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Module 1 β Foundations
Why performance matters, what βnβ means, and how common functions grow.
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01 β Introduction
Why algorithms + performance matter. Feasible vs infeasible intuition.
02 β What is input size (n)?
Define n for sorting, graphs (|V|,|E|), strings (n,m), matrices.
03 β Growth of functions (Visualizer)
Interactive plots comparing log n, n, n log n, nΒ², 2βΏ, n! etc.
04 β Feasible vs infeasible
Convert operations to time using machine speed.
Module 2 β Asymptotic Analysis
Big-O / Ξ© / Ξ, time vs space, and case analysis.
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05 β Asymptotic Notations Visualizer
Play with c and nβ to test O, Ξ©, and Ξ.
06 β Time vs Space (Hands-on)
See trade-offs using toy algorithms (search, merge sort, DP).
07 β Best / Average / Worst Case
Same algorithm, different inputs β different runtime behavior.
Module 3 β From Code to Recurrence
Turn loops into counts, recursion into recurrences, and build intuition before Master Theorem.
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09 β Cost From Code (Loops + Recurrence Playground)
Loops β summation, recursion β recurrence, then solve (3 methods).
10 β Step Counter Simulator (Loops vs Recursion)
Mini-debugger style view: see which line dominates runtime.
Module 4 β Recurrence & Recursion Trees
Build intuition for divide-and-conquer recurrences and prepare Master Theorem.
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08 β Recursion Tree Visualizer
Visual expansion of common recurrences and their growth.
11 β Master Theorem
Case 1/2/3 solver for T(n)=aT(n/b)+f(n).
Module 5 β Divide & Conquer
Binary search, max-min, merge sort, quick sort, randomized quick sort, Karatsuba intro.
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12 β Binary Search
Trace l/m/r step-by-step + comparisons count.
13 β Max & Min (D&C)
Fewer comparisons than linear scan (tournament method).
14 β Merge Sort
Split + merge animation, O(n log n).
15 β Quick Sort: Lomuto Partition
The pivot-placement subroutine used in Quick Sort (Lomuto scheme).
16 β Randomized Quick Sort
Expected performance intuition (random pivot).
17 β Integer Multiplication (Karatsuba)
3 multiplications instead of 4 + recurrence.
Module 6 β Graph Search
Graph representation, BFS, DFS (animations).
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18 β Graph Representation
Adjacency list vs matrix (space/time trade-offs).
19 β BFS
Queue animation + levels + shortest path (unweighted).
20 β DFS
Recursion/stack animation + traversal tree.
Module 7 β Greedy Strategy
Knapsack, job sequencing, Huffman, MST, shortest paths (Dijkstra).
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21 β Greedy Intro
Greedy-choice property + counterexamples.
22 β Fractional Knapsack
Sort by value/weight and fill capacity.
23 β Job Sequencing
Maximize profit with deadlines (slot filling).
24 β Huffman Coding
Min-heap merge to build optimal prefix codes.
25 β Union-Find
MakeSet / Find / Union with compression & rank.
26 β MST (Kruskal)
Sorted edges + union-find acceptance/rejection.
27 β MST (Prim)
Grow MST using priority queue (frontier edges).
28 β Dijkstra
Greedy relaxation for non-negative weights.
Module 8 β Dynamic Programming
Bellman-Ford, Floyd-Warshall, Knapsack DP, LCS, Edit distance, MCM, TSP (DP).
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29 β DP Intro
Memoization vs tabulation; overlapping subproblems.
30 β Bellman-Ford
Vβ1 relaxations + negative cycle detection.
31 β FloydβWarshall
APSP DP over intermediate k.
32 β 0/1 Knapsack (DP)
DP table fill + backtrack chosen items.
33 β LCS
DP grid visual + reconstruction.
34 β Matrix Chain Multiplication
Optimal parenthesization DP.
35 β Edit Distance
Insert/delete/replace DP grid.
36 β TSP (DP/Bitmask)
Small n demo + 2βΏ state explosion.
Module 9 β Backtracking
N-Queens, graph coloring, Hamiltonian cycle (state space + pruning).
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37 β Backtracking Intro
Decision tree + pruning visualization.
38 β N-Queens
Board animation + conflict checks.
39 β Graph Coloring
m-coloring backtracking + pruning.
40 β Hamiltonian Cycle
Path building + prune when no edge.
Module 10 β Branch & Bound
Bounding, live nodes, 0/1 knapsack and TSP using B&B.
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41 β Branch & Bound Intro
FIFO vs least-cost strategy + bounds.
42 β 0/1 Knapsack (B&B)
Upper bound pruning (via fractional knapsack bound).
43 β TSP (B&B)
Lower bound + pruning for TSP search.
Module 11 β String Matching
NaΓ―ve, RabinβKarp, KMP (pattern matching).
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44 β NaΓ―ve String Matching
O(nΒ·m) comparisons visualization.
45 β RabinβKarp
Rolling hash window demo + collisions note.
46 β KMP
LPS build + skip comparisons (O(n+m)).
Module 12 β NP & Complexity
P vs NP, NP-Complete, NP-Hard, reductions.
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47 β Complexity Classes
Quick map: P, NP, NP-Complete, NP-Hard + examples.
48 β Reductions (SAT β VC)
Reduction pipeline sketch + why it matters.