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01 Semesters (BSc)
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Semester 2
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Algorithms and Probability
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Lecture Notes
Folder: 01-Semesters-(BSc)/Semester-2/Algorithms-and-Probability/Lecture-Notes
25 items under this folder.
Jan 07, 2026
01 Introduction, Connectedness, Blocks
Jan 07, 2026
02 Finding Cut Vertices and Bridges, Cycles and Circuits, Hamiltonian Cycles and Gray Codes
Jan 07, 2026
03 Hamiltonian Cycles, Dirac's Theorem, Complexity Theory, Traveling Salesman
Jan 07, 2026
04 Cycles, Travelling Salesman Problem, Metric TSP, Matching, Augmenting Paths, Hall's Marriage Theorem
Jan 07, 2026
05 Matchings in Bipartite Graphs
Jan 07, 2026
06 Augmenting Paths, Hopcroft-Karp, 1.5 Approximation for Metric TSP
Jan 07, 2026
07 Graph Coloring, Greedy Coloring, Smallest-Last Heuristics, Block Graph Colorings
Jan 07, 2026
08 Five-Color Theorem, Brooks Theorem, 3-Colorable Coloring Approximation, Randomness
Jan 07, 2026
09 Discrete Probability Space, Properties of Probability, Union of Events, Laplace Space, Composite Probability, Combinatorics
Jan 07, 2026
10 Conditional Probability, Independence, and Bayes' Theorem
Jan 07, 2026
11 Independence of Multiple Events, Random Variables
Jan 07, 2026
12 Randomized QuickSort, Indicator Variables, Common Probability Distributions, Coupon Collector
Jan 07, 2026
13 Conditional Random Variables, Multiple Random Variables (Joint PMF, Marginal PMF), Independence of Random Variables, Sum of Independent Random Variables, Wald's Identity, Variance and Concentration
Jan 07, 2026
14 Rules for Moments (Expectation, Variance), Estimating Probabilities (Markov, Chebyshev), Chernoff Bounds
Jan 07, 2026
15 Randomized Algorithms, Monte Carlo vs Las Vegas, Reducing Error Probability
Jan 07, 2026
16 Target-Shooting, Finding Duplicates, Hashing, Bloom Filter
Jan 07, 2026
17 Floyd's Cycle-Finding (Tortoise and Hare), Primality Testing
Jan 07, 2026
18 Fermat and Miller-Rabin Primality Tests
Jan 07, 2026
19 Long-Path Problem and Reduction to Hamiltonian Cycle, Solving Hamiltonian Cycle using DP, Long-Path via Randomized Coloring
Jan 07, 2026
20 Detecting Colorful Paths using DP, Flow Networks
Jan 07, 2026
21 Flow Networks, Cuts, Max-Flow Min-Cut, Residual Networks, Ford-Fulkerson
Jan 07, 2026
22 Ford-Fulkerson with Integer Capacities, Applications of Max Flow (Max Bipartite Matching, Edge-Disjoint Paths, Image Segmentation)
Jan 07, 2026
23 Randomized Algorithms for Global Min-Cut in Undirected Graphs
Jan 07, 2026
24 Smallest Enclosing Disk via Randomized Algorithms
Jan 07, 2026
25 Convex Hulls - Geometry, Algorithms, and Complexity