<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> adj[100005], ele[100005];
    vector<int> sortItems(int n, int m, vector<int>& group, vector<vector<int>>& beforeItems) {
        vector<int> in(n+2,0), vis(n+2,0);

        for(int i = 0; i<n; i++){
            if(group[i] >= 0){
                ele[group[i]].push_back(i);
            }
        }

        for(int i = 0; i<beforeItems.size(); i++){
            for(int j = 0; j<beforeItems[i].size(); j++){
                if(group[i] >= 0 && group[i] == group[beforeItems[i][j]]){
                    adj[beforeItems[i][j]].push_back(i);
                    in[i]++;
                }
            }
        }

        vector<int> ts;
        for(int i = 0; i<m; i++){
            queue<int> q;
            for(int j = 0; j<ele[i].size(); j++){
                if(in[ele[i][j]] == 0)
                    q.push(ele[i][j]);
            }
            while(!q.empty()){
                int x = q.front(); q.pop();
                vis[x]=1;
                ts.push_back(x);
                for(auto it : adj[x]){
                    in[it]--;
                    if(!vis[it] && !in[it])
                        q.push(it);
                }
            }
            if(!q.empty() || ts.size() != ele[i].size())
                return {};
            ele[i].clear();
            ele[i] = ts;
            ts.clear();
        }

        vector<pair<int,int>> groupAdj[100005];
        vector<pair<int,int>> regularAdj[100005];
        vector<int> inGroup(m+2,0), visGroup(m+2,0), visRegular(n+2,0), inRegular(n+2,0);
        for(int i = 0; i<beforeItems.size(); i++){
            for(int j = 0; j<beforeItems[i].size(); j++){
                if(group[beforeItems[i][j]] == -1){
                    if(group[i] >= 0)
                        inGroup[group[i]]++, regularAdj[beforeItems[i][j]].push_back({group[i],0});
                    else inRegular[i]++, regularAdj[beforeItems[i][j]].push_back({i,1});
                }
                else if(group[i] != group[beforeItems[i][j]]){
                    if(group[i] >= 0){
                        groupAdj[group[beforeItems[i][j]]].push_back({group[i], 0});
                        inGroup[group[i]]++;
                    } else {
                        inRegular[i]++, groupAdj[group[beforeItems[i][j]]].push_back({i, 1});
                    }
                }
            }
        }

        queue<pair<int,int>> q;
        for(int i = 0; i<m; i++){
            if(!inGroup[i])
                q.push({i,0});
        }
        for(int i = 0; i<n; i++){
            if(group[i] == -1 && !inRegular[i])
                q.push({i,1});
        }
        while(!q.empty()){
            auto [node, type] = q.front(); q.pop();
            if(type == 0){
                visGroup[node]=1;
                for(auto it : ele[node])
                    ts.push_back(it);
                for(auto it : groupAdj[node]){
                    if(it.second == 0){
                        inGroup[it.first]--;
                        if(inGroup[it.first] == 0 && !visGroup[it.first]){
                            q.push({it.first, 0});
                        }
                    } else {
                        inRegular[it.first]--;
                        if(inRegular[it.first] == 0 && !visRegular[it.first]){
                            q.push({it.first, 1});
                        }
                    }
                }
            } else {
                visRegular[node]=1;
                ts.push_back(node);
                for(auto it : regularAdj[node]){
                    if(it.second == 0){
                        inGroup[it.first]--;
                        if(inGroup[it.first] == 0 && !visGroup[it.first]){
                            q.push({it.first, 0});
                        }
                    } else {
                        inRegular[it.first]--;
                        if(inRegular[it.first] == 0 && !visRegular[it.first]){
                            q.push({it.first, 1});
                        }
                    }
                }
            }
        }
        if(ts.size() != n)
            return {};
        return ts;
    }
};
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