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Program to find sum of non-adjacent elements in a circular list in python

Suppose we have a list of numbers called nums that is representing a circular list. We have to find the largest sum of non-adjacent numbers.

So, if the input is like nums = [10, 3, 4, 8], then the output will be 14, as we can take 10 and 4. We cannot take 10 and 8 as they are adjacent.

To solve this, we will follow these steps −

  • n := size of nums
  • nums1 := nums[from index 0 to n - 2]
  • nums2 := nums[from index 1 to end]
  • Define a function f() . This will take i
  • if i >= size of nums1 , then
    • return 0
  • return maximum of nums1[i] + f(i + 2) and f(i + 1)
  • Define a function g() . This will take j
  • if j >= size of nums2 , then
    • return 0
  • return maximum of nums2[j] + g(j + 2) and g(j + 1)
  • From the main method do the following −
  • return maximum of f(0) and g(0)

Let us see the following implementation to get better understanding −

Example

class Solution:
   def solve(self, nums):
      n = len(nums)
      nums1 = nums[: n - 1]
      nums2 = nums[1:]
      def f(i):
         if i >= len(nums1):
            return 0
         return max(nums1[i] + f(i + 2), f(i + 1))
      def g(j):
         if j >= len(nums2):
            return 0
         return max(nums2[j] + g(j + 2), g(j + 1))
      return max(f(0), g(0))
ob = Solution()
nums = [10, 3, 4, 8]
print(ob.solve(nums))

Input

[10, 3, 4, 8]

Output

14