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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