3311 - Construct 2D Grid Matching Graph Layout\.

Hard

You are given a 2D integer array edges representing an undirected graph having n nodes, where <code>edgesi = u_i, v_i</code> denotes an edge between nodes <code>u_i</code> and <code>v_i</code>.

Construct a 2D grid that satisfies these conditions:

• The grid contains all nodes from 0 to n - 1 in its cells, with each node appearing exactly once.

• Two nodes should be in adjacent grid cells ( horizontally or vertically ) if and only if there is an edge between them in edges.

It is guaranteed that edges can form a 2D grid that satisfies the conditions.

Return a 2D integer array satisfying the conditions above. If there are multiple solutions, return any of them.

Example 1:

Input: n = 4, edges = \[\[0,1],0,2,1,3,2,3]

Output: [3,1,2,0]

Explanation:

Example 2:

Input: n = 5, edges = \[\[0,1],1,3,2,3,2,4]

Output: [4,2,3,1,0]

Explanation:

Example 3:

Input: n = 9, edges = \[\[0,1],0,4,0,5,1,7,2,3,2,4,2,5,3,6,4,6,4,7,6,8,7,8]

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

Explanation:

Constraints:

• <code>2 <= n <= 5 * 10⁴</code>

• <code>1 <= edges.length <= 10⁵</code>

• <code>edgesi = u_i, v_i</code>

• <code>0 <= u_i< v_i< n</code>

• All the edges are distinct.

• The input is generated such that edges can form a 2D grid that satisfies the conditions.