## Posts

Showing posts from July, 2012

### Microsoft Azure Notebooks - Live code - F#, R, and Python

I was exploring Jupyter notebooks , that combines live code, markdown and data, through Microsoft's implementation, known as MS Azure Notebooks , putting together a small library of R and F# notebooks . As Microsoft's FAQ for the service describes it as : ...a multi-lingual REPL on steroids. This is a free service that provides Jupyter notebooks along with supporting packages for R, Python and F# as a service. This means you can just login and get going since no installation/setup is necessary. Typical usage includes schools/instruction, giving webinars, learning languages, sharing ideas, etc. Feel free to clone and comment... In R Azure Workbook for R - Memoisation and Vectorization Charting Correlation Matrices in R In F# Charnownes Constant in FSharp.ipynb Project Euler - Problems 18 and 67 - FSharp using Dynamic Programming

### Project Euler: Problems 18 and 67

Problem 18   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: 75 95 64 17 47 82 18 35 87 10 20 04 82 47 65 19 01 23 75 03 34 88 02 77 73 07 63 67 99 65 04 28 06 16 70 92 41 41 26 56 83 40 80 70 33 41 48 72 33 47 32 37 16 94 29 53 71 44 65 25 43 91 52 97 51 14 70 11 33 28 77 73 17 78 39 68 17 57 91 71 52 38 17 14 91 43 58 50 27 29 48 63 66 04 68 89 53 67 30 73 16 69 87 40 31 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23 NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o) Solution By extension, this solves problem 67 as well. This uses a tail-recursive f

### Project Euler - Problem 17 (Match-based Solution)

Problem 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? NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and forty-two) contains 23 letters and 115 (one hundred and fifteen) contains 20 letters. The use of "and" when writing out numbers is in compliance with British usage. Note I have done two (2) solutions for this problem. The original in a prior post requires less code, but is 'ugly' and is less reusable that this match-based solution. This solution is based on smaller methods using the match function, with larger number functions able to call and reuse code from the functions for smaller numbers.  Calling the method is much cleaner as well. Solution ( Match-Based ) let GetThousandthsLetters prefix fourth third second first =

### Project Euler - Problem 17

Problem 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? NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and forty-two) contains 23 letters and 115 (one hundred and fifteen) contains 20 letters. The use of "and" when writing out numbers is in compliance with British usage. Solution //this is a very ugly solution, which I will return to to properly factor to smaller recursive methods let GetThousandsLetters num =      match num with         | 1 -> "one thousand"         | 2 -> "two thousand"         | 3 -> "three thousand"         | 4 -> "four thousand"         | 5 -> "five thousand"         | 6 -> "six thousand"         | 7 -> "seven thousand&qu

### Project Euler - Problem 12

Description 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 be: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ... Let us list the factors of the first seven triangle numbers: 1: 1 3: 1,3 6: 1,2,3,6 10: 1,2,5,10 15: 1,3,5,15 21: 1,3,7,21 28: 1,2,4,7,14,28 We can see that 28 is the first triangle number to have over five divisors. What is the value of the first triangle number to have over five hundred (500) divisors? Solution  //from rosetta code site //code for finding the distinct factors of a number let factors number = seq {     for divisor in 1 .. (float >> sqrt >> int) number do     if number % divisor = 0 then         yield divisor         yield number / divisor } //verification of factor code let factorTest = Seq.toArray(factors 28) //basic method for calculating the triangle number oin a recursive function let rec gene

### Project Euler - Problem 28

Description Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:  21 22 23 24 25 20 7 8 9 10 19 6 1 2 11 18 5 4 3 12 17 16 15 14 13 It can be verified that the sum of the numbers on the diagonals is 101. What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?  Solution  //calculates the sum for the level of the square //each increase in level only requires calculating 4 new values, the corners let levelValue (start:int) (side:int) =     let diffAtLevel = side - 1     let sum = (start + diffAtLevel) + (start + (diffAtLevel * 2)) + (start + (diffAtLevel * 3)) + (start + (diffAtLevel * 4))      sum  //recursively iterates from level 0, which is the center //to the outer part of the array //and for each level calculates the additional sum and sums that to running sum let rec sumByPowers start priorLevelSquared level endSide sum =     if level > endSide