Section 1.2
1.9 略1.10 略
1.11
{- recursive stylef3' n | n<3 = n | otherwise = f3(n-1) + 2*f3(n-2) + 3*f3(n-3)-} getBegin n = n-(fromIntegral t)-1 where t = floor (n-3) ::Integerf3 n | n<3 = n | otherwise = f3_iter b (b-1) (b-2) (n-2) where b = getBegin n f3_iter a _ _ 0 = a f3_iter a b c k = f3_iter (a+2*b+3*c) a b (k-1) 1.12
pascal :: Integer -> Integer -> Integerpascal n k | k==1 = 1 | n==k = 1 | k<n= pascal (n-1) k + (pascal (n-1) (k-1)) | otherwise = error "Invalid!" 1.13 略
1.14 略
1.15 略
1.16
-- Iterative version of fast-expfast_exp :: (Num a)=> a -> Integer -> afast_exp b n = exp_iter b n 1 where exp_iter _ 0 a = a exp_iter b n a = if (even n ) then exp_iter (b*b) (n `div` 2) a else exp_iter b (n-1) (a*b) 1.17 略
1.18
fast_mult :: Integer -> Integer -> Integerfast_mult a b = fast_iter a b 0 where fast_iter _ 0 s = s fast_iter a b s = if (even b) then fast_iter (a*2) (b `div` 2) s else fast_iter a (b-1) (s+a) 1.19
fast_fib :: Integer -> Integerfast_fib n = fast_iter 1 0 0 1 n where fast_iter _ b _ _ 0 = b fast_iter a b p q count = if (even count) then fast_iter a b (p*p+q*q) (p*q+q*p+q*q) (count `div` 2) else fast_iter (b*q+a*q+a*p) (b*p+a*q) p q (count-1) fib :: Integer -> Integerfib 0 =1fib 1 =1fib n = fib (n-1) + fib (n-2) 1.20 略
1.21
smallestDivesor :: Integer -> IntegersmallestDivesor n = divTry 2 n where divTry a n | a*a > n= n | n `mod` a ==0 = a | otherwise = divTry (a+1) n main :: IO ()main = do mapM_ (putStrLn.show.smallestDivesor) 1.22 略
1.23
smallestDivesor' :: Integer -> IntegersmallestDivesor' n = divTry 2 n where divTry a n | a*a > n= n | n `mod` a ==0 = a | otherwise = divTry (next a) n next a = if a==2 then 3 else (a+2) 1.24~1.28 略 质数问题，以后总结
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