Free DSA Practice Sheet, Roadmap and Notes

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Most people learn data structures and algorithms by grinding random problems. It works better to learn patterns: once you recognize a sliding window or a monotonic stack, dozens of problems become the same problem. This free sheet is organized that way. Work top to bottom, and do not move on from a pattern until you can solve a new problem in it without hints.

How to use this sheet

Read or watch the idea behind the pattern first.
Solve the problems in order. Give each one 25 to 30 minutes before looking at hints.
After solving, write one sentence: what clue told me to use this pattern?
Revisit missed problems after 3 days and again after a week.

A simple DSA roadmap (8 weeks)

Week	Focus
1	Arrays and hashing, two pointers
2	Sliding window, stacks and monotonic stacks
3	Binary search, linked lists
4	Trees (DFS, BFS, BST properties)
5	Heaps, selection, intervals
6	Backtracking
7	Graphs (BFS/DFS on grids, topological sort, union find)
8	Dynamic programming, then mixed review

The sheet

Pattern	Problems (LeetCode #)
Arrays and hashing	Two Sum (1), Contains Duplicate (217), Group Anagrams (49), Top K Frequent Elements (347), Product of Array Except Self (238)
Two pointers	Valid Palindrome (125), 3Sum (15), Container With Most Water (11)
Sliding window	Best Time to Buy and Sell Stock (121), Longest Substring Without Repeating Characters (3), Minimum Window Substring (76), Sliding Window Maximum (239)
Stack and monotonic stack	Valid Parentheses (20), Daily Temperatures (739), Largest Rectangle in Histogram (84)
Binary search	Binary Search (704), Search in Rotated Sorted Array (33), Koko Eating Bananas (875)
Linked lists	Reverse Linked List (206), Merge Two Sorted Lists (21), Linked List Cycle (141)
Trees	Maximum Depth of Binary Tree (104), Binary Tree Level Order Traversal (102), Validate Binary Search Tree (98), Lowest Common Ancestor of a BST (235)
Heaps and selection	Kth Largest Element in an Array (215), Merge k Sorted Lists (23), Find Median from Data Stream (295)
Backtracking	Subsets (78), Combination Sum (39), Permutations (46)
Graphs	Number of Islands (200), Clone Graph (133), Course Schedule (207), Redundant Connection (684)
Dynamic programming	Climbing Stairs (70), House Robber (198), Coin Change (322), Longest Increasing Subsequence (300)

Quick DSA notes: when to use each pattern

Hashing: you need fast lookups or counts (“have I seen this before?”).
Two pointers: sorted input, or pairs/triples that must satisfy a condition.
Sliding window: a contiguous subarray or substring with a constraint (longest, shortest, at most k).
Monotonic stack: “next greater/smaller element” or spans and areas in histograms.
Binary search: sorted data, or a yes/no answer that flips at some value (search on the answer).
Heap: repeatedly need the smallest/largest item, top k, or merging sorted streams.
Backtracking: generate all subsets, permutations or combinations; prune early.
Graph BFS/DFS: connected regions, shortest steps in unweighted graphs, dependencies (topological sort).
Dynamic programming: overlapping subproblems; define the state, the transition and the base case (DP patterns guide).

Video walkthroughs from SDE Skills sessions

Sliding window (written guide)

Monotonic stack (written guide)

Binary search templates

QuickSelect (for Kth Largest Element) (written guide)

Practice it with other engineers, free

Working through a sheet alone is hard to keep up. SDE Skills, a volunteer-run 501(c)(3) nonprofit, runs free daily LeetCode practice on weekdays and a weekly data structures and algorithms session on Sundays, all on Zoom. See the schedule.

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