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Mathmatics for Computer Science

Computer_Science_Mathmatics_Princeton.pdf
Andrew's Algorithm Exercise Solutions

Competitive Algorithm Sites

Google Code Jam, Algo Spot, Backjoon, Geeks for Geeks, Top Coder, Projec Euler

Analysis of Algorithm and Master Method

Analysis of Algorithms | Set 1 (Asymptotic Analysis)
Analysis of Algorithms | Set 2 (Worst, Average and Best Cases)
Analysis of Algorithms | Set 3 (Asymptotic Notations)
Analysis of Algorithms | Set 4 (Analysis of Loops)
Analysis of Algorithm | Set 4 (Solving Recurrences RSP(rate of subproblem proliferation) and RWS(rate of work shrinkage)

Master Method

Recurrence Master Method Analysis

Analysis of Algorithm | Set 5 (Amortized Analysis Introduction)

Amortized Analysis


Divide and Conquer, Sorting and Searching, and Randomized Algorithms

Karatsuba algorithm - Wiki, C++ Implemntation
Strassen’s Matrix Multiplication - Geeks, Online Judge
Easy way to remember Strassen’s Matrix Equation - Geeks

Strassen Mutlpication Formula


Inversion Count - Geeks, C++ Implementation

Inversion Count Explain Graph


Closest pair of points - Wiki, Closest Pair of Points - Geeks, Online Judge

Close Point


Quick Sort - Wiki, Quick Sort - Geeks. QuickSort using Random Pivoting

Continuous and discrete probability distributions

Linearlity of Expectation

expectation_probability_Pivot

Probabilty based on quicksort partition - 0 < a < 0.5
Birthday problem among k people
Why is the expected value E(X2)≠E(X)2?

Order statistic, Median of medians, Quick Select

Reduce to Sorting

Randomized Selection


[Karger's algorithm]
Karger's algorithm - wiki
Karger’s algorithm for Minimum Cut | Set 1 (Introduction and Implementation)
Karger’s algorithm for Minimum Cut | Set 2 (Analysis and Applications)
Find minimum s-t cut in a flow network

Min-Cut

Graph Search, Shortest Paths, and Data Structures

BFS - Wiki, BFS - Geeks, Online Judge

DFS - Wiki, DFS - Geeks, Online Judge

Topological Sorting - Wiki, Topological Sorting - Geeks, Online Judge

SCC - strongly connected components, Tarjan’s Algorithm to find Strongly Connected Components

Dijkstra's algorithm - wiki, Geeks for Geeks, Implementation


Heap and Blanced Binary Search Tree

Heap Sort - wiki, Heap Sorting - Geeks

Self-balancing binary search tree, Convert a normal BST to Balanced BST

Splay Tree

splay_tree_zigzag

AVL Tree

AVL-tree-wBalance_K

Red-Black Tree

Red-Black Tree Example

Red-Black Tree 4 Invaraints

B+ Tree

B+ Tree Example


Hasing

Hash Table, Hashing - Geeeks, Hashing Function, Universal Hasing

djb2 Hashing

Bucket Size
good hash table primes

What are Hash Functions and How to choose a good Hash Function?

Bloom Filter, Bloom Filter - Geeks

Bloom Filter Example

Greedy Algorithms, Minimum Spanning Trees, and Dynamic Programming

Shortest Paths Revisited, NP-Complete Problems and What To Do About Them

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