2649. Nested Array Generator

Problem Description

The problem requires us to work with a multi-dimensional array structure. This is an array where each element can either be an integer or another array of similar structure (which again could contain integers or other arrays). Our objective is to create a generator function that traverses this nested array structure in an 'inorder' manner. In the context of this problem, 'inorder traversal' means sequentially iterating over each element in the array. If the element is an integer, it is yielded by the generator. If the element is a sub-array, the generator applies the same inorder traversal to it.

Intuition

The solution requires an understanding of recursive data structures and generator functions in TypeScript. The recursive nature of the problem suggests that a recursive function may be an elegant solution. The 'inorder traversal' hints at a depth-first search (DFS) approach where for any given array element, we explore as deep as possible along each branch before backing up, which is a typical recursive behavior.

So, the intuitive approach is to iterate over the array, check if the current element is a number or another array.

• If it is a number, we use 'yield' to return this number and pause the function's execution, allowing the numbers to be enumerated one by one.
• If it is another array, we apply recursion and 'yield*' to delegate to the recursive generator. The use of 'yield*' (yield delegation) is crucial because it allows the yielded values from the recursive call to come through directly to the caller. This maintains the proper sequence without needing to manage intermediate collections or states.

This recursive generator pattern allows us to elegantly handle the varying depths of nested arrays and maintain the inorder traversal logic without complicating the process of maintaining the current state during iteration.

Solution Approach

The solution employs a simple yet effective recursive generator function to perform the inorder traversal of a multi-dimensional array.

First, we outline the function signature:

1function* inorderTraversal(arr: MultidimensionalArray): Generator<number, void, unknown> {

We declare a TypeScript generator function inorderTraversal that accepts a parameter arr, which is of type MultidimensionalArray. This type is an alias for an array that can have elements that are either numbers or, recursively, MultidimensionalArray.

Next, we implement the core logic:

1for (const e of arr) {
2    if (Array.isArray(e)) {
3        yield* inorderTraversal(e);
4    } else {
5        yield e;
6    }
7}

• The generator function enters a loop, iterating over each element e in the input array arr.
• For each element, we check if e is an array using the Array.isArray(e) method. If this is true, it indicates that we have encountered a nested array, so we must traverse it as well, which is done recursively.
• yield* is used to delegate to another generator function—this allows the values from the recursive call to be yielded back to the caller of the original generator.

By using yield and yield*, the elements are yielded one by one, maintaining the expected order of an inorder traversal.

This recursive pattern allows us to succinctly handle the structure irrespective of the depth or complexity of the nesting. It elegantly scales to any level of nested arrays, effectively flattening the structure in an iterative fashion in the order the arrays are laid out. There is no need for additional data structures or managing a stack explicitly as the call stack of the recursive function calls handles this.

The TypeScript type system ensures that the generator function yields only numbers, and any attempt to yield something else will result in compile-time type-checking errors, which helps maintain the correctness of the implementation.

Example Walkthrough

To illustrate the solution approach, let's use a small example of a nested array structure and walk through how the generator function inorderTraversal operates on it.

Suppose we have the following multi-dimensional array:

1const nestedArray = [1, [2, [3, 4], 5], 6, [7, 8]];

The inorderTraversal function will traverse this nested structure and yield each number sequentially. Here's how it works step-by-step:

1. The function begins the first iteration of the top-level array.
2. It encounters the number 1 and yields it.
3. The next element is [2, [3, 4], 5], which is an array. The function calls itself recursively with this array.
4. Inside this recursive call:
   • It yields 2.
   • Encounters another nested array [3, 4] and recurses again.
   • In the next level of recursion, it yields 3 and 4 sequentially.
   • Having finished with the nested array [3, 4], the function backtracks to the previous level and yields 5.
5. The function continues with the top-level array and yields 6.
6. Lastly, it encounters another array [7, 8]:
   • It yields 7.
   • Then it yields 8.

The final order of yielded numbers reflects an inorder traversal of the multi-dimensional array:

11, 2, 3, 4, 5, 6, 7, 8

By utilizing recursion, the function correctly and efficiently handles nested structures of any depth without the need for explicitly managing the state or maintaining a stack. The yield and yield* keywords allow for a clear and concise definition of how values are passed back during the traversal.

Solution Implementation

Time and Space Complexity

The given TypeScript code performs an inorder traversal on a multidimensional (nested) array to yield all the numbers contained therein. A generator function is defined to achieve this, which allows the user to retrieve the numbers one by one.

Time Complexity

The time complexity of this function can be evaluated by considering that each element in the multidimensional array is visited exactly once. If there are N numbers within the nested arrays, regardless of their specific arrangement, each number will be yielded exactly once by the generator function.

While nested arrays necessitate recursive calls, this does not multiply the number of operations per element; rather, it dictates the depth of those recursion calls. Therefore, the time complexity of the function is O(N), where N is the total number of elements.

Space Complexity

The space complexity is determined by the maximum depth of recursion needed to reach the innermost array. In the worst-case scenario — that is, a deeply nested array where each array contains only one sub-array until the deepest level — the space complexity is O(D), where D is the depth of the nested arrays. This space is used by the call stack of the recursive function.

In a more general scenario with uneven distribution of elements, the space complexity will still be determined by the depth of the recursion required but would be less than the maximum depth of all the elements. Therefore, we can consider the space complexity to be O(D), with an understanding that D indicates the depth of the deepest nesting.

If we consider the generator state which also takes up memory, this could add a constant factor to the space complexity, but does not change the overall O(D) space complexity.