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Euler problems/121 to 130

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m (Corrected the links to the Euler project)
(Solution added for problem 122)
Line 11: Line 11:
 
Finding the most efficient exponentiation method.
 
Finding the most efficient exponentiation method.
   
Solution:
+
Solution using a depth first search, pretty fast :
 
<haskell>
 
<haskell>
problem_122 = undefined
+
import Data.List
  +
import Data.Array.Diff
  +
import Control.Monad
  +
  +
depthAddChain 12 branch mins = mins
  +
depthAddChain d branch mins = foldl' step mins $ nub $ filter (> head branch)
  +
$ liftM2 (+) branch branch
  +
where
  +
step da e | e > 200 = da
  +
| otherwise =
  +
case compare (da ! e) d of
  +
GT -> depthAddChain (d+1) (e:branch) $ da // [(e,d)]
  +
EQ -> depthAddChain (d+1) (e:branch) da
  +
LT -> da
  +
  +
baseBranch = [2,1]
  +
  +
baseMins :: DiffUArray Int Int
  +
baseMins = listArray (1,200) $ 0:1: repeat maxBound
  +
  +
problem_122 = sum . elems $ depthAddChain 2 baseBranch baseMins
 
</haskell>
 
</haskell>
   

Revision as of 23:13, 1 September 2007

Contents

1 Problem 121

Investigate the game of chance involving coloured discs.

Solution:

problem_121 = undefined

2 Problem 122

Finding the most efficient exponentiation method.

Solution using a depth first search, pretty fast :

import Data.List
import Data.Array.Diff
import Control.Monad
 
depthAddChain 12 branch mins = mins
depthAddChain d branch mins = foldl' step mins $ nub $ filter (> head branch)
                               $ liftM2 (+) branch branch
    where
      step da e | e > 200 = da
                | otherwise =
                    case compare (da ! e) d of
                      GT -> depthAddChain (d+1) (e:branch) $ da // [(e,d)]
                      EQ -> depthAddChain (d+1) (e:branch) da
                      LT -> da
 
baseBranch = [2,1]
 
baseMins :: DiffUArray Int Int
baseMins = listArray (1,200) $ 0:1: repeat maxBound
 
problem_122 = sum . elems $ depthAddChain 2 baseBranch baseMins

3 Problem 123

Determining the remainder when (pn − 1)n + (pn + 1)n is divided by pn2.

Solution:

problem_123 = undefined

4 Problem 124

Determining the kth element of the sorted radical function.

Solution:

problem_124 = undefined

5 Problem 125

Finding square sums that are palindromic.

Solution:

problem_125 = undefined

6 Problem 126

Exploring the number of cubes required to cover every visible face on a cuboid.

Solution:

problem_126 = undefined

7 Problem 127

Investigating the number of abc-hits below a given limit.

Solution:

problem_127 = undefined

8 Problem 128

Which tiles in the hexagonal arrangement have prime differences with neighbours?

Solution:

problem_128 = undefined

9 Problem 129

Investigating minimal repunits that divide by n.

Solution:

problem_129 = undefined

10 Problem 130

Finding composite values, n, for which n−1 is divisible by the length of the smallest repunits that divide it.

Solution:

problem_130 = undefined