<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:
    map<int,vector<int>> dp;
    vector<int> dfs(int src,auto &adj,auto &st){
        vector<int> ans(26,0);

        if(dp.count(src) > 0)return dp[src];

        for(auto i:adj[src]){
            auto vv = dfs(i,adj,st);

            for(int k = 0;k < 26;k++){
                ans[k] = max(ans[k],vv[k]);
            }
        }
        // cout<<src<<" -> ";
        // for(auto i:ans)cout<<i<<" ";
        // cout<<endl;
        ans[st[src] - 'a']++;
        return dp[src] = ans;
    }

    // int bfs(int src,auto &adj,auto &vis,auto &st){
    //     queue<pair<int,vector<int>>> q;
    //     vector<int> colors(26,0);
    //     colors[st[src] - 'a']++;
    //     q.push({src,colors});

    //     int maxi = 0;

    //     while(!q.empty()){
    //         auto fnode = q.front();
    //         q.pop();

    //         int node = fnode.first;
    //         auto vec = fnode.second;

    //         if(adj[node].size() == 0){
    //             maxi = max(maxi,*max_element(vec.begin(),vec.end()));
    //         }

    //         // if(vis[node])continue;
    //         // vis[node] = 1;

    //         for(auto i:adj[node]){
    //             int col = st[i] - 'a';
    //             vec[col]++;
    //             q.push({i,vec});
    //             vec[col]--;
    //         }
    //     }
    //     return maxi;
    // }

    bool isCycle(int src,auto &adj,auto &pathvis,auto &vis){
        vis[src] = 1;
        pathvis[src] = 1;

        bool ans = 0;

        for(auto i:adj[src]){
            if(!vis[i]){
                ans |= isCycle(i,adj,pathvis,vis);
            }
            else{
                if(pathvis[i])return 1;
            }
        }
        pathvis[src] = 0;
        return ans;
    }

    int largestPathValue(string colors, vector<vector<int>>& edges) {
        int n = colors.size();

        vector<vector<int>> adj(n);
        vector<int> indegree(n,0);

        for(auto i:edges){
            adj[i[0]].push_back(i[1]);
            indegree[i[1]]++;
        }

        vector<int> vis(n+1,0);
        vector<int> pathvis(n+1,0);

        for(int i = 0;i < n;i++){
            if(!vis[i]){
                if(isCycle(i,adj,pathvis,vis))return -1;
            }
        }

        int ans = 0;

        for(int i = 0;i < n;i++){
            if(!dp.count(i)){
                auto vec = dfs(i,adj,colors);
                ans = max(ans,*max_element(vec.begin(),vec.end()));
            }
        }

        return ans;

    }
};
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