2625. Flatten Deeply Nested Array - Detailed Explanation

Problem Statement

Given a multi‑dimensional array arr and an integer n, return a flattened version of arr up to depth n. Flattening means that for any sub‑array whose nesting depth (starting at 0 for the top‑level arr) is less than n, you replace that sub‑array with its individual elements. Do not use the built‑in Array.flat method.

Examples

1. Input:

   arr = [1, 2, 3, [4, 5, 6], [7, 8, [9, 10, 11], 12], [13, 14, 15]]
   n = 0
   

   Output:

   [1, 2, 3, [4, 5, 6], [7, 8, [9, 10, 11], 12], [13, 14, 15]]
   

   Explanation: depth 0 means “don’t flatten anything.”

2. Input:

   arr = [1, 2, 3, [4, 5, 6], [7, 8, [9, 10, 11], 12], [13, 14, 15]]
   n = 1
   

   Output:

   [1, 2, 3, 4, 5, 6, 7, 8, [9, 10, 11], 12, 13, 14, 15]
   

   Explanation: only sub‑arrays at depth 0 get flattened; deeper ones stay nested.

3. Input:

   arr = [[1, 2, 3], [4, 5, 6], [7, 8, [9, 10, 11], 12], [13, 14, 15]]
   n = 2
   

   Output:

   [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
   

   Explanation: all sub‑arrays up to depth 1 are flattened, which here empties all nesting.

Constraints

• Total number of integers and sub‑arrays combined ≤ 10⁵
• 0 ≤ n ≤ 1000
• Maximum nesting depth of arr ≤ 1000
• Each integer in arr is between -1000 and 1000

Hints

1. How would you “unwrap” the top level of nesting? What changes when you go one level deeper?
2. Could you write a helper function that carries along the current depth and decides whether to recurse or emit the element directly?

Approach 1 Recursive Depth‑First Flattening

Explanation

Use a helper dfs(subArr, depth) that walks through each element of subArr. If an element is itself an array and depth < n, recurse into it with depth+1; otherwise push the element (or the sub‑array object) onto your result.

Step‑by‑step Walkthrough

1. Call dfs(arr, 0).
2. For each item in arr:
   • If item is a list and current depth < n, call dfs(item, depth+1).
   • Else, append item to result.
3. Return result after the traversal.

Visual Example

arr = [1, [2, [3]], 4], n = 1
dfs([1, [2, [3]], 4], 0):
  1 → push 1
  [2, [3]] and depth=0<1 → dfs([2, [3]],1):
    2 → push 2
    [3] but depth=1==n → push [3] as array
  4 → push 4
Result = [1, 2, [3], 4]

Python Code