Problem catalog

Use this catalog after learning a pattern. Search the page for a signal such as “shortest,” “prefix,” “capacity,” or “version.” Before opening a solution, write the state, invariant, and target complexity.

Difficulty labels are orientation only: E easy, M medium, H hard.

flowchart LR
  accTitle: Deliberate practice loop for algorithm problems
  accDescr: Start from a problem signal, choose a candidate chapter, write the state and invariant before coding, test the solution, record the failure mode, and retry a related harder problem.
  A["Name the problem signal"] --> B["Choose a candidate pattern<br/>from this catalog"]
  B --> C["Write state, invariant,<br/>transition, and target cost"]
  C --> D["Implement without<br/>opening the solution"]
  D --> E["Test normal, boundary,<br/>and adversarial cases"]
  E --> F{"Accepted and<br/>proof still holds?"}
  F -->|"no"| G["Record the failed assumption<br/>and repair the model"]
  G --> C
  F -->|"yes"| H["Solve a nearby problem<br/>with one changed constraint"]
  H --> A

The catalog is most useful when the first written artifact is the invariant, not code. A wrong invariant exposes a modeling error earlier than a failed submission does.

Arrays, hashing, and windows

Problem	Level	Signal → pattern	Ask first
Two Sum	E	complement → hash map	What belongs to the scanned past?
Group Anagrams	M	canonical key → hash groups	Which representation makes equivalents equal?
Subarray Sum Equals K	M	signed subarray → prefix frequency	Which earlier prefix completes the target?
Longest Substring Without Repeating Characters	M	monotone validity → window	What forces the left edge forward?
Sliding Window Maximum	H	fixed-window extreme → deque	Which candidates are permanently dominated?

Read Chapter 3 and Chapter 4.

Linked lists and composite ownership

Problem	Level	Signal → pattern	Ask first
Reverse Linked List	E	pointer rewiring → reversed prefix	Did I save the unread suffix?
Linked List Cycle II	M	cycle entry → slow/fast	What distance relation holds at the meeting?
LRU Cache	M	lookup + recency → map + list	Which structure owns identity and which owns order?
LFU Cache	H	lookup + frequency + recency	What moves atomically after access?
Snapshot Array	M	versions + sparse writes → histories + binary search	What is the newest visible change?

Read linked lists and Chapter 11.

Trees, heaps, and range indexes

Problem	Level	Signal → pattern	Ask first
Binary Tree Level Order Traversal	M	layers → BFS queue	When does one level end?
Validate Binary Search Tree	M	global ordering → bounds	Which ancestor bounds constrain this node?
Kth Largest Element in an Array	M	top k → heap/selection	Must all values be sorted?
Implement Trie	M	prefix lookup → Trie	Where is word termination stored?
Range Sum Query – Mutable	M	updates + ranges → Fenwick/segment	Is update additive or assignment?

Read Chapter 5 and Chapter 13.

Graph traversal and structure

Problem	Level	Signal → pattern	Ask first
Number of Islands	M	components → DFS/BFS	What creates an edge between cells?
Rotting Oranges	M	simultaneous waves → multi-source BFS	Which sources enter at time zero?
Course Schedule	M	prerequisites → topological sort	Is the request an order or only cycle detection?
Network Delay Time	M	nonnegative shortest paths → Dijkstra	Are all edge weights nonnegative?
Critical Connections in a Network	H	edge failure → bridges	Can the child subtree reach an ancestor?

Read Chapter 6.

Advanced graphs

Problem	Level	Signal → pattern	Ask first
Min Cost to Connect All Points	M	cheapest connectivity → MST	Is a path cost or whole-network cost requested?
Cheapest Flights Within K Stops	M	bounded edges → layered Bellman–Ford/DP	Which iteration count represents allowed edges?
Find the City With the Smallest Number of Neighbors	M	all sources + small graph → Floyd/Dijkstra	Which V and density bound wins?
Maximum Employees to Be Invited to a Meeting	H	functional-graph cycles → SCC/cycle decomposition	Which vertices share a cycle?
Maximum Number of Accepted Invitations	M	bipartite assignment → matching/flow	What are the left and right partitions?

Read Chapter 10.

Binary search and greedy

Problem	Level	Signal → pattern	Ask first
Search in Rotated Sorted Array	M	one sorted half → exact binary search	Which half is provably ordered?
Koko Eating Bananas	M	minimum feasible rate → first true	Is feasibility monotone?
Find Minimum in Rotated Sorted Array	M	transition boundary → first true	Which side contains the pivot?
Non-overlapping Intervals	M	maximize compatible count → earliest finish	Can an optimum exchange its first interval?
Jump Game	M	reachable prefix → stay-ahead greedy	What is the farthest certified index?

Read Chapter 7 and greedy algorithms.

Backtracking and state search

Problem	Level	Signal → pattern	Ask first
Subsets II	M	choose/skip + duplicates → sorted backtracking	Which equal choice is redundant at this depth?
Combination Sum	M	reuse candidates → backtracking	Does the next call keep or advance the index?
Permutations	M	ordered choices → used set	What defines one decision-tree level?
Word Search	M	path with undo → grid backtracking	Which state must be restored?
N-Queens	H	constraint placement → backtracking sets	Which conflicts can be checked in O(1)?

Read Chapter 8.

Dynamic programming

Problem	Level	Signal → state shape	Ask first
House Robber	M	local exclusion → dp[i]	What does the prefix answer promise?
Coin Change	M	reusable amounts → dp[amount]	Is reuse allowed in the same stage?
Longest Common Subsequence	M	two prefixes → dp[i][j]	What happens on match versus mismatch?
Cherry Pickup II	H	row + two agents → dp[row][c1][c2]	Which coordinates determine the future?
Burst Balloons	H	choose last in interval → interval DP	Which choice makes the two sides independent?

Read Chapter 9.

External practice sets

• LeetCode 75 study plan
• LeetCode Top Interview 150
• HackerRank Interview Preparation Kit

Use the platform for the prompt and judge; use this book for choosing the model, stating the invariant, and reviewing the failure modes.