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Suffix Array Part 2–String Matching/Searching
This is part 2 of the post “suffix array”, which covers the string matching/searching problem that can be solved by suffix array. You may want to read part 1 first. String Matching/Searching Once we...
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Suffix Array Part 3 — Longest Common Substring (LCS)
Suffix array can be used to find longest common substring (LCS) among multiple strings. This post illustrate the algorithm by an example of finding LCS among two strings. Algorithm The idea is that LCS...
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Computing Fibonacci Numbers
Fibonacci series is a number sequence of 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 44, … It can be expressed by the formula below, Fibonacci series grows almost as fast as the power of 2. Fn ~= 2^(0.694n)....
View ArticlePrimality Testing–Part 1. Naïve Approaches
Primality refers to determining if a given input number is prime or not. This post covers two naive approaches for primality testing. Naive Approach 1 This most straightforward approach is to check if...
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Primality Testing — Part 2. Pre-computation with Sieve of Eratosthenes
Previous post covers two naive methods for primality testing. This post introduces an algorithm to generate prime numbers called Sieve of Eratosthenes. With this algorithm, an optimization can be...
View ArticlePrimality Testing — Part 3. A Further Optimized Method
The previous two posts cover the naive approaches for primality testing and a method with precomputation. This post introduces a new method which could perform better than previous approaches and it...
View ArticleHow to Calculate Modular Exponentiation
Modular exponentiation is a exponentiation performed over modulus. It is used in many cryptographic algorithms. Modular exponentiation accepts three input integers, say x, y and n and computes...
View ArticlePrimality Testing — Part 4. Fermat’s Little Theorem and A Probabilistic Approach
Previous posts on primality testing are all trying to factor the input number. For a very large number with few hundreds of bits, it is difficult to compute in that manner. This post introduce a...
View ArticleBig Integer Arithmetic
Most of computer applications operates on small integers which can be represented by 32 bit integers. However, there are times we’ll need to deal with extremely big integers which can only be...
View ArticleBit Set
One specific usage of bits is to represent sets. Suppose we have a set of N elements {e1, e2, …, en}, and we want to select a subset of K (K <= N) elements. We can use a bit pattern to represent the...
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Linear Regression
This is some notes taken when I summarize the things learned after taking Andrew Ng’s machine learning course at coursera. Introduction Regression is a technique to model relationships among variables....
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Logistic Regression
This is some notes taken when I summarize the things learned after taking Andrew Ng’s machine learning course at coursera. Introduction Linear regression predicts continuous values. At times, we need...
View ArticlePerformance Metrics for Binary Classification
Binary classification classifies samples as either 0 (negative) or 1(positive). Depending on which class/label the sample data belongs to and its predication result, each sample fits in a cell of the...
View ArticleNaive Bayes
Bayes’ Theorem Let’s start from Bayes’ theorem, also referred as Bayes’ law or Bayes’ rule. P(A|B) = P(B, A) / P(B) = P(B|A) * P(A) / P(B) = P(B|A) * P(A) / (P(B|A) * P(A) + P(B|^A) * P(^A)) P(A):...
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Support Vector Machine Concept: VC Dimension
Given a set of n samples , we want to label them as either -1 or 1. In total, there are possible label combinations. A class of learning machines H can be used to label the samples. If for each label...
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