diff options
| -rw-r--r-- | .gitignore | 7 | ||||
| -rw-r--r-- | haskell/092-square_digit_chains.hs | 30 | ||||
| -rw-r--r-- | haskell/wip/063-powerful_digit_counts.hs | 20 |
3 files changed, 56 insertions, 1 deletions
@@ -1,7 +1,12 @@ *.o a.out __pycache__ +# haskell/**/* +# !haskell/**/*.hs + haskell/* !haskell/*.hs -haskell/wip/ +!haskell/wip +haskell/wip/* !haskell/wip/*.hs + diff --git a/haskell/092-square_digit_chains.hs b/haskell/092-square_digit_chains.hs new file mode 100644 index 0000000..7f99eb8 --- /dev/null +++ b/haskell/092-square_digit_chains.hs @@ -0,0 +1,30 @@ +-- Square digit chains +-- +-- Problem 92 +-- A number chain is created by continuously adding the square of the digits in a +-- number to form a new number until it has been seen before. +-- +-- For example, +-- +-- 44 → 32 → 13 → 10 → 1 → 1 +-- 85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 → 58 → 89 +-- +-- Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop. +-- What is most amazing is that EVERY starting number will eventually arrive at 1 or 89. +-- +-- How many starting numbers below ten million will arrive at 89? + + +-- 2m31s (pretty bad) +-- digits concatenating at the end probably takes a lot of time +-- we can stop computing the chain when we hit a previously computed number +-- (from: https://projecteuler.net/thread=92) +main = print (length [n | n <- [1..10000000], chainEnd n == 89]) + +chainEnd :: Int -> Int +chainEnd n + | n == 1 || n == 89 = n + | otherwise = chainEnd (sum $ map (^2) (digits n)) + where digits x + | x < 10 = [x] + | otherwise = digits (x `div` 10) ++ [x `mod` 10] diff --git a/haskell/wip/063-powerful_digit_counts.hs b/haskell/wip/063-powerful_digit_counts.hs new file mode 100644 index 0000000..31f8912 --- /dev/null +++ b/haskell/wip/063-powerful_digit_counts.hs @@ -0,0 +1,20 @@ +-- Powerful digit counts +-- +-- Problem 63 +-- The 5-digit number, 16807=7^5, is also a fifth power. Similarly, the 9-digit number, +-- 134217728=8^9, is a ninth power. +-- +-- How many n-digit positive integers exist which are also an nth power? + + +-- when should i stop ? (maybe stop searching when x ^ y has more than y digits) +main = do + -- print (numbers) + print (length numbers) + +numbers = [x ^ y| x <- [1..200], y <- [1..x], digitCount (x ^ y) == y] + +digitCount :: Integer -> Integer +digitCount n + | n < 10 = 1 + | otherwise = 1 + digitCount (n `div` 10) |