<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 {
public:
    void bfs(int node,unordered_map<int, vector<int>>& mp, vector<int>& ans){
        queue<int>q;
        q.push(node);
        ans[node]=1;

        while(!q.empty()){
            int x=q.front();
            q.pop();
            bool used[5]={};

            for(auto& nbr_x: mp[x]){
                if(ans[nbr_x]!=0){
                    used[ans[nbr_x]]=true;
                } 
            }

            for(int f=1;f<=4; f++){
              if(used[f]==false){
                ans[x]=f;
                break;
              }
            }

            for(auto& nbr_x: mp[x]){
                if(ans[nbr_x]==0){
                    q.push(nbr_x);
                    ans[nbr_x]=1;
                } 
            }

            
        }
    } 
    vector<int> gardenNoAdj(int n, vector<vector<int>>& paths) {
        unordered_map<int, vector<int>> mp;
        for (auto& path : paths) {
            int u = path[0], v = path[1];
            mp[u-1].push_back(v-1);
            mp[v-1].push_back(u-1);
        }
        vector<int> ans(n, 0);
        for(int i=0;i<n;i++){
            if(ans[i]==0) bfs(i,mp,ans);
        }  
        return ans;     
    }
};




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