Euler problems/91 to 100
Problem 91
Find the number of right angle triangles in the quadrant.
Solution:
problem_91 = undefined
Problem 92
Investigating a square digits number chain with a surprising property.
Solution:
problem_92 = undefined
Problem 93
Using four distinct digits and the rules of arithmetic, find the longest sequence of target numbers.
Solution:
problem_93 = undefined
Problem 94
Investigating almost equilateral triangles with integral sides and area.
Solution:
problem_94 = undefined
Problem 95
Find the smallest member of the longest amicable chain with no element exceeding one million.
Solution which avoid visiting a number more than one time :
import Data.Array.Unboxed
import qualified Data.IntSet as S
import Data.List
chain n s = lgo [n] $ properDivisorsSum ! n
where lgo xs x | x > 1000000 || S.notMember x s = (xs,[])
| x `elem` xs = (xs,x : takeWhile (/= x) xs)
| otherwise = lgo (x:xs) $ properDivisorsSum ! x
properDivisorsSum :: UArray Int Int
properDivisorsSum = accumArray (+) 1 (0,1000000)
$ (0,-1):[(k,factor)|
factor<-[2..1000000 `div` 2]
, k<-[2*factor,2*factor+factor..1000000]
]
base = S.fromList [1..1000000]
problem_95 = fst $ until (S.null . snd) f ((0,0),base)
where f ((n,m), s) = ((n',m'), s')
where setMin = head $ S.toAscList s
(explored, chn) = chain setMin s
len = length chn
(n',m') = if len > m
then (minimum chn, len)
else (n,m)
s' = foldl' (flip S.delete) s explored
This solution need some space in its stack (it worked with 30M here).
Problem 96
Devise an algorithm for solving Su Doku puzzles.
Solution:
problem_96 = undefined
Problem 97
Find the last ten digits of the non-Mersenne prime: 28433 × 27830457 + 1.
Solution:
problem_97 = (28433 * 2^7830457 + 1) `mod` (10^10)
Problem 98
Investigating words, and their anagrams, which can represent square numbers.
Solution:
problem_98 = undefined
Problem 99
Which base/exponent pair in the file has the greatest numerical value?
Solution:
problem_99 = undefined
Problem 100
Finding the number of blue discs for which there is 50% chance of taking two blue.
Solution:
problem_100 = undefined