<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) {
        vector<int> grpIndegree(m);
        vector<vector<int>> graph(n);
        vector<vector<int>> groupGraph(m);
        for(int itm = 0, grp; itm < n;itm++ ){
            grp = group[itm];
            if(grp != -1) groupGraph[grp].push_back(itm);
            for(int prnt : beforeItems[itm]){
                if(grp != - 1 && group[prnt] != grp) grpIndegree[grp]++;
                graph[prnt].push_back(itm);
            }
        }
        // for(int i = 0; i < n; i++){
        //     cout<<i<<" : ";
        //     for(int j : graph[i]) cout<<j<<" ";
        //     cout<<endl;
        // }
        // cout<<"Group Graph : "<<endl;
        // for(int i  = 0; i < m; i++){
        //     cout<<i<<" : ";
        //     for(int j : groupGraph[i]) cout<<j<<" ";
        //     cout<<endl << "Indegree : "<<grpIndegree[i]<<endl;
        // }
        queue<int> grpQueue;
        queue<int> itmQueue;
        queue<int> ungrpQueue;
        for(int i = 0; i < n; i++){
            if(i<m && grpIndegree[i] == 0) grpQueue.push(i);
            if(group[i] == -1 && beforeItems[i].size() == 0) ungrpQueue.push(i);
        }   

        vector<int> ans;
        
        while(!ungrpQueue.empty() || !grpQueue.empty()){
            // cout<<"Ungrouped : ";
            while(!ungrpQueue.empty()){
                int itmTop = ungrpQueue.front();
                // cout<<itmTop<<" ";
                ans.push_back(itmTop);
                ungrpQueue.pop();
                for(int child : graph[itmTop]){
                    auto& chldBef = beforeItems[child];
                    chldBef.pop_back();
                    int chldDeg = chldBef.size();
                    int chldGrp = group[child];
                    if(chldGrp == -1){
                        if(chldDeg == 0) ungrpQueue.push(child);
                    }
                    else{
                        if(--grpIndegree[chldGrp] == 0) grpQueue.push(chldGrp);
                    }
                }
            }
            if(grpQueue.empty()) break;


            int grpTop = grpQueue.front();
            grpQueue.pop();
            for(int x : groupGraph[grpTop]){
                if (beforeItems[x].size() == 0) itmQueue.push(x);
            }
            // cout<<"Grouped : ";
            while(!itmQueue.empty()){
                int itmTop = itmQueue.front();
                // cout<<itmTop<<" ";
                int itmGrp = group[itmTop];
                ans.push_back(itmTop);
                itmQueue.pop();
                for(int child : graph[itmTop]){
                    auto& chldBef = beforeItems[child];
                    chldBef.pop_back();
                    int chldDeg = chldBef.size();
                    int chldGrp = group[child];
                    if(chldGrp == itmGrp){
                        if(chldDeg == 0) itmQueue.push(child);
                    }
                    else if(chldGrp == -1){
                        if(chldDeg == 0) ungrpQueue.push(child);
                    }
                    else{
                        if(--grpIndegree[chldGrp] == 0) grpQueue.push(chldGrp);
                    }
                }
            }
            // cout<<endl;
            

        }
        // for(int x : ans) cout<<x<<" ";
        // cout<<endl;
        if(ans.size() != n) return vector<int>();
        return ans;
    }
};
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