<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:
    unordered_map<char,int> umap;
    vector<int> topo_sort(vector<vector<int>>& adj ){
        // int count=0;
        // for(auto j:adj){
        //     cout<<count++<<" -> ";
        //     for( auto i:j){
        //         cout<<i<<" ";
        //     }
        //     cout<<endl;
        // }
        // indegree;
        int n= adj.size();
        vector<int> indegree( n,0 );
        for(auto ad:adj){
            for( auto i:ad){
                indegree[i]++;
            }
        }
        vector<bool> visited(n,0);
        queue<int> qu;
        for( int i=0;i<n;i++){
            if(indegree[i]==0){
                indegree[i]--;
                visited[i]=1;
                qu.push(i);
            }
        }
        vector<int> ret;
        while(!qu.empty()){
            int tp = qu.front();
            qu.pop();
            ret.push_back(tp);
            for(auto j: adj[tp]){
                indegree[j]--;
                if(indegree[j]==0 && visited[j]==0){
                    visited[j]=1;
                    qu.push(j);
                }
            }
        }
        // if(ret.size() != n) return {};
        return ret;
    }
    int dfs(vector<vector<int>>& graph_item, vector<vector<int>>& dp, int i, int clr, string& colors){
        if(dp[i][clr] != -1) return dp[i][clr];
        int maxx = 0;
        for( auto j:graph_item[i]){
            dp[j][clr] = dfs( graph_item, dp, j, clr, colors);
            maxx = max(maxx,dp[j][clr]);
        }
        if( clr == umap[colors[i]]) maxx +=1;
        return maxx;
    }
    int largestPathValue(string colors, vector<vector<int>>& edges) {
        int n = colors.size();
        vector<vector<int>> graph_item(n);
        for(auto edg: edges){
            // create item to item adj list
            int a = edg[0];
            int b = edg[1];
            graph_item[a].push_back(b);
        }

        vector<int> topo_item = topo_sort(graph_item);
        if(topo_item.size()!=n) return -1;
        // for(auto j: topo_item)
        //     cout<<j<<" ";

        // no of distinct color
        // unordered_map<char,int> umap; // declared above
        int count=0;
        for(char c:colors){
            if(umap.find(c)==umap.end()){
                umap[c] = count;
                count++;
            }
        }
        int m = count;
        vector<vector<int>> dp(n,vector<int> (m,-1));
        int ret=0;
        for(int i=0;i<n;i++){
            int clr = umap[colors[i]];
            if(dp[i][clr]!=-1) continue;
            dp[i][clr] = dfs( graph_item, dp, i, clr, colors);
            ret = max(ret,dp[i][clr]);
        }
        // int ret=0;
        // for(auto i:dp){
        //     for(auto j:i){
        //         ret = max(ret,j);
        //     }
        // }
        return ret;
    }
};
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