How to use this collection

Each weekly set contains interview-style problems selected because they exercise the technique taught that week. Start with the first two problems for pattern recognition, then use the remaining problems for transfer, proof practice, and implementation discipline. The notes identify what to look for while solving.

Week 1: Modelling, Constraints, and Baselines

Problem	Technique focus	Why it fits
Two Sum	hashing and constraint-based improvement	Shows the move from quadratic search to a linear hash-table model.
Valid Anagram	counting invariant	Turns a text problem into a frequency-vector equality check.
Merge Intervals	sorting plus invariant	Requires precise modelling of overlap and a clean loop invariant.
Container With Most Water	two pointers	Good interview example for explaining why one pointer can be discarded.

Week 2: Exhaustive Search, Backtracking, and Pruning

Problem	Technique focus	Why it fits
Subsets	binary choice recursion	Canonical state-space tree with clear output-size complexity.
Permutations	visited-set backtracking	Highlights recursion state, used elements, and factorial complexity.
Combination Sum	pruned enumeration	Uses monotone choices to avoid duplicate combinations.
N-Queens	constraint propagation	Classic pruning problem using columns and diagonal occupancy sets.

Week 3: Dynamic Programming I

Problem	Technique focus	Why it fits
Climbing Stairs	one-dimensional recurrence	Minimal example for state, base case, transition, and space compression.
House Robber	choice DP	Forces students to encode mutually exclusive local choices.
Unique Paths	grid DP	Clean two-dimensional tabulation with combinatorial interpretation.
Coin Change	unbounded knapsack	Introduces unreachable states and minimization over transitions.

Week 4: Dynamic Programming II

Problem	Technique focus	Why it fits
Longest Increasing Subsequence	DP and binary-search optimization	Good contrast between O(n squared) DP and O(n log n) patience sorting.
Longest Common Subsequence	two-sequence DP	Canonical table recurrence with reconstruction discussion.
Partition Equal Subset Sum	pseudo-polynomial DP	Connects subset-sum modelling to complexity and constraints.
Burst Balloons	interval DP	Requires choosing the final action in an interval, a useful advanced pattern.

Week 5: Greedy Algorithms

Problem	Technique focus	Why it fits
Jump Game	greedy reachability	Short problem with a strong invariant about farthest reachable index.
Non-overlapping Intervals	interval scheduling	Direct practice for earliest-finish-time exchange reasoning.
Task Scheduler	greedy counting	Shows how frequency constraints become a schedule-length formula.
Minimum Number of Arrows to Burst Balloons	interval stabbing	Nice variant for proving why sorting by right endpoint works.

Week 6: Divide and Conquer and Answer Search

Problem	Technique focus	Why it fits
Koko Eating Bananas	binary search on answer	Classic monotone feasibility predicate with integer boundary care.
Search in Rotated Sorted Array	modified binary search	Forces invariant design when the sorted half changes by case.
Count of Smaller Numbers After Self	divide and conquer counting	Merge-sort counting problem that connects recursion to order statistics.
Median of Two Sorted Arrays	partition search	Advanced interview problem for precise binary-search proof.

Week 7: Advanced Data Structures

Problem	Technique focus	Why it fits
Range Sum Query: Mutable	Fenwick tree or segment tree	Direct match for point updates and range queries.
Sliding Window Maximum	monotonic deque	Shows how a deque maintains candidates and gives amortized O(n).
Daily Temperatures	monotonic stack	Simple and effective for next-greater-element reasoning.
Accounts Merge	union-find	Models equivalence classes and component extraction through DSU.

Week 8: Graph Modelling and Traversal

Problem	Technique focus	Why it fits
Course Schedule	directed graph and topological order	Turns prerequisites into cycle detection and ordering.
Rotting Oranges	multi-source BFS	Good grid problem for levels, time, and queue invariants.
Pacific Atlantic Water Flow	reverse graph traversal	Shows how reversing the search direction simplifies reachability.
Word Ladder	implicit graph BFS	Interview staple for modelling words as graph vertices without materializing all edges.

Week 9: Shortest Paths, MST, SCCs, and Flow Ideas

Problem	Technique focus	Why it fits
Network Delay Time	Dijkstra	Direct weighted shortest-path application with adjacency-list design.
Cheapest Flights Within K Stops	bounded Bellman-Ford	Illustrates why a stop limit changes the shortest-path state.
Critical Connections in a Network	bridges and low-link values	Prepares students for SCC-style DFS timestamps and structural graph analysis.
Min Cost to Connect All Points	minimum spanning tree	Clean MST problem where Prim or Kruskal can be justified.

Week 10: String Algorithms and Hashing

Problem	Technique focus	Why it fits
Implement Trie	prefix tree	Direct implementation of dictionary operations and prefix queries.
Find All Anagrams in a String	sliding window counts	Connects string matching to frequency invariants.
Repeated DNA Sequences	rolling hash and encoding	Compact example for fixed-length string hashing.
Longest Duplicate Substring	binary search plus hashing	Combines answer search, suffix intuition, and collision discussion.

Week 11: Optimization Patterns and Hardness Awareness

Problem	Technique focus	Why it fits
Partition to K Equal Sum Subsets	NP-hard style search with pruning	Shows why exponential backtracking remains necessary under small constraints.
Sudoku Solver	constraint search	Practical exact search with strong pruning and constraint propagation.
Shortest Path Visiting All Nodes	state compression BFS	Uses exponential state space with polynomial graph traversal over states.
Word Ladder II	BFS plus path enumeration	Demonstrates output-sensitive complexity and why all shortest paths can be large.

Week 12: Technical Interview Simulation

Problem	Technique focus	Why it fits
LRU Cache	hash map plus linked list design	High-signal interview problem for data-structure design and invariants.
Merge k Sorted Lists	heap and divide and conquer	Allows multiple valid approaches and complexity comparison.
Serialize and Deserialize Binary Tree	tree traversal protocol	Tests representation choices, edge cases, and clear explanation.
Trapping Rain Water	two pointers or monotonic stack	Good simulation problem for explaining alternative approaches.

Week 13: Final Competition Practice

Problem	Technique focus	Why it fits
The Skyline Problem	sweep line and heap	Contest-style combination of events, ordering, and active-set maintenance.
Swim in Rising Water	Dijkstra or binary search plus BFS	Good final review problem with multiple defensible algorithmic routes.
Minimum Cost to Make at Least One Valid Path in a Grid	0-1 BFS	Introduces a contest-grade shortest-path variant with binary edge costs.
Word Ladder II	graph search and reconstruction	Useful capstone for modelling, BFS levels, predecessor graphs, and output size.