# Program to find length of longest sublist where difference between min and max smaller than k in Python

Suppose we have a list of numbers called nums and another value k, we have to find the length of longest sublist where the absolute difference between the largest and smallest element is ≤ k.

So, if the input is like nums = [2, 4, 6, 10] k = 4, then the output will be 3, as we can select pick [2, 4, 6] here the absolute difference is 4.

To solve this, we will follow these steps −

• Create two double ended queue maxd, mind
• i := 0, res := 1
• for each index j and value a in A, do
• while maxd is not 0 and a > last element of maxd, do
• delete last element from maxd
• while mind is not 0 and a < last element of mind, do
• delete last element from mind
• insert a at the end of maxd
• insert a at the end of mind
• while maxd[0] - mind[0] > limit, do
• if maxd[0] is same as A[i], then
• delete item from left of maxd
• if mind[0] is same as A[i], then
• delete item from left of mind
• i := i + 1
• res := maximum of res and (j - i + 1)
• return res

Let us see the following implementation to get better understanding −

## Example

Live Demo

from collections import deque, defaultdict
class Solution:
def solve(self, A, limit):
maxd = deque()
mind = deque()
i = 0
res = 1
for j, a in enumerate(A):
while maxd and a > maxd[-1]:
maxd.pop()
while mind and a < mind[-1]:
mind.pop()
maxd.append(a)
mind.append(a)
while maxd[0] - mind[0] > limit:
if maxd[0] == A[i]:
maxd.popleft()
if mind[0] == A[i]:
mind.popleft()
i += 1
res = max(res, j - i + 1)
return res
ob = Solution()
nums = [2, 4, 6, 10]
k = 4
print(ob.solve(nums, k))

## Input

[2, 4, 6, 10], 4

## Output

3

Updated on: 19-Nov-2020

155 Views