<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:
    int solve(int color, string & s, vector<int> adj[], int n, int node, vector<int> & dp)
    {
       if(dp[node]!=-1)
        return dp[node];

        int ans=0;
        for(auto i: adj[node])
        {
           ans= max(ans, solve(color, s, adj, n, i, dp));
        }

        dp[node]= ans;

        if(color== (s[node]-'a'))
        dp[node]++;

        return dp[node];
    }

    
    int largestPathValue(string colors, vector<vector<int>>& edges) {
        
        int n= colors.size();
        vector<int> degree(n, 0);
         
         vector<int> adj[n];

         for(int i=0; i<edges.size(); i++)
         {
            int u= edges[i][0];
            int v= edges[i][1];
            //swap(u, v);
            adj[u].push_back(v);
            degree[v]++;
         }
         queue<int> q;
        vector<int> topo;
         for(int i=0; i<n; i++)
         {
            if(degree[i]==0)
            q.push(i);
         }

         while(!q.empty())
         {
            int node= q.front();
            q.pop();

            topo.push_back(node);
            for(auto i: adj[node])
            {
                degree[i]--;
                if(degree[i]==0)
                q.push(i);
            }
         }

         if(topo.size()< n)
         return -1;
         
          int ans=0;
         for(int color=0; color<26; color++)
         {
            vector<int> dp(n, -1);
            for(int i=0; i<topo.size(); i++)
            {
                if(dp[topo[i]]==-1)
                {
                   ans= max(ans, solve(color, colors, adj, n, topo[i], dp));
                }
            }

         }

         return ans;




         









        
    }
};
146726