Program to find length of longest sublist with given condition in Python

Suppose we have a list of numbers called nums, we have to find the length of the longest sublist where 2 * minimum of sublist > maximum of sublist.

So, if the input is like nums = [10, 2, 6, 6, 4, 4], then the output will be 4, as the sublist [6, 6, 4,4] is the longest sublist that holds the criteria as 2 * 4 > 6.

To solve this, we will follow these steps−

• ret := 0

• define two double ended queues minq and maxq

• l := 0, r := 0

• while r < size of nums, do

  • n := nums[r]

  • while minq and n < nums[last element of minq], do

    • delete last element from minq

  • insert r at the end of minq

  • while maxq and n > nums[last element of maxq], do

    • delete last element from maxq

  • insert r at the end of maxq

  • r := r + 1

  • while l < r and nums[minq[0]] * 2 <= nums[maxq[0]], do

    • if minq[0] is same as l, then

      • delete first element of minq

    • if maxq[0] is same as l, then

      • delete first element of maxq

    • l := l + 1

  • ret := maximum of ret and (r - l)

• return ret

Let us see the following implementation to get better understanding −

Example

 Live Demo

class Solution:
   def solve(self, nums):
      from collections import deque
      ret = 0
      minq, maxq = deque(), deque()
      l, r = 0, 0
      while r < len(nums):
         n = nums[r]
         while minq and n < nums[minq[-1]]:
            minq.pop()
      minq.append(r)
      while maxq and n > nums[maxq[-1]]:
         maxq.pop()
      maxq.append(r)
      r += 1
      while l < r and nums[minq[0]] * 2 <= nums[maxq[0]]:
         if minq[0] == l:
            minq.popleft()
         if maxq[0] == l:
            maxq.popleft()
         l += 1
      ret = max(ret, r - l)
   return ret
ob = Solution()
nums = [10, 2, 6, 6, 4, 4]
print(ob.solve(nums))

Input

[10, 2, 6, 6, 4, 4]

Output

4