<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>& groups, vector<vector<int>>& beforeItems) {
        unordered_map<int,int> groups_indegree;
        unordered_map<int,vector<int>> groups_graph;
        unordered_map<int,int> num_items_in_groups;
        unordered_map<int,vector<int>> group_to_item_id;
        unordered_map<int,int> item_indegree;
        for(int i = 0; i < n; ++i) {
            // Initialize groups indegree to 0.
            groups_indegree[groups[i]] = 0;
            // Populate how many items are in each group
            ++num_items_in_groups[groups[i]];
            // initialize groups_to_item_id & groups_graph
            group_to_item_id[groups[i]] = vector<int>();
            groups_graph[groups[i]] = vector<int>();
            item_indegree[i] = 0;
        }
        vector<int> item_graph[n];
        for(int item_id = 0; item_id < n; ++item_id) {
            int& cur_group = groups[item_id];
            // Add this item to the groups_to_item_id 
            group_to_item_id[cur_group].push_back(item_id);
            for(int& required_item : beforeItems[item_id]) {
                // Add a directed edge from required_item to item_id
                item_graph[required_item].push_back(item_id);
                // Add an indegree to item_id
                ++item_indegree[item_id];

                int required_item_group = groups[required_item];
                if(required_item_group != cur_group) {
                    // Add a directed edge from the required_group to the cur_group
                    groups_graph[required_item_group].push_back(cur_group);
                    // Add an indegree to the cur_group
                    ++groups_indegree[cur_group];
                }
            }
        }
        
        vector<int> res(n);
        int res_idx = 0;
        bool pushed = false;

        queue<int> group_q;
        for(auto& e : groups_indegree) {
            if(e.second == 0) {
                // Add groups with no indegrees into the queue first.
                group_q.push(e.first);
            }
        }

        if(group_q.empty()) {
            group_q.push(-1);
        }


        while(!group_q.empty()) {
            int cur_group = group_q.front();
            group_q.pop();
            // Top sort every item in this group first.
            queue<int> item_q;
            for(int& item : group_to_item_id[cur_group]) {
                if(item_indegree[item] == 0) {
                    item_q.push(item);
                    --item_indegree[item];
                }
            }

            while(!item_q.empty()) {
                int cur_item = item_q.front();
                item_q.pop();

                res[res_idx] = cur_item;
                ++res_idx;
                --num_items_in_groups[cur_group];
                for(int& next_item : item_graph[cur_item]) {
                    --item_indegree[next_item];
                    if(item_indegree[next_item] == 0 && groups[next_item] == cur_group) {
                        item_q.push(next_item);
                    }
                }
            }

            if(cur_group != -1 && num_items_in_groups[cur_group] > 0) {
                return {};
            }

            for(int& next_group : groups_graph[cur_group]) {
                --groups_indegree[next_group];
                if(groups_indegree[next_group] == 0) {
                    group_q.push(next_group);
                }
            }
            if(group_q.empty() && !pushed) {
                group_q.push(-1);
                pushed = true;
            }
        }
        if(res_idx == n) return res;
        return {};
    }
};
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