<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:
        n = len(colors)
        graph = collections.defaultdict(list)
        in_degrees = [0] * n
        for u, v in edges:
            graph[u].append(v)
            in_degrees[v] += 1

        if 0 not in in_degrees:
            return -1
        q = collections.deque([i for i in range(n) if in_degrees[i] == 0])
        while q:
            curr = q.popleft()
            for v in graph[curr]:
                in_degrees[v] -= 1
                if in_degrees[v] == 0:
                    q.append(v)
        if 0 not in in_degrees or len(set(in_degrees)) > 1:
            return -1

        def dfs(curr, target):
            if curr in lengths:
                return lengths[curr]
            curr_val = 1 * (colors[curr] == target)
            res = curr_val
            for v in graph[curr]:
                if v in seen:
                    future = lengths[v]
                else:
                    seen.add(v)
                    future = dfs(v, target)
                res = max(res, curr_val + future)
            lengths[curr] = res
            return res
        
        res = 0
        for c in set(colors):
            lengths = {}
            for i in range(n):
                if i in lengths:
                    continue
                seen = set([i])
                dfs(i, c)
            print(lengths)
            res = max(res, max(lengths.values()))
        return res



















        # n = len(colors)
        # in_degree = [0] * n
        # adj = collections.defaultdict(list)
        # for u, v in edges:
        #     in_degree[v] += 1
        #     adj[u].append(v)

        # # dp[i] is the map which maps a color to the largest possible
        # # times it appears for a path ending at node i
        # dp = []
        # for _ in range(n):
        #     dp.append(collections.defaultdict(int))

        # res = 1
        # q = collections.deque()
        # for i in range(n):
        #     if in_degree[i] == 0:
        #         q.append(i)
        #         dp[i][colors[i]] = 1
        # visited = 0
        # while q:
        #     curr = q.popleft()
        #     visited += 1
        #     for neighbor in adj[curr]:
        #         in_degree[neighbor] -= 1
        #         for color in dp[curr]:
        #             x = dp[neighbor][color]
        #             x = max(
        #                 x,
        #                 dp[curr][color] + 1 * (color == colors[neighbor])
        #             )
        #             dp[neighbor][color] = x
        #             res = max(res, x)
        #         if dp[neighbor][colors[neighbor]] == 0:
        #             dp[neighbor][colors[neighbor]] = 1
        #         if in_degree[neighbor] == 0:
        #             q.append(neighbor)
        # # visited = n if and only if no cycles
        # if visited < n:
        #     return -1
        # return res
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