Merge branch 'master' of git://github.com/killy971/factor
Slava Pestov
commit
d84cfd1284
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USING: project-euler.072 tools.test ;
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IN: project-euler.072.tests
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[ 303963552391 ] [ euler072 ] unit-test
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! Copyright (c) 2009 Guillaume Nargeot.
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel math math.primes.factors math.ranges
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project-euler.common sequences ;
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IN: project-euler.072
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! http://projecteuler.net/index.php?section=problems&id=072
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! DESCRIPTION
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! -----------
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! Consider the fraction, n/d, where n and d are positive integers.
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! If n<d and HCF(n,d)=1, it is called a reduced proper fraction.
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! If we list the set of reduced proper fractions for d ≤ 8 in ascending order
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! of size, we get:
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! 1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3,
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! 5/7, 3/4, 4/5, 5/6, 6/7, 7/8
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! It can be seen that there are 21 elements in this set.
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! How many elements would be contained in the set of reduced proper fractions
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! for d ≤ 1,000,000?
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! SOLUTION
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! --------
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! The answer can be found by adding totient(n) for 2 ≤ n ≤ 1e6
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: euler072 ( -- answer )
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2 1000000 [a,b] [ totient ] [ + ] map-reduce ;
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! [ euler072 ] 100 ave-time
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! 5274 ms ave run time - 102.7 SD (100 trials)
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SOLUTION: euler072
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@ -0,0 +1,4 @@
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USING: project-euler.074 tools.test ;
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IN: project-euler.074.tests
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[ 402 ] [ euler074 ] unit-test
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@ -0,0 +1,67 @@
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! Copyright (c) 2009 Guillaume Nargeot.
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! See http://factorcode.org/license.txt for BSD license.
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USING: assocs hashtables kernel math math.ranges
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project-euler.common sequences ;
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IN: project-euler.074
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! http://projecteuler.net/index.php?section=problems&id=074
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! DESCRIPTION
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! -----------
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! The number 145 is well known for the property that the sum of the factorial
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! of its digits is equal to 145:
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! 1! + 4! + 5! = 1 + 24 + 120 = 145
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! Perhaps less well known is 169, in that it produces the longest chain of
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! numbers that link back to 169; it turns out that there are only three such
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! loops that exist:
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! 169 → 363601 → 1454 → 169
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! 871 → 45361 → 871
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! 872 → 45362 → 872
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! It is not difficult to prove that EVERY starting number will eventually get
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! stuck in a loop. For example,
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! 69 → 363600 → 1454 → 169 → 363601 (→ 1454)
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! 78 → 45360 → 871 → 45361 (→ 871)
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! 540 → 145 (→ 145)
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! Starting with 69 produces a chain of five non-repeating terms, but the
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! longest non-repeating chain with a starting number below one million is sixty
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! terms.
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! How many chains, with a starting number below one million, contain exactly
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! sixty non-repeating terms?
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! SOLUTION
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! --------
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! Brute force
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<PRIVATE
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: digit-factorial ( n -- n! )
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{ 1 1 2 6 24 120 720 5040 40320 362880 } nth ;
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: digits-factorial-sum ( n -- n )
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number>digits [ digit-factorial ] sigma ;
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: chain-length ( n -- n )
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61 <hashtable> [ 2dup at* nip f = ] [
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2dup dupd set-at [ digits-factorial-sum ] dip
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] while nip assoc-size ;
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PRIVATE>
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: euler074 ( -- answer )
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1000000 [1,b] [ chain-length 60 = ] count ;
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! [ euler074 ] 10 ave-time
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! 25134 ms ave run time - 31.96 SD (10 trials)
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SOLUTION: euler074
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@ -19,7 +19,7 @@ IN: project-euler.085
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! SOLUTION
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! --------
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! A grid measuring x by y contains x * (x + 1) * y * (x + 1) rectangles.
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! A grid measuring x by y contains x * (x + 1) * y * (x + 1) / 4 rectangles.
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<PRIVATE
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@ -56,6 +56,6 @@ PRIVATE>
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area-of-nearest ;
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! [ euler085 ] 100 ave-time
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! 2285 ms ave run time - 4.8 SD (100 trials)
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! 791 ms ave run time - 17.15 SD (100 trials)
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SOLUTION: euler085
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@ -0,0 +1,4 @@
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USING: project-euler.124 tools.test ;
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IN: project-euler.124.tests
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[ 21417 ] [ euler124 ] unit-test
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! Copyright (c) 2009 Guillaume Nargeot.
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! See http://factorcode.org/license.txt for BSD license.
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USING: arrays kernel math.primes.factors
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math.ranges project-euler.common sequences sorting ;
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IN: project-euler.124
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! http://projecteuler.net/index.php?section=problems&id=124
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! DESCRIPTION
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! -----------
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! The radical of n, rad(n), is the product of distinct prime factors of n.
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! For example, 504 = 2^3 × 3^2 × 7, so rad(504) = 2 × 3 × 7 = 42.
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! If we calculate rad(n) for 1 ≤ n ≤ 10, then sort them on rad(n),
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! and sorting on n if the radical values are equal, we get:
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! Unsorted Sorted
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! n rad(n) n rad(n) k
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! 1 1 1 1 1
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! 2 2 2 2 2
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! 3 3 4 2 3
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! 4 2 8 2 4
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! 5 5 3 3 5
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! 6 6 9 3 6
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! 7 7 5 5 7
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! 8 2 6 6 8
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! 9 3 7 7 9
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! 10 10 10 10 10
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! Let E(k) be the kth element in the sorted n column; for example,
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! E(4) = 8 and E(6) = 9.
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! If rad(n) is sorted for 1 ≤ n ≤ 100000, find E(10000).
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! SOLUTION
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! --------
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<PRIVATE
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: rad ( n -- n )
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unique-factors product ; inline
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: rads-upto ( n -- seq )
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[0,b] [ dup rad 2array ] map ;
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: (euler124) ( -- seq )
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100000 rads-upto sort-values ;
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PRIVATE>
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: euler124 ( -- answer )
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10000 (euler124) nth first ;
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! [ euler124 ] 100 ave-time
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! 373 ms ave run time - 17.61 SD (100 trials)
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! TODO: instead of the brute-force method, making the rad
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! array in the way of the sieve of eratosthene would scale
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! better on bigger values.
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SOLUTION: euler124
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@ -17,13 +17,14 @@ USING: definitions io io.files io.pathnames kernel math math.parser
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project-euler.049 project-euler.052 project-euler.053 project-euler.054
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project-euler.055 project-euler.056 project-euler.057 project-euler.058
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project-euler.059 project-euler.063 project-euler.067 project-euler.069
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project-euler.071 project-euler.073 project-euler.075 project-euler.076
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project-euler.079 project-euler.085 project-euler.092 project-euler.097
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project-euler.099 project-euler.100 project-euler.102 project-euler.112
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project-euler.116 project-euler.117 project-euler.134 project-euler.148
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project-euler.150 project-euler.151 project-euler.164 project-euler.169
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project-euler.173 project-euler.175 project-euler.186 project-euler.190
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project-euler.203 project-euler.215 ;
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project-euler.071 project-euler.072 project-euler.073 project-euler.074
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project-euler.075 project-euler.076 project-euler.079 project-euler.085
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project-euler.092 project-euler.097 project-euler.099 project-euler.100
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project-euler.102 project-euler.112 project-euler.116 project-euler.117
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project-euler.124 project-euler.134 project-euler.148 project-euler.150
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project-euler.151 project-euler.164 project-euler.169 project-euler.173
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project-euler.175 project-euler.186 project-euler.190 project-euler.203
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project-euler.215 ;
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IN: project-euler
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<PRIVATE
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