Pattern Studioalgorithmic thinking

32 Core & Advanced Interview Patterns

Everything you need for software engineering interviews. 32 patterns across 9 categories — all fully interactive with reactive, step-by-step visualizations.

Difficulty

Arrays & Strings

7
Beginner
Interactive

Hashing

Trade memory for constant-time membership checks.

O(n) average
O(n)
Beginner
Interactive

Linear Scan

Maintain a compact running state while scanning a sequence once.

O(n)
O(1)
Beginner
Interactive

Prefix Techniques

Precompute cumulative information so range questions become constant-time differences.

O(n) build, O(1) query
O(n)
Beginner
Interactive

Sliding Window

Grow and shrink a contiguous range to track a running property in O(n).

O(n)
O(k)
Beginner
Interactive

Two Pointers

Walk two indices toward each other to prune the search space linearly.

O(n)
O(1)
Intermediate
Interactive

Sequence Optimization

Decide at every value whether to extend the current run or start fresh.

O(n)
O(1)
Intermediate
Interactive

Sorting

See how seven sorting strategies create order through different invariants.

O(n log n) typical; O(n²) elementary
O(1) to O(n + range)

Searching

2
Beginner
Interactive

Binary Search

Discard half the candidates per comparison for O(log n) lookups.

O(log n)
O(1)
Intermediate
Interactive

Binary Search on Answer

Search a numeric answer space whose feasibility changes only once.

O(n log R)
O(1)

Stacks & Queues

3
Beginner
Interactive

Stack

Use last-in, first-out order to match nested delimiters.

O(n)
O(n)
Beginner
Interactive

Queue

Process work in first-in, first-out order.

O(n)
O(n)
Intermediate
Interactive

Monotonic Structures

Discard dominated candidates while preserving monotonic order.

O(n)
O(n)

Linked Lists

2
Intermediate
Interactive

Traversal & Pointer Manipulation

Reverse next pointers without losing the remaining chain.

O(n)
O(1)
Intermediate
Interactive

Fast & Slow Pointer

Move at two speeds until a cycle forces a meeting.

O(n)
O(1)

Trees

5
Intermediate
Interactive

Tree Traversals

Compare depth-first traversal orders, level-order waves, and Euler entry/exit times.

O(n)
O(h) DFS · O(w) BFS
Intermediate
Interactive

Binary Search Trees

Choose left or right using the ordering invariant.

O(h), O(log n) balanced
O(1) iterative
Intermediate
Interactive

Heaps

Restore heap order by bubbling an inserted value upward.

O(log n) insert
O(1) auxiliary
Intermediate
Interactive

Prefix Trees (Trie)

Follow one character edge per prefix symbol.

O(p) prefix lookup
O(total characters)
Advanced
Interactive

Range Trees

Precompute overlapping range sums, then update only the ancestors that depend on one value.

O(n log n) build, O(log n) query/update
O(n)

Graphs

4
Intermediate
Interactive

Graph Representation

Build adjacency lists from node-to-node relationships.

O(V + E) build
O(V + E)
Advanced
Interactive

Ordering

Order tasks so every dependency comes before its dependents.

O(V + E)
O(V)
Advanced
Interactive

Connectivity

Near-constant-time connectivity with path compression + union by rank.

O(α(n)) per op
O(n)
Advanced
Interactive

Shortest Paths

Choose the frontier rule that preserves minimum path cost under edge weights.

O(E log V)
O(V)

Backtracking & Recursion

2
Beginner
Interactive

Recursion

Watch recursive calls branch, reach a base case, and unwind.

Depends on the recurrence
O(recursion depth)
Intermediate
Interactive

Backtracking

Backtracking = choose, explore, and undo across many problem shapes, not just subsets.

Exponential in branching depth
O(depth) recursion + mutable candidate

Dynamic Programming

1
Intermediate
Interactive

Dynamic Programming

Choose a state representation, then build larger answers from solved states.

Depends on the state space
Depends on stored states

Greedy Algorithms & Mathematical Optimization

5
Intermediate
Interactive

Bit Manipulation

Clear the lowest set bit with n & (n-1).

O(number of set bits)
O(1)
Intermediate
Interactive

Greedy Choice

Choose the earliest finishing compatible interval.

O(n log n)
O(n)
Intermediate
Interactive

Interval Processing

Sort ranges and merge every overlap into the active span.

O(n log n)
O(n) output
Intermediate
Interactive

Number Theory

Use number theory or cross products to preserve a mathematical invariant.

O(log min(a,b)) for GCD; O(n) for polygon turns
O(1) algorithmically
Intermediate
Interactive

Simulation

Execute movement commands while preserving position state.

O(moves)
O(grid) for visualization