<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:
    def largestPathValue(
        self, colors: str, edges: List[List[int]]
    ) -> int:
        from collections import defaultdict
        adj = defaultdict(list)
        for src, dst in edges:
            adj[src].append(dst)

        def dfs(node):
            if node in path:
                return float("inf")
            if node in visit:
                return 0
            visit.add(node)
            path.add(node)

            colorIndex = ord(colors[node]) - ord('a')
            count[node][colorIndex] = 1

            for nei in adj[node]:
                if dfs(nei) == float("inf"):
                    return float("inf")
                for c in range(26):
                    count[node][c] = max(
                        count[node][c], 
                        (1 if c == colorIndex else 0) + count[nei][c]
                    )
            path.remove(node)
            return max(count[node])

        n, res = len(colors), 0
        visit, path = set(), set()
        # map count[node][color] -> max freq color
        count = [[0] * 26 for i in range(n)] 

        for i in range(n):
            res = max(dfs(i), res)

        return -1 if res == float("inf") else res


        # my sol
        from collections import defaultdict
        n = len(colors)
        adj = defaultdict(list)
        for e1, e2 in edges:
            adj[e1].append(e2)
        
        res = 0
        visit = set()
        cycle = [False] * n
        cache = {}

        def dfs(node, mfcolor, mfcount, counts):
            nonlocal res
            # cycle
            if cycle[node]:  # memoization
                return True
            if node in visit:  # initial detection
                return True

            visit.add(node)
            c = colors[node]
            counts[c] += 1
            if counts[c] > mfcount:
                mfcolor = c
                mfcount = counts[c]
                # update global

            for nei in adj[node]:
                if dfs(nei, mfcolor, mfcount, counts):
                    cycle[node] = True
                    return True

            # unchoose
            res = max(res, mfcount)
            visit.remove(node)
            counts[c] -= 1
            return False

        for i in range(n):
            if dfs(i, None, 0, defaultdict(int)):
                return -1

        return res
120545