What you need to know to solve basic combinatorial generation problems you might encounter on coding interviews, with plenty of examples in Python.
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From An Iterator of Iterators to Cantor's Paradise: A Deep Dive Into An Interview Question
A deep dive into flattening an iterator of iterators and a segue into set theory and some of its theorems based on the solutions to this problem, inspired by a coding interview question.
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Generating All Balanced Parentheses: A Deep Dive Into An Interview Question
A deep dive into the generation of balanced parentheses, inspired by a coding interview question.
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A Review of Basic Algorithms and Data Structures in Python - Part 1: Graph Algorithms
A quick review of basic graph algorithms and related data structures, with minimal implementations and unit tests provided in Python.
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Fun With Python Coroutines: Generating Permutations
A very short post on having fun with coroutines to generate all permutations of a given list.
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Understanding Recurrence Relations Using Automata, Python Code, And Javascript Visualizations
Recurrence relations are very often taught in first- or second-year computer science and discrete mathematics courses. This post takes a somewhat different and more visual approach to understanding linear recurrences and solving them by drawing the link between linear recurrences, automata, and matrices, using the problem of generating all domino-tilings of a board as the springboard. Code in Python and visualizations in JavaScript are used to demonstrate the ideas.
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Turing Recognizability of Turing Machines That Accept All Strings
A proof that the set of encodings of Turning machines that accept all strings is not Turing-recognizable.
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Combinatorial Generation Using Coroutines With Examples in Python
Approaching combinatorial generation algorithms using coroutines, with examples in Python. Inspired by Knuth's work in his volume 4 of The Art of Computer Programming, as well as his "Deconstructing Coroutines" paper, co-written with Frank Ruskey.
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Multilinear Representation of Boolean Functions
Algorithm to compute the multilinear representation of a boolean function given its truth table.
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Line Intersecting Maximal Number of Circles (Circle "Stabbing" Problem)
Developing an algorithm to find a line that intersects a maximal number of circles, given a set of circles. Based on an ACM ICPC regional competition problem.
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Expected Running Time of Two Randomized Sort Algorithms (ACM ICPC 2013 PACNW Regional)
Computing the expected running time of two randomized sort algorithms for a given input array. This problem appeared in ACM ICPC 2013 PACNW regional competition.
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Pattern Matching in Fibonacci Words (ACM ICPC World Finals 2012)
A discussion of calculating the number of occurrences of a given pattern in Fibonacci words, with a Java solution. Problem from the 2012 ACM ICPC world finals.
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Fibonacci Primitive Roots of Primes (Project Euler)
A problem on finding primes with Fibonacci primitive roots, from Project Euler and my Python solution.
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Common Substring Permutation
Short post on a simple problem on common subsequence permutations with a neat one-line Python solution.
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Hundred Prisonors and a Room With a Light Switch
A hundred prisoners are given a challenge that might set them free. See if you can solve the puzzle involving a light switch and help them gain their freedom.
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Interview Question: All Possible Products of a List of Primes
Interview question to list all possible products of a list of primes, with two Python solutions and a short discussion of the problem.
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Problem-Solving Lessons From George Pólya
What I learned from Newman's selections of Pólya's How to Solve It, the influential and beautifully written book on problem-solving techniques and heuristics.
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Interview Question: Fair and Unfair Coins and Bayes' Theorem
Interview question to infer the probability of an fair and unfair coins after a certain number of coin tosses using Bayes' theorem.
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Interview Question: Fairness from Unfairness and Randomness Extraction
Interview question to use an unfair coin to simulate a fair one. The question is the same as extracting randomness from an unfair Bernoulli process. A Python implementation is given.
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Interview Question: Grouping Words Into Anagrams
Simple Python solution to interview question to group words into anagrams.