<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>
from sortedcontainers import SortedList

class Solution:
    def largestPathValue(self, colors: str, edges: List[List[int]]) -> int:
        n = len(colors)
        edgesFromMap = {}
        edgesToMap = {}
        zeroFromSet = set()
        for edge in edges:
            edgeFom = edge[0]
            edgeTo = edge[1]
            if edgeTo in edgesToMap:
                edgesToMap[edgeTo].add(edgeFom)
            else:
                edgesToMap[edgeTo] = { edgeFom }

            if edgeFom in edgesFromMap:
                edgesFromMap[edgeFom].add(edgeTo)
            else:
                edgesFromMap[edgeFom] = { edgeTo }

        lengthPerColorFromMap = {}
        lengthFromPerColor = {}
        for i in range (0, n):
            color = colors[i]
            if(i not in edgesFromMap):
                zeroFromSet.add(i)
                lengthPerColorFromMap[i] = {}
                lengthPerColorFromMap[i][color] = 1


        while(len(zeroFromSet) > 0):
            nodeToDelete = zeroFromSet.pop()
            nodesFromEdgesToDelete = []
            if(nodeToDelete in edgesToMap):
                nodesFromEdgesToDelete = edgesToMap[nodeToDelete]
                del edgesToMap[nodeToDelete]

            nodeFromToDeleteList = []
            for nodeFrom in nodesFromEdgesToDelete:
                colorFrom = colors[nodeFrom]
                if(nodeFrom not in lengthPerColorFromMap):
                    lengthPerColorFromMap[nodeFrom] = {}
                    lengthPerColorFromMap[nodeFrom][colorFrom] = 1
                for color, colorLen in lengthPerColorFromMap[nodeToDelete].items():
                    addFrom = 0
                    if(colorFrom == color):
                        addFrom = 1
                    currentMax = 0
                    if(color in lengthPerColorFromMap[nodeFrom]):
                        currentMax = lengthPerColorFromMap[nodeFrom][color]

                    if(currentMax < addFrom + colorLen):
                        lengthPerColorFromMap[nodeFrom][color] = addFrom + colorLen

                print(nodeToDelete, nodeFrom, lengthPerColorFromMap[nodeFrom])
                # delete edges + add to zeroSet
                # nodeFrom, nodeToDelete
                nodeFromToDeleteList.append(nodeFrom)
            for nodeFrom in nodeFromToDeleteList:
                # print(edgesFromMap[nodeFrom])
                edgesFromMap[nodeFrom].remove(nodeToDelete)
                if(len(edgesFromMap[nodeFrom]) == 0):
                    del edgesFromMap[nodeFrom]
                    zeroFromSet.add(nodeFrom)

        if(len(edgesFromMap) > 0):
            return -1
        
        maxTotal = 0
        for idx, lenPerColor in lengthPerColorFromMap.items():
            for clr, l in lenPerColor.items():
                if(l > maxTotal):
                    maxTotal = l
        print(edgesFromMap, edgesToMap, zeroFromSet, lengthPerColorFromMap)
        return maxTotal
102395