Prime Factorization
A Python prime-factorization routine built on trial division and a Sieve of Eratosthenes-generated prime list.
Tag
#Algorithms
Writing about Algorithms.
Fibonacci sequence – Part 2
Comparing Python methods for generating Fibonacci terms, recognizing valid terms, and finding their indices.
Fibonacci sequence
Fibonacci identities, negative indices, the Golden ratio, and formulas for generating, indexing, and recognizing terms.
Searching Algorithms – Part 3
A C implementation of uniform binary search that uses a precomputed lookup table to reduce index calculations.
Searching Algorithms – Part 2
An explanation of binary search with iterative and recursive Python implementations and logarithmic complexity.
Searching Algorithms – Part 1
Python implementations of linear search, including iterative, recursive, reverse, sentinel, and ordered-list variants.
Project Euler 011
Two Python approaches to finding the greatest product of four adjacent values in the Project Euler problem 11 grid.
Project Euler 010
Comparing trial division and the Sieve of Eratosthenes for summing primes below two million in Java.
Sieve of Eratosthenes
An explanation and Java implementation of the Sieve of Eratosthenes for generating prime numbers below a limit.
Project Euler 009
Comparing brute force with Euclid’s formula for the Pythagorean triplet in Project Euler problem 9.
Project Euler 008
A Python sliding-window solution for the greatest product of five consecutive digits in Project Euler problem 8.
Project Euler 007
Comparing two Python primality tests while finding the 10,001st prime for Project Euler problem 7.
Primality Testing
Five Python primality tests, progressing from trial division through the 6k ± 1 optimization.
Project Euler 006
Using summation formulas to solve Project Euler problem 6, with proofs for the sums of natural numbers and their squares.
Project Euler 005
Solving Project Euler problem 5 in Python with a divisibility test and a GCD-based least common multiple.
Project Euler 004
Comparing brute-force and divisibility-based Python solutions for the largest palindromic product of two three-digit numbers.
Project Euler 003
Two Python solutions to Project Euler problem 3: the Unix factor command and a portable largest-prime-factor algorithm.
Project Euler 002 – More efficient
A faster solution to Project Euler problem 2 that generates only the even Fibonacci terms needed for the sum.
Project Euler 002
A Python and Java solution to Project Euler problem 2 that uses the Golden ratio to step between even Fibonacci terms.
Project Euler 001
Solving Project Euler problem 1 with inclusion-exclusion and arithmetic-series formulas in Python, Java, Perl, C++, and Ruby.