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DSA, Intermediate

You have the toolkit. Now learn the structures and techniques that cover most real interview questions: trees and BSTs, graphs and grid BFS, topological sort, backtracking, DP, greedy, tries, the monotonic stack, bit tricks and math.

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Trees

23 min read · 13 exercises

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  1. TreesA linked list that's allowed to branch — and the three orders you can walk it in.
    23 min read13 exercises
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    13 exercises
  2. BST operations and ordered dataInsert, delete, successor, kth smallest and an iterator — and the honest truth about balancing and about a language with no TreeMap.
    44 min read14 exercises
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    14 exercises
  3. Tree problems in depthConstruction, LCA, balance and serialization — the four questions traversal alone doesn't answer.
    28 min read21 exercises
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    21 exercises
  4. Heaps & priority queuesYou don't need the whole thing sorted — you need the extreme value, fast, repeatedly.
    38 min read24 exercises
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    24 exercises
  5. Graphs: representation & traversalA tree is a graph with no cycles and one root — now drop both restrictions.
    22 min read13 exercises
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    13 exercises
  6. BFS on grids and implicit graphsA grid, a word list and a lock are all the same graph: states, a rule for the next states, and a queue that finishes one distance before starting the next.
    42 min read20 exercises
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    20 exercises
  7. Graph problemsComponents, cycles, colouring, trees and reachability: the same traversal each time, with a different thing to track.
    20 min read15 exercises
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    15 exercises
  8. Topological patternsAny problem phrased as "X must come before Y" is a DAG asking to be linearized.
    29 min read11 exercises
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    11 exercises
  9. BacktrackingTry a choice, recurse, undo the choice — DFS over a tree of decisions instead of a graph.
    22 min read13 exercises
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    13 exercises
  10. Dynamic programming: 1DRecursion, minus the part where you solve the same subproblem twice.
    29 min read17 exercises
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    17 exercises
  11. Dynamic programming: 2DSame idea as 1D, one more dimension — a grid table instead of a row.
    41 min read18 exercises
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    18 exercises
  12. DP state machines and the knapsack familyWhen one number per position cannot remember enough, keep one number per mode, and let the loop order say what you are counting.
    41 min read18 exercises
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    18 exercises
  13. Greedy algorithmsThe best DP alternative — when the locally best choice happens to be globally best too.
    33 min read16 exercises
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    16 exercises
  14. IntervalsEvery interval question starts the same way: sort by start time. Then it's bookkeeping.
    23 min read12 exercises
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    12 exercises
  15. Bit manipulationA small, fixed toolkit of tricks that turn up constantly once you recognize them.
    27 min read29 exercises
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    29 exercises
  16. Matrix problemsA grid is an array of arrays — every trick here is index bookkeeping, done carefully.
    17 min read18 exercises
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    18 exercises
  17. TriesStore the string as a path, not a value — and every prefix question becomes a walk instead of a scan.
    20 min read9 exercises
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    9 exercises
  18. Monotonic stack & queue in depthThrow away every element that can never win again — what survives is already sorted.
    26 min read15 exercises
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    15 exercises
  19. Math for interviewsSmall, exact facts about numbers: how Euclid, the sieve, modular arithmetic and a few counting identities turn huge inputs into short loops, and where JavaScript's numbers stop being exact.
    47 min read19 exercises
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    19 exercises
  20. Design and simulation problemsTurn a paragraph of requirements into a small machine: state, operations, costs, and the sentences that stay true.
    45 min read16 exercises
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    16 exercises
  21. Divide and conquer and selectionCut the input in two, solve each half, and the whole difficulty moves into one question: what can the answer be that neither half sees?
    52 min read15 exercises
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    15 exercises
  22. Randomization and samplingMake the generator a parameter, count the outcomes, and prove every outcome gets its fair share before you trust the code.
    58 min read17 exercises
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    17 exercises

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