求最大子序列和 - Haskell

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本文介绍了一种使用Haskell实现的最大子序列和算法，该算法能够找出整数序列中具有最大和的连续子序列及其起始和结束位置。通过递归方式实现了对不同长度子序列的求和比较，并给出了具体的实现代码及测试示例。

module Main where

import System.Random as Random

maxSubSumSeq :: [Int] -> Maybe (Int, Int)
maxSubSumSeq xs | null xs = Nothing
                | otherwise = let len = length xs in Just $ maxSubSumSeq' xs 1 (div (1+len) 2) len

maxSubSumSeq' :: [Int] -> Int -> Int -> Int -> (Int, Int)
maxSubSumSeq' xs i c j | i == j = (i, j)
                       | i == c = let leftValue = xs !! (i-1)
                                      rightSubSeqIndex = maxSubSumSeq' xs (c+1) (div (c+1+j) 2) j
                                      rightMaxSubSumSeq = takeSubList (fst rightSubSeqIndex) (snd rightSubSeqIndex) xs
                                      rightValue = sum rightMaxSubSumSeq
                                      sums = [(leftValue,(i,c)), (leftValue+rightValue,(i,snd rightSubSeqIndex)), (rightValue,rightSubSeqIndex)]
                                  in snd $ maximum sums
                       | otherwise = let leftSubSeqIndex = maxSubSumSeq' xs i (div (i+c) 2) c
                                         leftMaxSubSumSeq = takeSubList (fst leftSubSeqIndex) (snd leftSubSeqIndex) xs
                                         leftValue = sum leftMaxSubSumSeq
                                         rightSubSeqIndex = maxSubSumSeq' xs (c+1) (div (c+1+j) 2) j
                                         rightMaxSubSumSeq = takeSubList (fst rightSubSeqIndex) (snd rightSubSeqIndex) xs
                                         rightValue = sum rightMaxSubSumSeq
                                         midValue = sum $ takeSubList (fst leftSubSeqIndex) (snd rightSubSeqIndex) xs
                                         sums = [(leftValue,leftSubSeqIndex), (midValue,(fst leftSubSeqIndex,snd rightSubSeqIndex)), (rightValue,rightSubSeqIndex)]
                                     in snd $ maximum sums

takeSubList :: Int -> Int -> [Int] -> [Int]
takeSubList = (\i j xs -> take (j-i+1) $ drop (i-1) xs)

makeOutPutStr :: Maybe (Int, Int) -> [Int] -> String -> String
makeOutPutStr value xs name = case value of
                                 Nothing -> "invalid value"
                                 Just index -> let subseq = takeSubList (fst index) (snd index) xs
                                                in name ++ " maxsubseq index is: " ++ show index ++ " it's maxsumseq is: " ++ show subseq ++ " sum is: "++ show (sum $ subseq)

testValue1 = [-2,11,-4,13,-5,-2]
testValue2 = [-6,2,4,-7,5,3,2,-1,6,-9,10,-2]

main :: IO()
main = do
    let testValue1Index = maxSubSumSeq testValue1
    let testValue2Index = maxSubSumSeq testValue2
    putStrLn $ makeOutPutStr testValue1Index testValue1 "testValue1"
    putStrLn $ makeOutPutStr testValue2Index testValue2 "testValue2"
    return ()