<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:
    void bfs(unordered_map<int, vector<int>> &adj, unordered_map<int, bool> &visited, int root, vector<int> &ans)
    {
        ans[root-1] = 1;
        queue<int> q;
        q.push(root);
        visited[root]=true;
        int i;
        
        while(!q.empty())
        {
            int temp = q.front();
            q.pop();
            i=-1;

            for(auto x: adj[temp])
            {
                unordered_map<int, bool> marked;
                if(visited[x])
                continue;
                i++;
                q.push(x);
                visited[x]=true;
                if(ans[x-1]==0)
                {
                    for(auto y: adj[x])
                    {
                        if(visited[y])
                        marked[ans[y-1]]=true;
                    }
                    for(int i=1; i<=4; i++)
                    {
                        if(!marked[i])
                        ans[x-1]=i;
                    }
                }
            }
        }
    }
public:
    vector<int> gardenNoAdj(int n, vector<vector<int>>& paths) {
        unordered_map<int, vector<int>> adj;
        int s = paths.size();
        for(int i=0; i<s; i++)
        {
            adj[paths[i][0]].push_back(paths[i][1]);
            adj[paths[i][1]].push_back(paths[i][0]);
        }
        unordered_map<int, bool> visited;
        vector<int> ans(n, 0);
        for(int i=0; i<n; i++)
        {
            if(!visited[i+1])
            bfs(adj, visited, i+1, ans);
        }
        return ans;
    }
};
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