最大子串和

好吧，这个题目已经滥大街了，不过还是很有意思的。

复杂的解法容易想到，O(n)的则需要一些思考。

关键在于想明白，在遍历这个序列时，如何记录当前元素之前的最大子串和，加入当前元素后应该如何更新最大子串和。

正好python练练手

def findMaxStr(s):
    # start,end are array indexes(indices) of the max subsequence
    start = 0
    end = 0
    # cur is the maximum sum of subsequence if s[i] is included, working
    # accumulator
    cur = s[0]
    # maxSub is the maximum sum among all subsequences
    maxSub = s[0]
    for i in range(1, len(s)):
        cur += s[i]
        if (cur <= s[i]):
            cur = s[i]
            if(s[i] > 0):
                start = i
            if(s[i] > maxSub):
                start = i
                end = i
        if(maxSub < cur):
            maxSub = cur
            end = i
    return maxSub, start, end


def curRecords(seq):
    # make a copy of the original sequence, otherwise original values will be
    # changed, it is a reference.
    s = seq[:]

    for i in range(1, len(s)):
        # THE CRUCIAL LOGIC
        s[i] = max(s[i - 1] + s[i], s[i])
    return s


def line():
    print("*************************************")


def show(s):
    print (s)
    print (curRecords(s))
    print (findMaxStr(s))
    line()

# assuming sequences contain both positive and negative values
# Not assuming there are both positive and negative values, all negative sequence now return the correct result. In my opinion.
s1 = [3, -4, 8, -5, 0, 2, 6, -7, 6]
s2 = [-1, 3, 5, -2, 3, 0, -2, 9, -2, 3, -1]
s3 = [2, -2, 3, 2, 32, -5, -2, 8, -3, 11, 0, -11, -3, 5, -1]
s4 = [3, -4]
s5 = [-4, 3, 56, -15, 34, 0, -14, 4]
s6 = [-4, -3, -1, -5, -2]
ss = [s1, s2, s3, s4, s5, s6]
line()

for s in ss:
    show(s)

结果是这样。原序列；cur的更新过程；（最后结果，子序列起始下标，子序列结束下标）都很清楚

*************************************
[3, -4, 8, -5, 0, 2, 6, -7, 6]
[3, -1, 8, 3, 3, 5, 11, 4, 10]
(11, 2, 6)
*************************************
[-1, 3, 5, -2, 3, 0, -2, 9, -2, 3, -1]
[-1, 3, 8, 6, 9, 9, 7, 16, 14, 17, 16]
(17, 1, 9)
*************************************
[2, -2, 3, 2, 32, -5, -2, 8, -3, 11, 0, -11, -3, 5, -1]
[2, 0, 3, 5, 37, 32, 30, 38, 35, 46, 46, 35, 32, 37, 36]
(46, 2, 9)
*************************************
[3, -4]
[3, -1]
(3, 0, 0)
*************************************
[-4, 3, 56, -15, 34, 0, -14, 4]
[-4, 3, 59, 44, 78, 78, 64, 68]
(78, 1, 4)
*************************************
[-4, -3, -1, -5, -2]
[-4, -3, -1, -5, -2]
(-1, 2, 2)
*************************************