尋找最大的子串（分治法）

O(nlgn)

#!/usr/bin/python

'''file name: maxsum.py
   --P71
   --find maximum subarray sum, divide-and-conquer O(nlng)
   --author: zevolo, 2012.05.11
'''

def find_max_across_mid(list, low, high, mid):
    ret = list[mid]
    right = mid
    sum = ret 
    for i in range(mid + 1, high + 1):
        sum = sum + list[i]
        if sum > ret:
            ret = sum 
            right = i 
    left = mid
    for i in range(mid - 1, low - 1, -1):
        sum = sum + list[i]
        if sum > ret:
            ret = sum
            left = i
    return left, right, ret
        
    
def find_max_sum(list, low, high):
    if high == low:
        return (low, high, list[low])
    
    mid = (low + high) / 2
    (l_low, l_high, l_sum) = find_max_sum(list, low, mid)
    (r_low, r_high, r_sum) = find_max_sum(list, mid + 1, high)
    (m_low, m_high, m_sum) = find_max_across_mid(list, low, high, mid)

    sum = max(l_sum, r_sum)
    sum = max(sum, m_sum)
    s_low = r_low
    s_high = r_high
    if sum == l_sum:
        s_low = l_low
        s_high = l_high
    elif sum == m_sum:
        s_low = m_low
        s_high = m_high
        
    return (s_low, s_high, sum)

if __name__ == '__main__':
    l = [1, -2, 3, 10, -4, 7, 2, -5]
    print l
    (low, high, sum) = find_max_sum(l, 0, len(l) - 1)
    out = l[low:high+1]
    print (out, sum)