Construct 2D Grid Matching Graph Layout
<p>You are given a 2D integer array <code>edges</code> representing an <strong>undirected</strong> graph having <code>n</code> nodes, where <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> denotes an edge between nodes <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code>.</p>

<p>Construct a 2D grid that satisfies these conditions:</p>

<ul>
	<li>The grid contains <strong>all nodes</strong> from <code>0</code> to <code>n - 1</code> in its cells, with each node appearing exactly <strong>once</strong>.</li>
	<li>Two nodes should be in adjacent grid cells (<strong>horizontally</strong> or <strong>vertically</strong>) <strong>if and only if</strong> there is an edge between them in <code>edges</code>.</li>
</ul>

<p>It is guaranteed that <code>edges</code> can form a 2D grid that satisfies the conditions.</p>

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

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">n = 4, edges = [[0,1],[0,2],[1,3],[2,3]]</span></p>

<p><strong>Output:</strong> <span class="example-io">[[3,1],[2,0]]</span></p>

<p><strong>Explanation:</strong></p>

<p><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3300-3399/3311.Construct%202D%20Grid%20Matching%20Graph%20Layout/images/screenshot-from-2024-08-11-14-07-59.png" style="width: 133px; height: 92px;" /></p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">n = 5, edges = [[0,1],[1,3],[2,3],[2,4]]</span></p>

<p><strong>Output:</strong> <span class="example-io">[[4,2,3,1,0]]</span></p>

<p><strong>Explanation:</strong></p>

<p><img src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3300-3399/3311.Construct%202D%20Grid%20Matching%20Graph%20Layout/images/screenshot-from-2024-08-11-14-06-02.png" style="width: 325px; height: 50px;" /></p>
</div>

<p><strong class="example">Example 3:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">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]]</span></p>

<p><strong>Output:</strong> <span class="example-io">[[8,6,3],[7,4,2],[1,0,5]]</span></p>

<p><strong>Explanation:</strong></p>

<p><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3300-3399/3311.Construct%202D%20Grid%20Matching%20Graph%20Layout/images/screenshot-from-2024-08-11-14-06-38.png" style="width: 198px; height: 133px;" /></p>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= n &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= edges.length &lt;= 10<sup>5</sup></code></li>
	<li><code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>]</code></li>
	<li><code>0 &lt;= u<sub>i</sub> &lt; v<sub>i</sub> &lt; n</code></li>
	<li>All the edges are distinct.</li>
	<li>The input is generated such that <code>edges</code> can form a 2D grid that satisfies the conditions.</li>
</ul>
Graph; Array; Hash Table; Matrix
class Solution {
public:
    vector<vector<int>> constructGridLayout(int n, vector<vector<int>>& edges) {
        vector<vector<int>> g(n);
        for (auto& e : edges) {
            int u = e[0], v = e[1];
            g[u].push_back(v);
            g[v].push_back(u);
        }

        vector<int> deg(5, -1);
        for (int x = 0; x < n; ++x) {
            deg[g[x].size()] = x;
        }

        vector<int> row;
        if (deg[1] != -1) {
            row.push_back(deg[1]);
        } else if (deg[4] == -1) {
            int x = deg[2];
            for (int y : g[x]) {
                if (g[y].size() == 2) {
                    row.push_back(x);
                    row.push_back(y);
                    break;
                }
            }
        } else {
            int x = deg[2];
            row.push_back(x);
            int pre = x;
            x = g[x][0];
            while (g[x].size() > 2) {
                row.push_back(x);
                for (int y : g[x]) {
                    if (y != pre && g[y].size() < 4) {
                        pre = x;
                        x = y;
                        break;
                    }
                }
            }
            row.push_back(x);
        }

        vector<vector<int>> ans;
        ans.push_back(row);
        vector<bool> vis(n, false);
        int rowSize = row.size();
        for (int i = 0; i < n / rowSize - 1; ++i) {
            for (int x : row) {
                vis[x] = true;
            }
            vector<int> nxt;
            for (int x : row) {
                for (int y : g[x]) {
                    if (!vis[y]) {
                        nxt.push_back(y);
                        break;
                    }
                }
            }
            ans.push_back(nxt);
            row = nxt;
        }

        return ans;
    }
};
