341. Flatten Nested List Iterator - Detailed Explanation

Problem Statement

You are given a nested list of integers where each element is either an integer or a list of integers (which may themselves be nested). Your task is to implement an iterator that flattens this nested list structure so that you can iterate over the integers in a sequential (flattened) order.

The interface for a nested integer is defined (conceptually) as follows:

• isInteger(): Returns true if this NestedInteger holds a single integer, rather than a nested list.
• getInteger(): Returns the single integer that this NestedInteger holds (if it holds a single integer).
• getList(): Returns the nested list that this NestedInteger holds (if it holds a nested list).

Your iterator should implement the following methods:

• next(): Returns the next integer in the flattened list.
• hasNext(): Returns true if there are still integers to iterate over.

Example Inputs and Outputs

Example 1

• Input:

  nestedList = [[1,1],2,[1,1]]
  

• Flattened Order:
  [1, 1, 2, 1, 1]
• Usage:
  Calling next() repeatedly should return: 1, 1, 2, 1, 1.

Example 2

• Input:

  nestedList = [1,[4,[6]]]
  

• Flattened Order:
  [1, 4, 6]
• Usage:
  Calling next() repeatedly should return: 1, 4, 6.

Hints for the Approach

• Hint 1:
  Consider how you might traverse a nested list recursively. If you visit every element and "unpack" nested lists, you can create a flattened list of integers.

• Hint 2:
  To avoid processing the same elements multiple times or getting into infinite loops with cycles (if any), use recursion with proper base checks or manage your traversal using a stack.

• Hint 3:
  There are two main strategies:

  • Pre-Flattening: Traverse the entire nested list during initialization, store the results in an array, and then simply iterate over that array.
  • Lazy Flattening Using a Stack: Flatten only as much as needed when calling hasNext() or next(), which can be more memory-efficient if you don’t need all the elements immediately.

Approaches

Approach 1: Pre-Flattening with Recursion

Idea

• Traverse and Flatten:
  In the constructor, recursively traverse the nested list and extract all integers into a flat list.
• Iterator Methods:
  The next() method returns the next integer from the flat list, and hasNext() checks if there are remaining elements.

Pseudocode

function flatten(nestedList):
    for each element in nestedList:
        if element.isInteger():
            add element.getInteger() to flatList
        else:
            flatten(element.getList())

class NestedIterator:
    constructor(nestedList):
         flatList = []
         flatten(nestedList)
         pointer = 0

    method next():
         return flatList[pointer++]

    method hasNext():
         return pointer < length of flatList

Approach 2: Lazy Flattening Using a Stack

Idea

• Stack-Based Processing:
  Instead of pre-flattening the entire structure, maintain a stack of iterators or lists. In hasNext(), ensure the top of the stack is an integer. If it’s a nested list, push its iterator onto the stack.
• On-Demand Flattening:
  This way, the iterator only processes parts of the list as needed, potentially saving memory for large inputs.

Pseudocode

class NestedIterator:
    constructor(nestedList):
         stack = new Stack()
         push nestedList iterator onto stack

    method hasNext():
         while stack is not empty:
              if current iterator has no next:
                  pop the stack
              else if next element is an integer:
                  return true
              else:
                  next element is a list:
                  replace current element with its iterator
         return false

    method next():
         ensure hasNext() is true, then return the next integer from the top iterator

Detailed Step-by-Step Walkthrough (Pre-Flattening Approach)

Consider the nested list:

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

1. Initialization:

   • Create an empty list flatList and set pointer = 0.

2. Flattening Process:

   • Traverse the outer list:
     • First element is [1,1]:
       • Recursively traverse [1,1] and add 1 then 1 to flatList.
     • Second element is 2:
       • Add 2 to flatList.
     • Third element is [1,1]:
       • Recursively traverse and add 1 then 1 to flatList.
   • The resulting flatList becomes: [1, 1, 2, 1, 1].

3. Iteration:

   • hasNext() checks if pointer < length(flatList).
   • next() returns the element at the current pointer and increments the pointer.

Code Implementation

Python Implementation (Pre-Flattening)