<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 i, vector<int> adj[], vector<int>& color) {
    queue<int> q;
    q.push(i);
    vector<int> used(5, 0); // Track used colors for neighbors

    // Iterate over the garden's neighbors to determine which colors are used
    while (!q.empty()) {
        int node = q.front();
        q.pop();

        // Determine which colors are used by adjacent gardens
        for (auto it : adj[node]) {
            if (color[it] != 0) {
                used[color[it]] = 1;
            } else {
                q.push(it);
            }
        }

        // Assign the smallest unused color to the current node
        for (int c = 1; c <= 4; ++c) {
            if (!used[c]) {
                color[node] = c;
                break;
            }
        }

        // Reset used colors for the next node
        fill(used.begin(), used.end(), 0);
    }
}

vector<int> gardenNoAdj(int n, vector<vector<int>>& paths) {
    vector<int> adj[n + 1];
    for (auto it : paths) {
        adj[it[0]].push_back(it[1]);
        adj[it[1]].push_back(it[0]);
    }

    vector<int> color(n + 1, 0); // Initialize all gardens with color 0
    for (int i = 1; i <= n; ++i) {
        if (color[i] == 0) {
            bfs(i, adj, color);
        }
    }

    // Return colors starting from index 1 (ignoring 0)
    return vector<int>(color.begin() + 1, color.end());
}
};
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