Patterns — AlgoCliff

Use two pointers moving toward or away from each other to solve problems on sorted arrays or linked lists in linear time.

Maintain a dynamic window over a sequence to efficiently compute running aggregates or find optimal subarrays.

Modified Binary Search

Adapt classic binary search to handle rotated arrays, fuzzy boundaries, and non-trivial search conditions.

Dynamic Programming

Break problems into overlapping subproblems and cache results to avoid redundant computation.

Explore all candidate solutions incrementally, pruning branches that violate constraints.

Navigate tree structures using pre-order, in-order, post-order, or level-order strategies.

Monotonic Stack

Use a stack that maintains a monotonic order to solve next-greater-element and histogram problems in linear time.

In-Place Reversal

Reverse portions of a linked list in place without extra memory by re-wiring node pointers.

Fast & Slow Pointers

Advance two pointers at different speeds to detect cycles, find midpoints, or identify patterns in sequences.

Precompute cumulative sums to answer range-sum queries and subarray-sum problems in constant time.

Matrix Traversal

Traverse 2D grids using BFS, DFS, or directional iteration to solve island, path, and region problems.

Explore graphs depth-first or breadth-first to find paths, connected components, and shortest routes.

Overlapping Intervals

Sort and merge or compare intervals to detect overlaps, insert new ranges, or find gaps.

Use heaps or quickselect to efficiently find the k largest, smallest, or most frequent elements.

Store and search strings efficiently using a prefix tree that shares common prefixes between words.

Track connected components using disjoint sets with union-by-rank and path compression for near-constant time operations.

Topological Sort

Order vertices in a directed acyclic graph so every edge points forward, solving dependency and scheduling problems.

Make the locally optimal choice at each step to build a globally optimal solution without backtracking.

Bit Manipulation

Use bitwise operators (AND, OR, XOR, shifts) to solve problems involving binary representations in constant space.

Monotonic Queue

Maintain a double-ended queue in sorted order to find sliding window minimums or maximums in O(n) time.

Use a max-heap and a min-heap together to efficiently track the median or partition elements into two balanced groups.

Place each number at its correct index in one pass to find missing, duplicate, or out-of-place elements in O(n) time.

Subsets & Combinations

Enumerate all subsets, combinations, or permutations using systematic backtracking with distinct templates for each variant.

Linked List Techniques

Master dummy heads, merge strategies, partitioning, and intersection detection for linked list manipulation problems.

Design Patterns

Implement custom data structures like LRU caches, min stacks, and iterators that combine multiple primitives.

Answer range queries and point updates in O(log n) using a binary tree that stores aggregate values over intervals.

String Matching

Find patterns within text efficiently using KMP, Rabin-Karp, or Z-algorithm to avoid brute-force O(nm) comparisons.