TADM2E 8.21

1

Sum every range and keep track of the maximum.

Given a set of numbers N = { x0, x1 ... xn }

M = 0

for i in (0 .. n)
  S[i, i] = xi
  for j in (i + 1 .. n)
    S[i, j] = S[i, j - 1] + xj
    if M < S[i, j]
      M = S[i, j]

2

   def max_range(items):
       max_diff = max(items[0], 0)
       temp_diff = 0
       for number in items:
           temp_diff = max(0, temp_diff + number)
           max_diff = max(max_diff, temp_diff)
       return max_diff

   assert max_range([1, 2, 3, 4, 5]) == 15
   assert max_range([-1, -2, -3, -4, -5]) == 0
   assert max_range([31, -41, 59, 26, -53, 58, 97, -93, -23, 84]) == 187
   assert max_range([31, -41, 59, 26, -53, 58, 97, -93, -23, 84, -200, 3]) == 187
   assert max_range([11, -1, 11, -1, 11, -1, 11, -1, 11, -1, -100, 40, 5]) == 51
   assert max_range([-100, 40, 5, -100, 11, -1, 11, -1, 11, -1, 11, -1, 11, -1]) == 51