<p>There are&nbsp;<code>n</code>&nbsp;items each&nbsp;belonging to zero or one of&nbsp;<code>m</code>&nbsp;groups where <code>group[i]</code>&nbsp;is the group that the <code>i</code>-th item belongs to and it&#39;s equal to <code>-1</code>&nbsp;if the <code>i</code>-th item belongs to no group. The items and the groups are zero indexed. A group can have no item belonging to it.</p>

<p>Return a sorted list of the items such that:</p>

<ul>
	<li>The items that belong to the same group are next to each other in the sorted list.</li>
	<li>There are some&nbsp;relations&nbsp;between these items where&nbsp;<code>beforeItems[i]</code>&nbsp;is a list containing all the items that should come before the&nbsp;<code>i</code>-th item in the sorted array (to the left of the&nbsp;<code>i</code>-th item).</li>
</ul>

<p>Return any solution if there is more than one solution and return an <strong>empty list</strong>&nbsp;if there is no solution.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2019/09/11/1359_ex1.png" style="width: 191px; height: 181px;" /></strong></p>

<pre>
<strong>Input:</strong> n = 8, m = 2, group = [-1,-1,1,0,0,1,0,-1], beforeItems = [[],[6],[5],[6],[3,6],[],[],[]]
<strong>Output:</strong> [6,3,4,1,5,2,0,7]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 8, m = 2, group = [-1,-1,1,0,0,1,0,-1], beforeItems = [[],[6],[5],[6],[3],[],[4],[]]
<strong>Output:</strong> []
<strong>Explanation:</strong>&nbsp;This is the same as example 1 except that 4 needs to be before 6 in the sorted list.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= m &lt;= n &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>group.length == beforeItems.length == n</code></li>
	<li><code>-1 &lt;= group[i] &lt;= m - 1</code></li>
	<li><code>0 &lt;= beforeItems[i].length &lt;= n - 1</code></li>
	<li><code>0 &lt;= beforeItems[i][j] &lt;= n - 1</code></li>
	<li><code>i != beforeItems[i][j]</code></li>
	<li><code>beforeItems[i]&nbsp;</code>does not contain&nbsp;duplicates elements.</li>
</ul>

from collections import deque


class DfsException(Exception):
    pass
class Solution:
    def sortItems(self, n: int, m: int, group: List[int], beforeItems: List[List[int]]) -> List[int]:
        maxGroups = m
        newGroup = []
        newGroupDict = {}
        try:
            for i in range(0, n):
                if group[i]==-1:
                    newGroup.append(maxGroups)
                    newGroupDict[maxGroups] = [i]
                    maxGroups+=1
                else: 
                    if(group[i] in newGroupDict.keys()): newGroupDict[group[i]].append(i)
                    else: 
                        newGroupDict[group[i]] = [i]
                        #print(newGroupDict)
                    newGroup.append(group[i])
            self.newAfterItems = {}
            self.newAfterItemsGroup = {}
            for i in range(0,n):
                self.newAfterItems[i] = set()
            for i in range(0,maxGroups):
                self.newAfterItemsGroup[i] = set()
            for i in range(0,n):
                for j in beforeItems[i]:
                    self.newAfterItems[j].add(i)
                    if(newGroup[j]!=newGroup[i]):
                        self.newAfterItemsGroup[newGroup[j]].add(newGroup[i])
            #topologically sort groups
            outStack = deque()
            self.topologicalSort(range(0,maxGroups),self.newAfterItemsGroup,outStack)
            groupOrdering = [0]*maxGroups
            res = []
            #print("=======")
            #print("newGroup= " + str(newGroup))
            #print("newGroupDict= " + str(newGroupDict))
            #print("newAfterItems= " + str(self.newAfterItems))
            #print("newAfterItemsGroup= " + str(self.newAfterItemsGroup))
            #print(newGroupDict)
            #print(outStack)
            while len(outStack)>0:
                currentGroup = outStack.pop()
                #print(currentGroup)
                grpStack = deque()
                if currentGroup in newGroupDict:
                    self.topologicalSort(newGroupDict[currentGroup],self.newAfterItems,grpStack)
                    #print("currentGroup: " + str(currentGroup))
                    #print(grpStack)
                    while len(grpStack)>0:  
                        res.append(grpStack.pop())
            return res
        except DfsException as e:
            #print(e)
            return []
    
    def topologicalSort(self, items, edges, stack=deque()):
        visited = set()
        parents = {}
        for i in items:
            parents[i] = []
        for i in items:
            if not(i in visited):
                self.dfs(i, edges, visited, items, stack,parents)
        #print("SORT")
        #print("items=" + str(items))
        #print("edges=" + str(edges))
        #print("parents=" + str(parents))
        
    def dfs(self,i,edges, visited, items,stack,parents):
        #print(i)
        visited.add(i)
        for j in edges[i]:
            if(j in items): 
                parents[j].append(i)
                for k in parents[i]:
                    parents[j].append(k)

            if(j in parents[i]): raise DfsException("not a DAG")
            if not(j in visited) and (j in items):
                self.dfs(j,edges,visited,items,stack,parents)
        stack.append(i)


        #reassign -1 to new groups
        #reassign befores to groups
        #topological sort groups? 
51593