Fill A Special Grid · Interview Problem

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Fill A Special Grid

Construct a grid by placing values so that a special row-and-column condition is satisfied.

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Problem Statement

Problem

You are given an integer $n$ . Build an $n \times n$ grid using the values from $0 $to$ n^2 - 1$ exactly once each.

The grid must be filled so that the arrangement follows a special rule based on the recursive structure of the grid: values are assigned in groups to sub-squares, and each smaller square is filled consistently according to the same rule until the grid is complete.

Your task is to return any valid grid that satisfies the rule.

Notes

Every number from $0 $to$ n^2 - 1$ must appear exactly once.
The grid must be $n$ rows by $n$ columns.
If multiple valid grids exist, return any one of them.

Input Format

An integer n describing the side length of the grid.

Output Format

Return an n x n integer grid containing every value from 0 to n^2 - 1 exactly once.

Constraints

$1 \le n \le 32$
All values in the output must be integers in the range $[0, n^2 - 1]$ .
Each value must appear exactly once.

Examples

Sample cases returned by the problem API.

Example 1

Input

n = 2

Output

[[0,1],[2,3]]

Explanation

This is one valid 2x2 grid using each value exactly once.

Example 2

Input

n = 3

Output

[[0,1,2],[3,4,5],[6,7,8]]

Explanation

This is another valid grid example that uses every number from 0 to 8 exactly once.

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