Problem Description

The problem requires writing a parser that can take a string s which represents the serialized form of a nested list, and to deserialize it into a NestedInteger. A NestedInteger can be either a single integer or a nested list where each element can in turn be an integer or another nested list. The input string follows a specific format where integers are represented as usual, lists start with a left square bracket [, end with a right square bracket ], and are separated by commas ,. The challenge is to methodically process this string and construct the corresponding NestedInteger with the correct nesting of lists and integers.

Flowchart Walkthrough

Let's analyze Leetcode 385. Mini Parser using the Flowchart. Here's a step-by-step walkthrough based on the description of the problem:

Is it a graph?

• Yes: Though not a typical graph problem, nested integers can be represented as a tree-like graph where each node can have multiple children.

Is it a tree?

• Yes: The NestedInteger structure given in the problem can be visualized as a tree since it can recursively contain other NestedInteger objects. Each NestedInteger could be a node in the tree.

Now, the graph in this case has been identified as a tree. Let's take the path optimized for tree-based problems.

• Conclusion: Based on the flowchart, since it is identified as a tree and the structure of the data is hierarchical and recursive, Depth-First Search (DFS) is a suitable pattern here. DFS allows efficiently traversing and constructing the hierarchical structure as specified in Mini Parser.

This method aligns with how DFS provides a natural way to dive into deeper nested structures recursively, which is essential for parsing and constructing the NestedInteger objects as described in the problem.

Intuition

To arrive at a solution for deserializing the nested list, the key realization is that we need to handle two cases differently: when we encounter an integer and when we encounter a nested list. For integers, the process is straightforward as we just need to read the digits (taking into account the sign, if present) and convert them to an integer value. When dealing with nested lists, however, we need to parse the list recursively or maintain a stack to keep track of the current nested list being constructed.

For the solution involving recursion, we observe that a list contains elements separated by commas and each element can either be an integer or a nested list. We need a way to detect the level of nesting we are at, so when we encounter a comma or the end of the current list, we can decide whether to form an integer NestedInteger or initiate a nested recursive call for a deeper level list.

Otherwise, for a non-recursive approach using stacks, we can simulate the call stack used in recursion manually. Each time we encounter a new list represented by the [ character, we create a new NestedInteger and push it onto the stack. Numbers are constructed character by character, and when we hit a delimiter like , or ], we either finalize the number or a sub-list and add it to the NestedInteger at the top of the stack. If the delimiter is a ] and we have more than one NestedInteger in the stack, we pop the top one and add it to the new top as its child, effectively building the nested structures from the inside out.

Both approaches take into account the depth when parsing the string and handle the processing of digits (with their potential negative signs) and the initiation of new lists. The recursion approach is more straightforward but can be more challenging to understand at first glance. The stack approach is an iterative translation of the same process, representing the nesting with a stack data structure.

Learn more about Stack and Depth-First Search patterns.

Solution Approach

Algorithm

The problem can be approached using two methods: recursion or iteration with a stack. Both methods will systematically parse the input string and construct the NestedInteger object accordingly.

Solution 1: Recursion

With recursion, the function will call itself to handle the complexity of nested structures. Starting at the outermost list and working inwards each time we encounter a new nested list:

• If we come across a number, we create a NestedInteger with this value.
• When a comma or end of the string is found at the base level (depth 0), we know we've finished parsing a list item, so we recursively parse this item.
• If we encounter a left bracket '[', we increase our depth to parse a new nested list.
• A right bracket ']' indicates that we've finished the current nested list, so we decrease our depth.

The recursion takes into consideration the depth we're currently at, managing integers at the current depth by converting them to NestedInteger objects and initiating recursive calls for nested lists.

The time complexity is O(n) where n is the length of the string, as it processes each character once. The space complexity is also O(n) accounting for the recursive call stack.

Solution 2: Stack

The stack approach mimics the call stack that would be created by recursion. Here's a step-by-step explanation of our implementation strategy using a stack:

• The stack is initialized with an empty NestedInteger.
• Each time we encounter a digit, we build the number by multiplying the current number by 10 and adding the new digit.
• A negative sign sets a boolean flag that will be used to negate the number when it is complete.
• Encountering a left bracket '[' means a new nested list is started, and an empty NestedInteger is pushed onto the stack.
• A right bracket ']' or comma ',' signifies the end of a number or list. If it's the end of a number, we complete the number and add it to the NestedInteger at the top of the stack.
• If it's a right bracket, and the stack has more than one NestedInteger, we pop the stack and add the popped NestedInteger to the next item as a nested list.

The flow of the stack effectively captures the opening and closing of nested lists, accumulating elements as it parses through the string. Upon reaching the end of the input, the stack will contain a single NestedInteger representing the fully constructed nested list.

The stack-based approach also has a time complexity of O(n) as it processes each character in the string once, while the space complexity is O(n) due to the stack used to simulate the nested levels.

Both methods utilize the NestedInteger API functions such as isInteger(), add(), setInteger(), getInteger(), and getList() to manipulate and check the types of NestedInteger.

In both solutions, handling negative numbers and converting string representations of integers to actual integer values are key operations. Additionally, both methods ensure that we construct the NestedInteger objects piecemeal, according to the syntactic structure of the input string.

Example Walkthrough

Consider the input serialized string s = "[123,[456,[789]]]". Let's apply the stack approach to see how the NestedInteger is constructed step-by-step.

1. Initialize an empty stack and push a new NestedInteger onto it. The stack now contains one empty NestedInteger, which will eventually be our result.

2. Start parsing the string from the first character:

   • [ encountered: This indicates the start of a nested list. Push a new NestedInteger onto the stack. The stack now has two elements: an empty NestedInteger and a new one just pushed.

3. Next, we encounter 123:

   • Characters 1, 2, 3 are digits, so we construct the number 123. Since the digits came with no preceding negative sign, the number remains positive.

4. Upon encountering the comma ,, we've reached the end of an integer:

   • Add 123 as a NestedInteger to the top NestedInteger in the stack.

5. [ is found after the comma:

   • This signals a new nested list. Push an empty NestedInteger onto the stack.

6. Then we see 456:

   • As with 123, we parse 456 as an integer and add it as a NestedInteger to the top NestedInteger of the stack at this point.

7. After 456, another [ is encountered:

   • Again, the opening of a new nested list. Push a new NestedInteger onto the stack.

8. Now we parse 789:

   • The digits 7, 8, 9 form the integer 789, which is added as a NestedInteger to the top NestedInteger on the stack.

9. We encounter the closing bracket ]:

   • This indicates the end of the most recent nested list. Pop the top NestedInteger from the stack (which contains 789) and add it to the new top NestedInteger (which currently contains 456). The stack has one less nested list now.

10. Another ] comes after:

    • Similar to the previous step, we pop the top NestedInteger (which now contains 456 and the nested 789) and add it to the new top NestedInteger. This results once more in one less nested list on the stack.

11. The final ] is encountered:

    • We are now at the end of the input string. If there was another NestedInteger in the stack, we would pop and add as before; otherwise, this is the terminating step.

By the end of the parsing process, the stack has a single NestedInteger containing the entire nested structure equivalent to the input string. In this example, the final NestedInteger would represent the nested list structure with 123 at the first level, and the nested list [456,[789]] as its child.

The stack approach has allowed us to parse and construct the nested structure without the need for recursion, effectively handling the hierarchies and complexities of the input serialized string.

Solution Implementation

Time and Space Complexity

The time complexity of the code is O(n) where n is the length of the input string s. This is because the function involves a single loop through the input string, performing a constant amount of work for each character in the string.

The space complexity of the code is O(n), also dependent on the length of the string s. In the worst case, the input string could represent a deeply nested list, requiring a new NestedInteger object for every [ encountered before any ] is encountered, which are stored in the stack stk. In the worst-case scenario, this stack could have as many nested NestedInteger objects as there are characters in the input string if the structure were to be very unbalanced. However, this is a very conservative estimation. In practical scenarios, the number of NestedInteger objects will often be less than n.

Learn more about how to find time and space complexity quickly using problem constraints.