Pattern Studioalgorithmic thinking

Learning Roadmap

A deliberate order — each stage builds the intuition the next one assumes. Start at the top and work down.

About 27 focused learning hours across 31 patterns
1

Arrays & Strings

7 patterns

Hashing
Trade memory for constant-time membership checks.
Beginner35 min
Linear Scan
Maintain a compact running state while scanning a sequence once.
Beginner35 min
Prefix Techniques
Precompute cumulative information so range questions become constant-time differences.
Beginner35 min
Sliding Window
Grow and shrink a contiguous range to track a running property in O(n).
Beginner35 min
Two Pointers
Walk two indices toward each other to prune the search space linearly.
Beginner35 min
Sequence Optimization
Decide at every value whether to extend the current run or start fresh.
Intermediate55 min
Sorting
See how seven sorting strategies create order through different invariants.
Intermediate90 min
2

Searching

2 patterns

Binary Search
Discard half the candidates per comparison for O(log n) lookups.
Beginner35 min
Binary Search on Answer
Search a numeric answer space whose feasibility changes only once.
Intermediate70 min
3

Stacks & Queues

3 patterns

Stack
Use last-in, first-out order to match nested delimiters.
Beginner35 min
Queue
Process work in first-in, first-out order.
Beginner35 min
Monotonic Structures
Discard dominated candidates while preserving monotonic order.
Intermediate75 min
4

Linked Lists

2 patterns

Traversal & Pointer Manipulation
Reverse next pointers without losing the remaining chain.
Intermediate50 min
Fast & Slow Pointer
Move at two speeds until a cycle forces a meeting.
Intermediate50 min
5

Trees

5 patterns

Tree Traversals
Compare depth-first traversal orders, level-order waves, and Euler entry/exit times.
Intermediate50 min
Binary Search Trees
Choose left or right using the ordering invariant.
Intermediate50 min
Heaps
Restore heap order by bubbling an inserted value upward.
Intermediate50 min
Prefix Trees (Trie)
Follow one character edge per prefix symbol.
Intermediate50 min
Range Trees
Precompute overlapping range sums, then update only the ancestors that depend on one value.
Advanced85 min
6

Graphs

4 patterns

Graph Representation
Build adjacency lists from node-to-node relationships.
Intermediate50 min
Ordering
Order tasks so every dependency comes before its dependents.
Advanced70 min
Connectivity
Near-constant-time connectivity with path compression + union by rank.
Advanced70 min
Shortest Paths
Choose the frontier rule that preserves minimum path cost under edge weights.
Advanced70 min
7

Backtracking & Recursion

2 patterns

Recursion
Watch recursive calls branch, reach a base case, and unwind.
Beginner35 min
Backtracking
Backtracking = choose, explore, and undo across many problem shapes, not just subsets.
Intermediate50 min
8

Dynamic Programming

1 pattern

Dynamic Programming
Choose a state representation, then build larger answers from solved states.
Intermediate50 min
9

Greedy Algorithms & Mathematical Optimization

5 patterns

Bit Manipulation
Clear the lowest set bit with n & (n-1).
Intermediate50 min
Greedy Choice
Choose the earliest finishing compatible interval.
Intermediate50 min
Interval Processing
Sort ranges and merge every overlap into the active span.
Intermediate50 min
Number Theory
Use number theory or cross products to preserve a mathematical invariant.
Intermediate50 min
Simulation
Execute movement commands while preserving position state.
Intermediate50 min