0876_middle_of_the_linked_list.py)
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- [ ] [LeetCode 202 - Happy Number](https://github.com/lufftw/neetcode/blob/main/solutions/0202_happy_number.py)
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---
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## 🧩 “Same problem, different lens” (transfer learning)
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- **Selection**: [LeetCode 215 - Kth Largest Element in an Array](https://github.com/lufftw/neetcode/blob/main/solutions/0215_kth_largest_element_in_an_array.py)
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- Option A: `quickselect_partition` (expected $O(n)$)
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- Option B: `heap_kth_element` ($O(n\log k)$, streaming-friendly)
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- **Merging**:
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- 2-way: [LeetCode 21 - Merge Two Sorted Lists](https://github.com/lufftw/neetcode/blob/main/solutions/0021_merge_two_sorted_lists.py), [LeetCode 88 - Merge Sorted Array](https://github.com/lufftw/neetcode/blob/main/solutions/0088_merge_sorted_array.py)
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- K-way: [LeetCode 23 - Merge k Sorted Lists](https://github.com/lufftw/neetcode/blob/main/solutions/0023_merge_k_sorted_lists.py)
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- “boundary + merge thinking”: [LeetCode 4 - Median of Two Sorted Arrays](https://github.com/lufftw/neetcode/blob/main/solutions/0004_median_of_two_sorted_arrays.py)
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---
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## 🧱 Minimal reusable templates (mental API)
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```python
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# Sliding Window (variable, maximize)
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def max_window(seq):
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state = {}
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L = 0
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ans = 0
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for R, x in enumerate(seq):
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add(state, x)
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while invalid(state):
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remove(state, seq[L]); L += 1
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ans = max(ans, R - L + 1)
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return ans
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# Two pointers (opposite)
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def opposite(arr):
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L, R = 0, len(arr) - 1
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while L < R:
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if should_move_left(arr, L, R):
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L += 1
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else:
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R -= 1
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```
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---

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