Program to find length of longest sublist whose sum is 0 in Python

Suppose we have a list with only two values 1 and −1. We have to find the length of the longest sublist whose sum is 0.

So, if the input is like nums = [1, 1, −1, 1, 1, −1, 1, −1, 1, −1], then the output will be 8, as the longest sublist is [−1, 1, 1, −1, 1, −1, 1, −1] whose sum is 0.

To solve this, we will follow these steps −

• table := a new empty map

• cs := 0, max_diff := 0

• for i in range 0 to size of nums − 1, do

  • cs := cs + nums[i]

  • if cs is same as 0, then

    • max_diff := maximum of i + 1 and max_diff

  • if cs is in table, then

    • max_diff := maximum of max_diff and (i − table[cs])

  • otherwise,

    • table[cs] := i

• return max_diff

Let us see the following implementation to get better understanding −

Example

class Solution:
   def solve(self, nums):
      table = {}
      cs = 0
      max_diff = 0
      for i in range(len(nums)):
         cs += nums[i]
         if cs == 0:
            max_diff = max(i + 1, max_diff)
         if cs in table:
            max_diff = max(max_diff, i − table[cs])
         else:
            table[cs] = i
      return max_diff
ob = Solution()
nums = [1, 1, −1, 1, 1, −1, 1, −1, 1, −1]
print(ob.solve(nums))

Input

[1, 1, −1, 1, 1, −1, 1, −1, 1, −1]

Output

8