<p>You have <code>n</code> gardens, labeled from <code>1</code> to <code>n</code>, and an array <code>paths</code> where <code>paths[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> describes a bidirectional path between garden <code>x<sub>i</sub></code> to garden <code>y<sub>i</sub></code>. In each garden, you want to plant one of 4 types of flowers.</p>

<p>All gardens have <strong>at most 3</strong> paths coming into or leaving it.</p>

<p>Your task is to choose a flower type for each garden such that, for any two gardens connected by a path, they have different types of flowers.</p>

<p>Return <em><strong>any</strong> such a choice as an array </em><code>answer</code><em>, where </em><code>answer[i]</code><em> is the type of flower planted in the </em><code>(i+1)<sup>th</sup></code><em> garden. The flower types are denoted </em><code>1</code><em>, </em><code>2</code><em>, </em><code>3</code><em>, or </em><code>4</code><em>. It is guaranteed an answer exists.</em></p>

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

<pre>
<strong>Input:</strong> n = 3, paths = [[1,2],[2,3],[3,1]]
<strong>Output:</strong> [1,2,3]
<strong>Explanation:</strong>
Gardens 1 and 2 have different types.
Gardens 2 and 3 have different types.
Gardens 3 and 1 have different types.
Hence, [1,2,3] is a valid answer. Other valid answers include [1,2,4], [1,4,2], and [3,2,1].
</pre>

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

<pre>
<strong>Input:</strong> n = 4, paths = [[1,2],[3,4]]
<strong>Output:</strong> [1,2,1,2]
</pre>

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

<pre>
<strong>Input:</strong> n = 4, paths = [[1,2],[2,3],[3,4],[4,1],[1,3],[2,4]]
<strong>Output:</strong> [1,2,3,4]
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>
	<li><code>0 &lt;= paths.length &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>paths[i].length == 2</code></li>
	<li><code>1 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= n</code></li>
	<li><code>x<sub>i</sub> != y<sub>i</sub></code></li>
	<li>Every garden has <strong>at most 3</strong> paths coming into or leaving it.</li>
</ul>

class Solution {
private:
  vector<int> result;
  vector<vector<int>> buildGraph(int n, vector<vector<int>>& paths) {
    vector<vector<int>> graph(n);
    for(int i = 0; i < paths.size(); i++) {
      int x = paths[i][0] - 1;
      int y = paths[i][1] - 1;
      graph[x].push_back(y);
      graph[y].push_back(x);
    }
    return graph;
  }

  int solve(int n, vector<vector<int>>& graph) {
    if(result[n] != -1) return result[n];
    result[n] = 0;

    unordered_set<int> availableTypes = {1, 2, 3, 4};

    for(int &child: graph[n]) {
      int taken = solve(child, graph);
      if(availableTypes.count(taken)) availableTypes.erase(taken);
    }

    result[n] = *availableTypes.begin();
    return result[n];
  }

public:
  vector<int> gardenNoAdj(int n, vector<vector<int>>& paths) {
    vector<vector<int>> graph = buildGraph(n, paths);
    result.resize(n, -1);
    for(int i = 0; i < result.size(); i++) {
      if(result[i] == -1) solve(i, graph);
    }
    return result;
  }
};
79945