<p>There is a <strong>directed graph</strong> of <code>n</code> colored nodes and <code>m</code> edges. The nodes are numbered from <code>0</code> to <code>n - 1</code>.</p>

<p>You are given a string <code>colors</code> where <code>colors[i]</code> is a lowercase English letter representing the <strong>color</strong> of the <code>i<sup>th</sup></code> node in this graph (<strong>0-indexed</strong>). You are also given a 2D array <code>edges</code> where <code>edges[j] = [a<sub>j</sub>, b<sub>j</sub>]</code> indicates that there is a <strong>directed edge</strong> from node <code>a<sub>j</sub></code> to node <code>b<sub>j</sub></code>.</p>

<p>A valid <strong>path</strong> in the graph is a sequence of nodes <code>x<sub>1</sub> -&gt; x<sub>2</sub> -&gt; x<sub>3</sub> -&gt; ... -&gt; x<sub>k</sub></code> such that there is a directed edge from <code>x<sub>i</sub></code> to <code>x<sub>i+1</sub></code> for every <code>1 &lt;= i &lt; k</code>. The <strong>color value</strong> of the path is the number of nodes that are colored the <strong>most frequently</strong> occurring color along that path.</p>

<p>Return <em>the <strong>largest color value</strong> of any valid path in the given graph, or </em><code>-1</code><em> if the graph contains a cycle</em>.</p>

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

<p><img alt="" src="https://assets.leetcode.com/uploads/2021/04/21/leet1.png" style="width: 400px; height: 182px;" /></p>

<pre>
<strong>Input:</strong> colors = &quot;abaca&quot;, edges = [[0,1],[0,2],[2,3],[3,4]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The path 0 -&gt; 2 -&gt; 3 -&gt; 4 contains 3 nodes that are colored <code>&quot;a&quot; (red in the above image)</code>.
</pre>

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

<p><img alt="" src="https://assets.leetcode.com/uploads/2021/04/21/leet2.png" style="width: 85px; height: 85px;" /></p>

<pre>
<strong>Input:</strong> colors = &quot;a&quot;, edges = [[0,0]]
<strong>Output:</strong> -1
<strong>Explanation:</strong> There is a cycle from 0 to 0.
</pre>

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

<ul>
	<li><code>n == colors.length</code></li>
	<li><code>m == edges.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= m &lt;= 10<sup>5</sup></code></li>
	<li><code>colors</code> consists of lowercase English letters.</li>
	<li><code>0 &lt;= a<sub>j</sub>, b<sub>j</sub>&nbsp;&lt; n</code></li>
</ul>
class Solution {
public:
vector<int>v1;
int maxi=0;
bool isCyclic(int V, vector<int> adj[],string& colors,vector<vector<int>>dp) {
		vector<int>indegree(V,0);
		for (int i = 0; i < V; i++) {
			for (auto it : adj[i]) {
				indegree[it]++;
			}
		}

		queue<int> q;
		for (int i = 0; i < V; i++) {
			if (indegree[i] == 0) {
                dp[i][colors[i]-'a']++;
				q.push(i);
			}
		}

		int cnt = 0;
		// o(v + e)
		while (!q.empty()) {
			int node = q.front();
			q.pop();
			cnt++;
			for (auto it : adj[node]) {
                for(int i=0;i<26;i++)
                {
                    dp[it][i]=max(dp[it][i],dp[node][i]+(i==colors[it]-'a'));
                    maxi=max(maxi,dp[it][i]);
                }
				indegree[it]--;
				if (indegree[it] == 0) q.push(it);
			}
		}

		if (cnt == V) return false;
		return true;
	}

    int largestPathValue(string colors, vector<vector<int>>& edges) {
        if(edges.size()==0)return 1;
        vector<int>adj[colors.size()];
        for(int i=0;i<edges.size();i++)
        {
            adj[edges[i][0]].push_back(edges[i][1]);
        }
        vector<vector<int>>dp(colors.size(),vector<int>(26,0));
        if(isCyclic(colors.size(),adj,colors,dp))return -1;
      
        return maxi;
    }
};
223755