DSA Mastery

What you'll learn

• Boot CampThe JavaScript you need, and how to measure speed
• Linear LandArrays, strings, maps, lists, stacks, queues
• Thinking LoopsRecursion and sorting
• Branching ForestTrees, BSTs, heaps, graphs and tries
• WorkshopBits, math and designing your own data structures
• Pointer PassPatterns 1–3: move indices cleverly
• Counting CavesPatterns 4–7: count, scan and precompute
• Choice CanyonPatterns 8–10: sort, choose, keep the best
• Explorer PeaksPatterns 11–14: walk every path
• Graph SummitDependencies, groups, weighted paths and spanning trees
• Expert RidgeString matching and range queries
• Boss CastlePattern 15: dynamic programming

Course outline

12 units and 56 lessons. Each lesson has a short read with examples you run, a quiz, and coding problems tested in your browser; most have a step-through visualizer.

1. 1

   Unit 1:Boot Camp

   The JavaScript you need, and how to measure speed

   Free
   1. { }
      JS Toolkit for DSA Arrays, loops, objects, Map and Set: the only JavaScript most interview problems need.
      2 problems
   2. O(n)
      Big-O Notation How to describe the speed of an algorithm as the input grows.
      2 problems
2. 2

   Unit 2:Linear Land

   Arrays, strings, maps, lists, stacks, queues

   Free
   1. [ ]
      Arrays The workhorse structure: instant reads, costly middle inserts.
      2 problems
   2. "ab"
      Strings Arrays of characters, with one catch: you cannot change them in place.
      2 problems
   3. k→v
      Hash Maps & Sets Trade a little memory for instant "have I seen it?" answers.
      2 problems
   4. #[]
      Hashing Internals: Build a Hash Map How a Map finds keys in O(1): hash functions, buckets, collisions, load factor and resizing.
      3 problems
   5. ○→○
      Linked Lists Nodes holding a value and a pointer to the next node.
      2 problems
   6. ▤
      Stacks Last in, first out. The most recent thing is always on top.
      2 problems
   7. ⇶
      Queues First in, first out. Fair lines, task schedulers and BFS.
      2 problems
3. 3

   Unit 3:Thinking Loops

   Recursion and sorting

   Pro
   1. f(f)
      Recursion Solve a problem by solving a smaller copy of it.
      2 problems
   2. ▁▃▅
      Sorting Basics Put things in order, then many problems become easy.
      2 problems
   3. P|
      Quick Sort, Quickselect & Counting Sort Partition around a pivot, find the k-th element in O(n) on average, and beat n log n for small integers.
      3 problems
   4. T(n)
      Analysing Recursive & Amortized Cost Recursion trees, the four recurrences to know, amortized O(1), and the hidden costs in everyday JavaScript.
      2 problems
4. 4

   Unit 4:Branching Forest

   Trees, BSTs, heaps, graphs and tries

   Pro
   1. ⋔
      Binary Trees Nodes with up to two children. Recursion was made for them.
      2 problems
   2. <·>
      Binary Search Trees Smaller to the left, bigger to the right, at every node.
      2 problems
   3. △
      Heaps A tree packed into an array that always knows its minimum.
      2 problems
   4. ⛰
      Heap Sort and Stable Sorting Sort in place in O(n log n) with a heap, sort nearly sorted data with a small heap, and know when order among equals matters.
      3 problems
   5. ◇—◇
      Graphs Nodes and edges: maps, networks, dependencies, grids.
      2 problems
   6. a·b·c
      Tries A tree of letters for lightning-fast prefix search.
      2 problems
   7. a.c
      Trie II: Wildcards and Grid Words Wildcard search by branching, many-word grid search pruned by a trie, and prefix replacement.
      3 problems
5. 5

   Unit 5:Workshop

   Bits, math and designing your own data structures

   Pro
   1. 0b1
      Bit Manipulation Numbers as rows of bits: AND, OR, XOR and shifts, the tricks built on them, and bitmasks as sets.
      3 problems
   2. gcd
      Math for Coding Interviews Remainder against modulo, gcd and lcm, primes and the sieve, fast exponentiation and safe integers.
      3 problems
   3. LRU
      Designing Data Structures: LRU Cache Turn required complexities into a design: a min stack, an LRU cache (map + doubly linked list), a time map.
      3 problems
6. 6

   Unit 6:Pointer Pass

   Patterns 1–3: move indices cleverly

   Pro
   1. L R
      Two Pointers Two indices walk toward each other (or together) to skip useless pairs.
      3 problems
   2. T H
      Fast & Slow Pointers A hare that moves twice as fast finds cycles and middles in one pass; a dummy head removes edge cases.
      3 problems
   3. [k]
      Sliding Window Keep a running window over a range and slide it instead of recomputing.
      3 problems
   4. L M R
      Binary Search Halve the search space every step: O(log n).
      3 problems
   5. lo hi
      Binary Search on the Answer Boundaries with lower/upper bound, rotated arrays, and binary searching a monotonic yes/no question.
      3 problems
7. 7

   Unit 7:Counting Caves

   Patterns 4–7: count, scan and precompute

   Pro
   1. #×n
      Frequency Counting Count everything once in a map, then answer questions instantly.
      3 problems
   2. ▦
      Matrix Traversal Walk a 2D grid in the order the problem needs: rows, columns, diagonals, spirals.
      3 problems
   3. ⟳▦
      Matrix II: Rotate, Zero and Search Rotate an image in place, zero rows and columns with O(1) extra space, and search a sorted grid from a corner.
      3 problems
   4. ▟
      Monotonic Stack A stack kept in sorted order answers "next greater / smaller" in O(n).
      3 problems
   5. ⇤⇥
      Monotonic Queue: Window Maximum A deque of indexes, decreasing front to back, gives the maximum of every window in O(n).
      3 problems
   6. Σ
      Prefix Sum Precompute running totals once, answer any range sum in O(1).
      3 problems
8. 8

   Unit 8:Choice Canyon

   Patterns 8–10: sort, choose, keep the best

   Pro
   1. ⊏⊐
      Overlapping Intervals Sort by start time, then merge or compare neighbours.
      3 problems
   2. $→
      Greedy Make the best-looking choice now and never look back, when that provably works.
      3 problems
   3. ⇥⇥
      Greedy II: Jumps, Circuits, Intervals Three greedy classics with the argument that makes each one correct.
      3 problems
   4. k▲
      Top K Elements Keep only the k best candidates in a heap as you scan.
      3 problems
   5. ⋀⋁
      Two Heaps: Running Median A max-heap for the lower half and a min-heap for the upper half give the median of a stream in O(log n).
      2 problems
9. 9

   Unit 9:Explorer Peaks

   Patterns 11–14: walk every path

   Pro
   1. ↺
      Backtracking Choose, explore, un-choose: systematically try every possibility.
      3 problems
   2. ♛
      Backtracking on Grids & Constraints Mark, explore, restore on a grid; O(1) constraint checks for N-Queens; prune and skip duplicates.
      3 problems
   3. ↙↘
      Binary Tree Traversal Preorder, inorder, postorder: three orders, one recursive shape.
      3 problems
   4. LCA
      Tree Recipes: Invert, Diameter, LCA Return one thing while tracking another: height and diameter, path sums, and the lowest common ancestor.
      3 problems
   5. ↧
      Depth-First Search Go as deep as you can, then back up. Recursion or a stack.
      3 problems
   6. ≋
      Breadth-First Search Explore in rings of distance with a queue. Finds shortest paths.
      3 problems
10. 10

    Unit 10:Graph Summit

    Dependencies, groups, weighted paths and spanning trees

    Pro
    1. A→B
       Topological Sort Order tasks so every prerequisite comes first, and detect when a cycle makes that impossible.
       3 problems
    2. ⊔
       Union-Find (Disjoint Sets) Group items into sets and ask "same set?" in near-constant time, even while edges keep arriving.
       3 problems
    3. d[v]
       Weighted Shortest Paths Dijkstra for non-negative weights, Bellman-Ford for negative ones, stop limits and negative cycles.
       3 problems
    4. ⋯⋯
       Graph Extras: Many Sources, Two Colours, All Pairs Multi-source BFS, bipartite checks, Floyd-Warshall for all pairs, and 0-1 BFS with a deque.
       4 problems
    5. MST
       Minimum Spanning Tree Connect every node for the least total weight: Kruskal sorts edges and uses union-find; Prim grows a tree.
       2 problems
11. 11

    Unit 11:Expert Ridge

    String matching and range queries

    Pro
    1. abab
       String Matching: KMP and Rolling Hash Find a pattern in a text in O(n + m) with KMP's prefix function, or with a rolling hash.
       3 problems
    2. [l,r]
       Range Queries: Fenwick and Segment Trees Answer range sums and minimums while the array keeps changing, in O(log n) per operation.
       3 problems
12. 12

    Unit 12:Boss Castle

    Pattern 15: dynamic programming

    Pro
    1. dp[i]
       Dynamic Programming Solve each small subproblem once, store it, build the big answer from it.
       4 problems
    2. W
       Knapsack DP Take it or leave it: 0/1 and unbounded knapsack, subset sums, and counting the ways to make change.
       3 problems
    3. LCS
       Sequence DP: Kadane, LIS, LCS Best subarray, longest increasing subsequence, longest common subsequence and edit distance.
       4 problems
    4. i..j
       Interval DP & DP on Trees Fill a table by substring length for palindromes, and return tuples up a tree for house robber III.
       3 problems