<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 Solution:
    def sortItems(self, n: int, m: int, group: List[int], beforeItems: List[List[int]]) -> List[int]:
        group_map = collections.defaultdict(list)
        counter = -1
        for i in range(len(group)):
            if group[i] == -1:
                group_map[str(i) + '*'].append(i)
            else:
                group_map[group[i]].append(i)

        group_graph = collections.defaultdict(set)
        item_graph = collections.defaultdict(list)

        for i in range(n):
            for pre in beforeItems[i]:
                item_graph[i].append(pre)
                if group[i] != group[pre]:
                    x, y = group[i], group[pre]
                    if group[i] == -1:
                        x = str(i) + '*'
                    if group[pre] == -1:
                        y = str(pre) + '*'
                    group_graph[x].add(y)
        
        def dfs(node, visited, result, graph):
            if node in visited:
                return visited[node]
            visited[node] = False
            for neigh in graph[node]:
                if not dfs(neigh, visited, result, graph):
                    return False
            visited[node] = True
            result.append(node)
            return True
        
        graph_ordering = []
        visited = {}
        for g in group_map:
            if not dfs(g, visited, graph_ordering, group_graph):
                return []
        item_ordering = []
        visited = {}
        for g in graph_ordering:
            for item in group_map[g]:
                if not dfs(item, visited, item_ordering, item_graph):
                    return []
        return item_ordering


                    

                    

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