AOCP/Harmonic Numbers: Difference between revisions
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While it does not occur often in classical mathematics, it crops up more often in algorithm analysis. | While it does not occur often in classical mathematics, it crops up more often in algorithm analysis. | ||
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Revision as of 07:08, 20 July 2017
Volume 1
Chapter 1: Basic Concepts: Harmonic numbers
Harmonic numbers become important in analyses of algorithms. Define
$ H_n = 1 + \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{4} + \dots + \dfrac{1}{n} = \sum_{1 \leq k \leq n} \dfrac{1}{k} \qquad n \geq 0 $
While it does not occur often in classical mathematics, it crops up more often in algorithm analysis.
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The Art of Computer Programming notes from reading Donald Knuth's Art of Computer Programming
Volume 1: Fundamental Algorithms Mathematical Foundations: AOCP/Infinite Series · AOCP/Binomial Coefficients · AOCP/Multinomial Coefficients AOCP/Harmonic Numbers · AOCP/Fibonacci Numbers Puzzles/Exercises:
Volume 2: Seminumerical Algorithms AOCP/Random Numbers · AOCP/Positional Number Systems AOCP/Floating Point Arithmetic · AOCP/Euclids Algorithm AOCP/Factoring into Primes · AOCP/Polynomial Arithmetic AOCP/Power Series Manipulation
Volume 3: Sorting and Searching AOCP/Internal Sorting · AOCP/Optimal Sorting · AOCP/External Sorting AOCP/Binary Tree Searching · AOCP/Hashing AOCP/Combinatorics · AOCP/Multisets · Rubiks Cube/Permutations
AOCP/Combinatorial Algorithms · AOCP/Boolean Functions AOCP/Five Letter Words · Rubiks Cube/Tuples AOCP/Generating Permutations and Tuples
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