Important Topics for Competitive Programming.

vishalpanwar

You may have wondered about the vast and endless nature of topics important(or I should say sufficient) for competitive programming point of view. Well to sum it all I have prepared a list(huge one!!!). It contains all the famous problems,algorithms and data structure…………………………

(a)Number Theory

1. Prime Number Generation  (Sieve, Segmented Sieve)
2. Euler Totient Theorem
3. Fermat’s Theorem
4. HCF & LCM (Euclid)
5. Linear Diophantine Equations (Extended Euclid)
6. Modulus Arithmetic (addition,multiplication,subtraction,modular Inverse)
7. Cycle Finding (Floyd Algo and Brent Algo)
8. Integer Factorization (Trial Division , Pollard Rho method)
9. Lucas Theorem  (Simple & Advance)
10. Chinese Remainder Theorem
11. Wilson Theorem
12. Miller – Rabin Primality Testing
13. Perfect Numbers
14. Goldbach Conjecture

(b)Probability

1. Basic Probability and Conditional Probability
2. Random Variables
3. Probability Generating Functions
4. Expectation
5. Probability Distribution [Binomial, Poisson, Normal,Bernoulli]

(c)Counting

1. Pigeonhole principle
2. Inclusion Exclusion
3. Special Numbers  [Stirling,Fibonacci,Catalan, Eulerian, Harmonic, Bernoulli]
4. Polya Counting
5. Burnside lemma

(d)Permutation Cycles

(e)Linear Algebra

1. Addition And Subtraction Of Matrices
2. Multiplication ( Strassen’s algorithm ), Logarithmic…

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