Problem Family Derivation¶

2026-01-102026-01-10

Base template problems and their derived variants. Learn the base pattern first, then apply to variants with small modifications.

BacktrackingExploration¶

🎯 Base Template:LeetCode 46 - Permutations · Solution¶

BASE TEMPLATE for permutation enumeration. Track usage with boolean array. At each position, try every unused element. This is the canonical backtracking permutation pattern.

Derived Problems¶

• 🟡 LeetCode 47 - Permutations II · Solution(n! × n) time, O(n) space`

🎯 Base Template:LeetCode 78 - Subsets · Solution¶

BASE TEMPLATE for subset enumeration. Use start_index for canonical ordering. Every node (including empty) is a valid subset. Key difference from permutations: no 'used' array needed, collect at every node.

Derived Problems¶

• 🟡 LeetCode 90 - Subsets II · Solution(n × 2^n) time, O(n) space`
• 🟡 LeetCode 77 - Combinations · Solution(k × C(n,k)) time, O(k) space`

BinarySearchBoundary¶

🎯 Base Template:LeetCode 33 - Search in Rotated Sorted Array · Solution¶

Sorted-half detection: identify which half is sorted, then check if target lies in that range.

Derived Problems¶

• 🟡 LeetCode 81 - Search in Rotated Sorted Array II · Solution(n) worst case, O(log n) average time, O(1) space`

🎯 Base Template:LeetCode 34 - Find First and Last Position of Element in Sorted Array · Solution¶

Two binary searches: lower_bound for first occurrence, upper_bound - 1 for last. This is the BASE TEMPLATE for boundary search problems.

Derived Problems¶

• 🟢 LeetCode 35 - Search Insert Position · Solution(log n) time, O(1) space`
• LeetCode 0278 (metadata not yet added)

🎯 Base Template:LeetCode 162 - Find Peak Element · Solution¶

Slope direction invariant: if ascending (mid < mid+1), peak is on right; if descending, peak is at mid or left. Boundary condition nums[-1] = nums[n] = -infinity guarantees peak exists.

Derived Problems¶

• LeetCode 0852 (metadata not yet added)

🎯 Base Template:LeetCode 875 - Koko Eating Bananas · Solution¶

Binary search on answer space [1, max(piles)]. Predicate: can_finish(speed) = total_hours <= h. Monotonic property ensures correctness.

Derived Problems¶

• 🟡 LeetCode 1011 - Capacity To Ship Packages Within D Days · Solution(n log S) time, O(1) space, where S = sum(weights)`
• LeetCode 0410 (metadata not yet added)

BitmaskDP¶

🎯 Base Template:LeetCode 847 - Shortest Path Visiting All Nodes · Solution¶

BASE TEMPLATE for BFS with bitmask state. State = (node, visited_mask). Multi-source BFS from all nodes. Early termination when full_mask reached.

Derived Problems¶

• LeetCode 0943 (metadata not yet added)
• 🔴 LeetCode 1494 - Parallel Courses II

🎯 Base Template:LeetCode 1125 - Smallest Sufficient Team · Solution¶

BASE TEMPLATE for set cover with bitmask DP. dp[mask] = smallest team to cover skills in mask. Encode skills as bitmask, iterate people to expand coverage.

Derived Problems¶

• LeetCode 1723 (metadata not yet added)
• LeetCode 1986 (metadata not yet added)

DifferenceArray¶

🎯 Base Template:LeetCode 1109 - Corporate Flight Bookings · Solution¶

Canonical difference array: mark range starts/ends, prefix sum for final values.

Derived Problems¶

• 🟡 LeetCode 1094 - Car Pooling · Solution(n + m) time, O(m) space`

General¶

🎯 Base Template:LeetCode 110 - Balanced Binary Tree · Solution¶

Early termination pattern: return -1 as sentinel when balance fails. Avoids redundant subtree traversal.

Derived Problems¶

• (No derived problems listed)

🎯 Base Template:LeetCode 124 - Binary Tree Maximum Path Sum · Solution¶

Return vs Update pattern: update global max with path through node as apex, return single-branch gain for parent. Skip negative subtrees to maximize sum.

Derived Problems¶

• LeetCode 0687 (metadata not yet added)
• LeetCode 0129 (metadata not yet added)

🎯 Base Template:LeetCode 133 - Clone Graph · Solution¶

Map old→new nodes. On first visit create clone, on revisit return existing clone. Handles cycles via the mapping.

Derived Problems¶

• 🟡 LeetCode 138 - Copy List with Random Pointer · Solution(n) time, O(n) space`

🎯 Base Template:LeetCode 253 - Meeting Rooms II · Solution¶

Min-heap of end times for greedy room assignment. Classic interval scheduling pattern.

Derived Problems¶

• (No derived problems listed)

🎯 Base Template:LeetCode 295 - Find Median from Data Stream · Solution¶

Two heaps: max-heap for lower half, min-heap for upper half. Classic streaming median pattern.

Derived Problems¶

• LeetCode 0480 (metadata not yet added)

🎯 Base Template:LeetCode 543 - Diameter of Binary Tree · Solution¶

Return vs Update pattern: diameter through node = left_height + right_height. Return single-branch height for parent, update global max for answer.

Derived Problems¶

• 🔴 LeetCode 124 - Binary Tree Maximum Path Sum · Solution(n) time, O(h) space`
• LeetCode 0687 (metadata not yet added)

🎯 Base Template:LeetCode 621 - Task Scheduler · Solution¶

Mathematical formula: (max_freq - 1) * (n + 1) + max_freq_count.

Derived Problems¶

• LeetCode 0767 (metadata not yet added)

🎯 Base Template:LeetCode 785 - Is Graph Bipartite? · Solution¶

BFS naturally alternates levels. Color each level with opposite color. Conflict = not bipartite.

Derived Problems¶

• LeetCode 0886 (metadata not yet added)

🎯 Base Template:LeetCode 1046 - Last Stone Weight · Solution¶

Max-heap simulation of stone smashing. Repeatedly extract two largest.

Derived Problems¶

• LeetCode 1049 (metadata not yet added)

GraphDFS¶

🎯 Base Template:LeetCode 200 - Number of Islands · Solution¶

Base template for connected components. DFS flood fill marks entire island, count equals number of DFS calls from unvisited cells.

Derived Problems¶

• 🟡 LeetCode 695 - Max Area of Island · Solution(m*n) time, O(m*n) space`
• LeetCode 0463 (metadata not yet added)
• 🟡 LeetCode 130 - Surrounded Regions · Solution(m*n) time, O(m*n) space`

IntervalMerge¶

🎯 Base Template:LeetCode 56 - Merge Intervals · Solution¶

Base template for interval merging. Sort by start, merge adjacent overlaps.

Derived Problems¶

• 🟡 LeetCode 57 - Insert Interval · Solution(n) time, O(n) space`
• 🟢 LeetCode 252 - Meeting Rooms · Solution(n log n) time, O(1) space`
• 🟡 LeetCode 253 - Meeting Rooms II · Solution(n log n) time, O(n) space`

IntervalScheduling¶

🎯 Base Template:LeetCode 435 - Non-overlapping Intervals · Solution¶

Base template for interval scheduling. Sort by end, greedily select non-overlapping.

Derived Problems¶

• 🟡 LeetCode 452 - Minimum Number of Arrows to Burst Balloons · Solution(n log n) time, O(1) space`
• LeetCode 0646 (metadata not yet added)

LinkedListInPlaceReversal¶

🎯 Base Template:LeetCode 206 - Reverse Linked List · Solution¶

Iterative three-pointer reversal. Canonical base template for in-place linked list reversal.

Derived Problems¶

• 🟡 LeetCode 92 - Reverse Linked List II · Solution(N) time, O(1) space`
• 🔴 LeetCode 25 - Reverse Nodes in k-Group · Solution(N) time, O(1) space`

MonotonicStack¶

🎯 Base Template:LeetCode 84 - Largest Rectangle in Histogram · Solution¶

Single-pass with sentinel for cleaner termination.

Derived Problems¶

• 🔴 LeetCode 85 - Maximal Rectangle · Solution(rows * cols) time, O(cols) space`

🎯 Base Template:LeetCode 496 - Next Greater Element I · Solution¶

Canonical monotonic stack template with hash map for lookup.

Derived Problems¶

• 🟡 LeetCode 503 - Next Greater Element II · Solution(n) time, O(n) space`
• 🟡 LeetCode 739 - Daily Temperatures · Solution(n) time, O(n) space`
• 🟡 LeetCode 901 - Online Stock Span · Solution(1) amortized per call, O(n) space`

PrefixProduct¶

🎯 Base Template:LeetCode 238 - Product of Array Except Self · Solution¶

Two-pass: prefix products forward, suffix products backward.

Derived Problems¶

• (No derived problems listed)

PrefixSum2D¶

🎯 Base Template:LeetCode 304 - Range Sum Query 2D - Immutable · Solution¶

2D prefix sum with inclusion-exclusion for rectangle queries.

Derived Problems¶

• LeetCode 0308 (metadata not yet added)

PrefixSumRangeQuery¶

🎯 Base Template:LeetCode 303 - Range Sum Query - Immutable · Solution¶

Base template for prefix sum range queries.

Derived Problems¶

• 🟡 LeetCode 304 - Range Sum Query 2D - Immutable · Solution(m*n) init, O(1) query`
• 🟡 LeetCode 560 - Subarray Sum Equals K · Solution(n) time, O(n) space`
• 🟡 LeetCode 525 - Contiguous Array · Solution(n) time, O(n) space`

PrefixSumSubarraySum¶

🎯 Base Template:LeetCode 560 - Subarray Sum Equals K · Solution¶

Prefix sum + hash map for counting subarrays. Key: initialize {0: 1}.

Derived Problems¶

• 🟡 LeetCode 525 - Contiguous Array · Solution(n) time, O(n) space`
• 🟡 LeetCode 523 - Continuous Subarray Sum · Solution(n) time, O(min(n, k)) space`
• LeetCode 0974 (metadata not yet added)

ShortestPath¶

🎯 Base Template:LeetCode 743 - Network Delay Time · Solution¶

Base template for Dijkstra's shortest path algorithm.

Derived Problems¶

• 🟡 LeetCode 1631 - Path With Minimum Effort · Solution(m*n log(m*n)) time, O(m*n) space`
• 🟡 LeetCode 787 - Cheapest Flights Within K Stops · Solution(K * E) time, O(V) space`
• 🔴 LeetCode 1368 - Minimum Cost to Make at Least One Valid Path in a Grid · Solution(m*n) time, O(m*n) space`
• 🔴 LeetCode 2290 - Minimum Obstacle Removal to Reach Corner · Solution(m*n) time, O(m*n) space`

StringDP¶

🎯 Base Template:LeetCode 10 - Regular Expression Matching · Solution¶

Bottom-up DP handling . and * wildcards

Derived Problems¶

• 🔴 LeetCode 44 - Wildcard Matching(m*n) time, O(m*n) space`

🎯 Base Template:LeetCode 72 - Edit Distance · Solution¶

Levenshtein distance with insert, delete, replace operations

Derived Problems¶

• LeetCode 0583 (metadata not yet added)
• LeetCode 0712 (metadata not yet added)

🎯 Base Template:LeetCode 1143 - Longest Common Subsequence · Solution¶

Classic 2D DP for comparing two strings

Derived Problems¶

• 🟡 LeetCode 516 - Longest Palindromic Subsequence · Solution(n^2) time, O(n^2) space`
• LeetCode 0583 (metadata not yet added)
• LeetCode 1092 (metadata not yet added)

SubstringSlidingWindow¶

🎯 Base Template:LeetCode 3 - Longest Substring Without Repeating Characters · Solution¶

Canonical sliding window template with last-seen index array. Uses jump optimization instead of while-loop contraction. This is the BASE TEMPLATE for all SubstringSlidingWindow problems.

Derived Problems¶

• 🔴 LeetCode 76 - Minimum Window Substring · Solution(|s| + |t|) time, O(|t|) space`
• LeetCode 0159 (metadata not yet added)
• 🟡 LeetCode 209 - Minimum Size Subarray Sum · Solution(n) time, O(1) space`
• 🟡 LeetCode 340 - Longest Substring with At Most K Distinct Characters · Solution(n) time, O(K) space`
• 🟡 LeetCode 438 - Find All Anagrams in a String · Solution(|s| + |p|) time, O(1) space for maps, O(k) for output`
• 🟡 LeetCode 567 - Permutation in String · Solution(|s1| + |s2|) time, O(1) space`

TopologicalSort¶

🎯 Base Template:LeetCode 207 - Course Schedule · Solution¶

Base template for topological sort using Kahn's algorithm.

Derived Problems¶

• 🟡 LeetCode 210 - Course Schedule II · Solution(V+E) time, O(V+E) space`
• 🟡 LeetCode 802 - Find Eventual Safe States · Solution(V+E) time, O(V) space`
• 🔴 LeetCode 1203 - Sort Items by Groups Respecting Dependencies · Solution(V+E) time, O(V+E) space`

TreeTraversalBFS¶

🎯 Base Template:LeetCode 102 - Binary Tree Level Order Traversal · Solution¶

Base template for tree BFS. Process level by level using queue size batching.

Derived Problems¶

• LeetCode 0103 (metadata not yet added)
• LeetCode 0107 (metadata not yet added)
• 🟡 LeetCode 199 - Binary Tree Right Side View · Solution(n) time, O(w) space`
• LeetCode 0637 (metadata not yet added)

TreeTraversalDFS¶

🎯 Base Template:LeetCode 94 - Binary Tree Inorder Traversal · Solution¶

Base template for tree DFS. Inorder: Left → Node → Right. Fundamental for BST operations.

Derived Problems¶

• LeetCode 0144 (metadata not yet added)
• LeetCode 0145 (metadata not yet added)
• 🟡 LeetCode 230 - Kth Smallest Element in a BST · Solution(H + k) time, O(H) space`

Trie¶

🎯 Base Template:LeetCode 208 - Implement Trie (Prefix Tree) · Solution(Prefix Tree)¶

Base template for Trie operations.

Derived Problems¶

• 🟡 LeetCode 211 - Design Add and Search Words Data Structure · Solution(L) add, O(26^D * L) search with D wildcards`
• 🔴 LeetCode 212 - Word Search II · Solution(M*N*4^L) time, O(W*L) space`
• 🟡 LeetCode 648 - Replace Words · Solution(D*L + W*L) time, O(D*L) space`
• 🟡 LeetCode 1268 - Search Suggestions System · Solution(N*L*log N + N*L) time, O(N*L) space`

UnionFindConnectivity¶

🎯 Base Template:LeetCode 547 - Number of Provinces · Solution¶

Base template for Union-Find connectivity.

Derived Problems¶

• 🟡 LeetCode 1319 - Number of Operations to Make Network Connected · Solution(E × α(n)) time, O(n) space`
• LeetCode 0323 (metadata not yet added)

🎯 Base Template:LeetCode 684 - Redundant Connection · Solution¶

Base template for cycle detection with Union-Find.

Derived Problems¶

• LeetCode 0685 (metadata not yet added)