<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>

class CyclicDependencyException(Exception):
    "Raised when there is a cyclic dependecy in graph"
    pass

class Solution:
    def sortItems(self, n: int, m: int, group: List[int], beforeItems: List[List[int]]) -> List[int]:

        # 1. Fill item to group mapping to create new groups for items non in any group
        def create_and_fill_groups():
            nonlocal m
            for i in range(n):
                if group[i] == -1:
                    group[i] = m
                    m += 1
            return m
        
        def get_items_in_group():
            nonlocal m
            items_in_group = [ [] for _ in range(m)]
            for i in range(n):
                items_in_group[group[i]].append(i)
            return items_in_group
        
        # 2. Create adjacency list from beforeItems[] also calculate indegree
        def get_adjacency_list_from_beforeItems():     
            nonlocal m, n
            group_indegree = [0] * m
            group_adj = [ set() for _ in range(m)]
            group_item_adj = []
            item_adj = [ [] for _ in range(n)]
            item_indegree = [0] * n

            for i in range(n):
                for beforeItem in beforeItems[i]:
                    if group[beforeItem] == group[i]:
                        item_adj[beforeItem].append(i)
                        item_indegree[i] += 1
                    else:
                        if group[i] not in group_adj[group[beforeItem]]:
                            group_adj[group[beforeItem]].add(group[i])
                            group_indegree[group[i]] += 1
            
            return item_adj, item_indegree, group_adj, group_indegree
                

        def get_topological_order_of_items_in_group(items: List[int]) -> List[int]:
            queue = []
            items_topological_order = []

            for i in items:
                if item_indegree[i] == 0:
                    queue.append(i)
            
            while len(queue):
                new_queue = []
                for item in queue:
                    items_topological_order.append(item)
                    for after_item in item_adj[item]:
                        item_indegree[after_item] -= 1
                        if item_indegree[after_item] == 0:
                            new_queue.append(after_item)
                queue = new_queue
            
            for item in items:
                if item_indegree[item] != 0:
                    raise CyclicDependencyException
            
            return items_topological_order

        # 3. Perform topological sorting based on groups
        def get_topological_order(items_in_group: List[List[int]]):
            nonlocal m
            queue = []
            for group_id in range(m):
                if group_indegree[group_id] == 0:
                    queue.append(group_id)

            topological_order = []
            while len(queue):
                new_queue = []
                for group_id in queue:
                    try:
                        # topological order of items with in group
                        items_topological_order = get_topological_order_of_items_in_group(items_in_group[group_id])
                    except CyclicDependencyException:
                        # fail fast and return empty list if items with in group have cyclic dependency
                        return []
                    topological_order.extend(items_topological_order)
                    for after_group_id in group_adj[group_id]:
                        group_indegree[after_group_id] -= 1
                        if group_indegree[after_group_id] == 0:
                            new_queue.append(after_group_id)
                queue = new_queue
            
            for group_id in range(m):
                if group_indegree[group_id] != 0:
                    # fail fast and return empty list if groups have cyclic dependency 
                    return []
            return topological_order

        create_and_fill_groups()
        item_adj, item_indegree, group_adj, group_indegree =  get_adjacency_list_from_beforeItems()
        items_in_group = get_items_in_group()

        return get_topological_order(items_in_group)
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