Is Create Grid With Exactly K Paths II easy or hard?

Create Grid With Exactly K Paths II is classified as Hard because the challenge is constructive reasoning rather than standard traversal. You must control the exact number of paths, which requires understanding DP state propagation and combinatorial encoding.

Create Grid With Exactly K Paths II Python/Java solution

Python solutions usually use lists and iterative grid construction, while Java implementations rely on arrays and explicit matrix initialization. Both versions follow the same DP or binary construction logic with O(log k) or O(n^2) complexity.

How to solve Create Grid With Exactly K Paths II in O(n)?

Most optimized solutions reduce the problem to controlled path generation using a layered DAG or binary grid encoding. Each layer doubles the number of available paths, allowing exact reconstruction of k using binary digits. The actual implementation complexity is commonly O(log k) or O(n^2).

What is the best approach for Create Grid With Exactly K Paths II?

The best approach uses constructive dynamic programming with binary decomposition. You design grid layers that contribute powers of two paths, then enable or disable transitions based on the binary representation of k. This avoids brute force enumeration and scales efficiently for large inputs.

Is Create Grid With Exactly K Paths II asked at Google/Amazon/Meta?

Constructive graph and dynamic programming problems similar to this appear in Google, Meta, and Amazon interview preparation sets. Interviewers use these problems to test combinatorial reasoning, DP transitions, and graph modeling skills.

What data structure is used in Create Grid With Exactly K Paths II?

The solution primarily uses a 2D grid combined with dynamic programming tables or graph-style adjacency reasoning. Some implementations also rely on bit manipulation to encode the contribution of each layer to the final path count.

What is the time complexity of Create Grid With Exactly K Paths II?

The optimal construction usually runs in O(log k) or O(n^2) time depending on the grid representation. Space complexity is typically O(n^2) because the grid itself must be stored. Brute force approaches are exponential and fail on large constraints.

Description

3990. Create Grid With Exactly K Paths II

Hard64.4% acceptancePremium elsewhere, free here

You are given an integer k.

Construct any grid consisting only of the characters '.' and '#', where:

'.' represents a free cell.
'#' represents an obstacle cell.

The grid must contain at most 25 rows and at most 25 columns.

A valid path is a sequence of free cells that:

Starts at the top-left cell (0, 0).
Ends at the bottom-right cell (m - 1, n - 1), where m and n are the dimensions of your constructed grid.
Moves only:
- Right, from (i, j) to (i, j + 1), or
- Down, from (i, j) to (i + 1, j).

Return any grid such that there are exactly k valid paths from the top-left cell to the bottom-right cell. If no such grid exists, return an empty array.

Example 1:

Input: k = 2

Output: ["..#","#..","#.."]

Explanation:

The grid contains exactly 2 valid paths from (0, 0) to (2, 2):

(0, 0) → (0, 1) → (1, 1) → (1, 2) → (2, 2)
(0, 0) → (0, 1) → (1, 1) → (2, 1) → (2, 2)

Example 2:

Input: k = 3

Output: ["...","#..","#.."]

Explanation:

The grid contains exactly 3 valid paths from (0, 0) to (2, 2):

(0, 0) → (0, 1) → (0, 2) → (1, 2) → (2, 2)
(0, 0) → (0, 1) → (1, 1) → (1, 2) → (2, 2)
(0, 0) → (0, 1) → (1, 1) → (2, 1) → (2, 2)

Constraints:

1 <= k <= 1000

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1class Solution:
  def solve(self):
      pass


Starter codePython 3Spaces: 4

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