I am trying to solve a generative recursion problem in Python. The question is:
I have to follow the given algorithm to solve find_max:
I have tried the following:
def find_max(L):
length = len(L)
mid_index = length/2
if length == 1:
return L[0]
else:
left = find_max(L[0:(length/2)])
right = find_max(L[(length/2):length])
max_subset = max(left,right,left+right)
return max_subset
This is able to solve for lists with length 2. How do I extend this to work for a list with more elements?
You didn't consider following:
L
is [2, -5, 3]
, in the first recursion, left + right
will yield 5. def find_max(L):
length = len(L)
mid_index = length/2
if length == 0:
return 0
elif length == 1:
return max(L[0], 0)
left = find_max(L[:mid_index])
right = find_max(L[mid_index:])
left_half = right_half = 0
# to the left
accum = 0
for x in L[mid_index-1::-1]:
accum += x
left_half = max(left_half, accum)
# to the right
accum = 0
for x in L[mid_index:]:
accum += x
right_half = max(right_half, accum)
return max(left, right, left_half + right_half)
assert find_max([]) == 0
assert find_max([-1]) == 0
assert find_max([1, 2, 3]) == 6
assert find_max([2, -5, 3]) == 3
assert find_max([-5, 1, 4, -2, 2, -1, 2, -3, 1, -3, 4]) == 6
Without for loop:
def sum_max(L, accum=0, max_value=0):
if not L:
return max_value
accum += L[0]
return sum_max(L[1:], accum, max(max_value, accum))
def find_max(L):
...
left_half = sum_max(L[mid_index-1::-1])
right_half = sum_max(L[mid_index:])
...
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