LeetCode #2625 — MEDIUM

Flatten Deeply Nested Array

Move from brute-force thinking to an efficient approach using core interview patterns strategy.

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The Problem

Problem Statement

Given a multi-dimensional array arr and a depth n, return a flattened version of that array.

A multi-dimensional array is a recursive data structure that contains integers or other multi-dimensional arrays.

A flattened array is a version of that array with some or all of the sub-arrays removed and replaced with the actual elements in that sub-array. This flattening operation should only be done if the current depth of nesting is less than n. The depth of the elements in the first array are considered to be 0.

Please solve it without the built-in Array.flat method.

Example 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
Passing a depth of n=0 will always result in the original array. This is because the smallest possible depth of a subarray (0) is not less than n=0. Thus, no subarray should be flattened.

Example 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
The subarrays starting with 4, 7, and 13 are all flattened. This is because their depth of 0 is less than 1. However [9, 10, 11] remains unflattened because its depth is 1.

Example 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
The maximum depth of any subarray is 1. Thus, all of them are flattened.

Constraints:

  • 0 <= count of numbers in arr <= 105
  • 0 <= count of subarrays in arr <= 105
  • maxDepth <= 1000
  • -1000 <= each number <= 1000
  • 0 <= n <= 1000

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: Given a multi-dimensional array arr and a depth n, return a flattened version of that array. A multi-dimensional array is a recursive data structure that contains integers or other multi-dimensional arrays. A flattened array is a version of that array with some or all of the sub-arrays removed and replaced with the actual elements in that sub-array. This flattening operation should only be done if the current depth of nesting is less than n. The depth of the elements in the first array are considered to be 0. Please solve it without the built-in Array.flat method.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: General problem-solving

Example 1

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

Example 2

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

Example 3

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

Related Problems

  • JSON Deep Equal (json-deep-equal)
  • Convert Object to JSON String (convert-object-to-json-string)
  • Nested Array Generator (nested-array-generator)
Step 02

Core Insight

What unlocks the optimal approach

  • Write a recursive function that keeps track of the current depth.
  • if the current depth >= the maximum depth, always just push the value to the returned array. Otherwise recursively call flat on the array.
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2625: Flatten Deeply Nested Array
// Auto-generated Java example from ts.
class Solution {
    public void exampleSolution() {
    }
}
// Reference (ts):
// // Accepted solution for LeetCode #2625: Flatten Deeply Nested Array
// type MultiDimensionalArray = (number | MultiDimensionalArray)[];
// 
// var flat = function (arr: MultiDimensionalArray, n: number): MultiDimensionalArray {
//     if (!n) {
//         return arr;
//     }
//     const ans: MultiDimensionalArray = [];
//     for (const x of arr) {
//         if (Array.isArray(x) && n) {
//             ans.push(...flat(x, n - 1));
//         } else {
//             ans.push(x);
//         }
//     }
//     return ans;
// };
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(n)
Space
O(1)

Approach Breakdown

BRUTE FORCE
O(n²) time
O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED
O(n) time
O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.