Factorial function is simple enough. But there is still some fun about it. In Stirling’s Approximation article we’ve seen how to calculate good factorial approximation faster than exact value. By the way, there is an algorithm to calculate exact value of factorial faster than “by definition”. Factor...

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. 3 7 4 2 4 6 8 5 9 3 That is, 3 + 7 + 4 + 9 = 23. Find the maximum total from top to bottom of the triangle below: [Check out big triangle in original link] NOTE: ...

Why math is needed for developers, what is REST, how to become experienced developer…in 10 years, “coding it’s just writing” and some practice: Naive Bayes Classifier, functional programming and Java 8. 1. Math For Programmers Another great post by Steve Yegge about math. Math for developers. As eve...

If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total. If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would be used? Permalink: http://projecteuler.net/problem=1...

Conway’s Game of Life in a tweet. Recently, my friend pointed out me an article Life in a tweet where Game of Life was implemented in one tweet (less than 140 characters) in Ruby and F#. I took this challenge. Tweet Here is the final version in 137 characters of Clojure: (fn[g r](reduce(fn[i j](upda...

2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26. What is the sum of the digits of the number 2^1000 ? Permalink: http://projecteuler.net/problem=16 Are you kidding me? Find 1000th power of two Sum its digits In Clojure Euler: Problem 008 we learned how to sum digits in the number. J...

Java is a safe programming language and prevents programmer from doing a lot of stupid mistakes, most of which based on memory management. But, there is a way to do such mistakes intentionally, using Unsafe class. This article is a quick overview of sun.misc.Unsafe public API and few interesting cas...

Have you heard about Elephant-Oriented Programming? 1. Read very clever book with an elephant on cover. 2. I bet you didn’t understand anything, so choose easy programming language with an elephant. 3. What is IDE? We already have elephant text editor. 4. For real life programming tasks we need stor...

Do you like factorials? Probably, you do. If no, whatever, read this post to know how get rid of factorials. TL;DR \[ln(n!) = n \cdot ln(n) - n + 1\] It is Stirling’s approximation or just Stirling’s formula. It allows to replace factorials with their approximation. If you not interested in math, sk...

It is so obvious, so I decided to write about it. Heisenberg principle came from quantum mechanics and means that you can’t know exactly both coordinates and speed of particle. If you improve accuracy of detecting position, you lose accuracy in detecting speed and vice versa. Uncertain stuff. In hum...

Starting in the top left corner of a 2 x 2 grid, there are 6 routes (without backtracking) to the bottom right corner. How many routes are there through a 20 x 20 grid? Permalink: http://projecteuler.net/problem=15 Picture is always a huge help to find correct the solution. Let’s see the pattern her...

Last weekend I was hacking Standard ML a bit. Coursera There are excellent course on coursera called Programming Languages Currently, the first half is available, that explains basic and advanced functional programming constructions with Standard ML as primary language. Later some idioms will be pre...

Which starting number, under one million, produces the longest Collatz chain? Permalink: http://projecteuler.net/problem=14 The following iterative sequence is defined for the set of positive integers: n → n/2 (n is even) n → 3n + 1 (n is odd) Using the rule above and starting with 13, we generate t...

How to get job at Google, estimate complexity of your algorithm, what is Structural Immutability, why PHP is awful and Java is awesome, best programming jokes and lot more. 1. Get that job at Google …it’s highly likely that someone on the loop will be unimpressed with you, even if you are Alan Turin...

Recently, I come up with idea to share my favorite articles I found on the internet and give basic description for them. I do not plan this digest as periodical thing, so the first pattern I found appropriate is to publish this as soon as I have ten articles marked as favorite somewhere. That’s the ...

What programming language is most used? To answer this question we use results from the qualification round of Facebook Hacker Cup 2013 If you only interested in statistics, skip! 0. Intro As you may know, Facebook Hacker Cup is a programming contest. You have programming problem and you need to sol...

Work out the first ten digits of the sum of the following one-hundred 50-digit numbers. Permalink: http://projecteuler.net/problem=13 Assume, here is a huge amount of digits. In any case, you can always find them in permalink. What is the problem to sum one-hundred numbers? (reduce + numbers) Done. ...

What is the value of the first triangle number to have over five hundred divisors? Permalink: http://projecteuler.net/problem=12 The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would ...

Little journey through the history of most critical software bugs with some code examples. Do not try to reproduce any of these! Intro Every last bug is the last but one. Bugs are bad. Some of them cause uncomfortable work, more actions than expected, inconsistency, layout issues, etc. Some of them ...

What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20 x 20 grid? Permalink: http://projecteuler.net/problem=11 In the 20 x 20 grid below, four numbers along a diagonal line have been enclosed into square brackets 08 02 22 97 38 1...

Have you been in situation where most of the time in eclipse you were waiting for some operation to be finished? If you here, probably, the answer is yes. You are bored with that slow functionality and want to increase eclipse performance to make your development work more comfortable. It is the rig...

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. Permalink: http://projecteuler.net/problem=10 We have already worked with prime numbers in Problem 003 and Problem 007. We also decided that the best way to work with prime numbers in clojure to u...

A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a^2 + b^2 = c^2 For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2 There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc. Permalink: http://projecteuler.net/problem=9 Thinking about clever ...

Find the greatest product of five consecutive digits in the 1000-digit number. Permalink: http://projecteuler.net/problem=8 Large number under the cut. 73167176531330624919225119674426574742355349194934 96983520312774506326239578318016984801869478851843 8586156078911294949545950173795833195285320880...

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the 10001st prime number? Permalink: http://projecteuler.net/problem=7 It’s also pretty clear problem to make you more familiar with prime numbers. As I said in Clojure Euler: Problem 003, bi...

Every experienced java programmer should know that finally block always executed. But is it true? It depends on our definition of program execution. But, generally speaking, yes. Normal program execution Aha, look at this, someone might retort: try { System.exit(1); } finally { System.out.println("I...

The sum of the squares of the first ten natural numbers is, 1^2 + 2^2 + … + 10^2 = 385 The square of the sum of the first ten natural numbers is, (1 + 2 + … + 10)^2 = 55^2 = 3025 Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − ...

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20? Permalink: http://projecteuler.net/problem=5 It’s a tricky problem. First look gives us straigh...

You can answer almost immediately using calculator, but what if you don’t have it? I don’t remember the exact origin of this meme, but this situation was almost every time when we played with numbers. – Propose a number. – e^π. – Integer, shithead! This even might appear in usual conversations: – Wh...

Did you know that all java classes start with the same 4 bytes. In hex it’s CAFEBABE. To make sure, create simple java file, call it Hello.java: public class Hello { public static void main(String[] args) { System.out.println("Hell, O'World!"); } } Compile it by javac Hello.java, and open Hello.clas...