<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 {
public:
    vector<int> sortItems(int n, int m, vector<int>& group, vector<vector<int>>& beforeItems) 
    {
        unordered_map<int, unordered_set<int>>groupItems;
        int nextGroupId = m;

        for (int i=0; i<n; i++)
        {
            if (group[i]==-1)
            {
                group[i] = nextGroupId;
                nextGroupId += 1;
            }
            groupItems[group[i]].insert(i);
        }

        // build graph inside each group
        unordered_map<int, unordered_set<int>>next;
        unordered_map<int, int>inDegree;
        for (int i=0; i<n; i++)        
            for (int j: beforeItems[i])
            {
                if (group[i]!=group[j]) continue;
                if (next[j].find(i)==next[j].end())                
                {
                    next[j].insert(i);
                    inDegree[i] += 1;
                }
            }
        // sort nodes inside each group
        unordered_map<int, vector<int>>groupItemsOrdered;
        for (auto x: groupItems)
        {
            int groupId = x.first;
            groupItemsOrdered[groupId] = topologySort(groupItems[groupId], next, inDegree);
            if (groupItemsOrdered[groupId].size() != groupItems[groupId].size())
                return {};
        }

        // build graph among groups
        next.clear();
        inDegree.clear();
        for (int i=0; i<n; i++)        
            for (int j: beforeItems[i])
            {
                if (group[i]==group[j]) continue;
                if (next[group[j]].find(group[i])==next[group[j]].end())                
                {
                    next[group[j]].insert(group[i]);
                    inDegree[group[i]] += 1;
                }
            }
        // sort groups
        unordered_set<int>groups;
        for (int i=0; i<n; i++) groups.insert(group[i]);
        vector<int>groupOrdered = topologySort(groups, next, inDegree);

        vector<int>rets;
        for (int groupId: groupOrdered)
        {
            for (auto node: groupItemsOrdered[groupId])
                rets.push_back(node);
        }
        return rets;
    }

    vector<int> topologySort (unordered_set<int>&nodes, unordered_map<int, unordered_set<int>>&next, unordered_map<int, int>&inDegree)
    {
        queue<int>q;
        vector<int>ret;
        for (auto node: nodes)
        {
            if (inDegree[node]==0)
                q.push(node);
        }
         while (!q.empty())
        {
            int cur = q.front();
            q.pop();
            ret.push_back(cur);            
            for (auto next: next[cur] )
            {
                inDegree[next] -= 1;
                if (inDegree[next] == 0)
                    q.push(next);
            }
        }
        
        if (ret.size()==nodes.size())
            return ret;
        else
            return {};
    }
};
110987