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Program to find the maximum sum of circular sublist in Python
Suppose we have a list of numbers nums, now consider a circular list of nums where the start and end of nums are neighbors. We have to find the maximum sum of a non-empty sublist in the circular list.
So, if the input is like nums = [2, 3, -7, 4, 5], then the output will be 14, as we can take the sub list [4, 5, 2, 3] which sums to 14.
To solve this, we will follow these steps −
max_sum := negative infinity, cur_max := 0
min_sum := positive infinity, cur_min := 0
for each num in nums, do
cur_max := maximum of num and cur_max + num
max_sum := maximum of max_sum and cur_max
cur_min := minimum of num and cur_min + num
min_sum := minimum of min_sum and cur_min
if max_sum <= 0, then
return max_sum
return maximum of max_sum and (sum of all elements in nums - min_sum)
Let us see the following implementation to get better understanding −
Example
import math class Solution: def solve(self, nums): max_sum = -math.inf cur_max = 0 min_sum = math.inf cur_min = 0 for num in nums: cur_max = max(num, cur_max + num) max_sum = max(max_sum, cur_max) cur_min = min(num, cur_min + num) min_sum = min(min_sum, cur_min) if max_sum <= 0: return max_sum return max(max_sum, sum(nums) - min_sum) ob = Solution() nums = [2, 3, -7, 4, 5] print(ob.solve(nums))
Input
[2, 3, -7, 4, 5]
Output
14
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