# Nested List Weight Sum II in Python

Given a nested list of integers, return the sum of all integers in the list weighted by their depth. Each element is either an integer, or a list -- whose elements may also be integers or other lists. Different from the previous question where weight is increasing from root to leaf, now the weight is defined from bottom up. i.e., the leaf level integers have weight 1, and the root level integers have the largest weight.

So, if the input is like [[1,1],2,[1,1]], then the output will be 8, as four 1's at depth 1, one 2 at depth 2.

To solve this, we will follow these steps −

• Define a function depthSumInverse() . This will take nestedList

• flats:= a new list

• maxd:= 0

• Define a function flatten() . This will take nlst,dist

• dist := dist + 1

• maxd:= maximum of maxd, dist

• for each node in nlst, do

• if node is an integer is non-zero, then

• insert (node,dist) at the end of flats

• otherwise,

• flatten(node, dist)

• flatten(nestedList, 0)

• summ:= 0

• for each v,d in flats, do

• summ := summ + v*(maxd+1-d)

• return summ

## Example

Let us see the following implementation to get a better understanding −

Live Demo

class Solution(object):
def depthSumInverse(self, nestedList):
flats=[]
self.maxd=0
def flatten(nlst,dist):
if isinstance(nlst,list):
nlst=nlst
dist+=1
self.maxd=max(self.maxd,dist)
for node in nlst:
if isinstance(node,int):
flats.append((node,dist))
else:
flatten(node,dist)
flatten(nestedList,0)
summ=0
for v,d in flats:
summ+=v*(self.maxd+1-d)
return summ

ob = Solution()
print(ob.depthSumInverse([[1,1],2,[1,1]]))

## Input

[[1,1],2,[1,1]]

## Output

8