<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:
    inline int encode(int n, int grpIdx, int i) {
        return (grpIdx == -1) ? i : (n + grpIdx);
    }

    vector<int> topoSort(unordered_map<int, vector<int>>& edges, unordered_map<int, int>& inDeg) {
        queue<int> q;
        for (auto& p : inDeg) {
            if (p.second == 0) {
                q.push(p.first);
            }
        }

        vector<int> res;
        while (!q.empty()) {
            int curr = q.front();
            q.pop();
            res.push_back(curr);
            for (int nxt : edges[curr]) {
                if (--inDeg[nxt] == 0) {
                    q.push(nxt);
                }
            }
        }

        if (res.size() < edges.size()) {
            return {};
        }
        return res;
    }

    vector<int> sortItems(int n, int m, vector<int>& group, vector<vector<int>>& beforeItems) {
        vector<unordered_map<int, vector<int>>> edgeMaps(m);
        vector<unordered_map<int, int>> inDegMaps(m);
        unordered_map<int, vector<int>> grpEdges;
        unordered_map<int, int> grpInDeg;
        for (int i = 0; i < m; ++i) {
            grpInDeg[i] = 0;
        }
        for (int i = 0; i < n; ++i) {
            int grp = group[i];
            if (grp == -1) {
                continue;
            }
            inDegMaps[grp][i] = 0;

            for (int bf : beforeItems[i]) {
                int grpB = group[bf];
                if (grp == grpB) {
                    edgeMaps[grp][bf].push_back(i);
                    ++inDegMaps[grp][i];
                } else if (grpB != -1) {
                    grpEdges[grpB].push_back(grp);
                    ++grpInDeg[grp];
                }
            }
        }

        vector<int> grpOrder = topoSort(grpEdges, grpInDeg);
        if (grpOrder.size() < m) {
            return {};
        }
        vector<vector<int>> orders(m);
        for (int i = 0; i < m; ++i) {
            orders[i] = topoSort(edgeMaps[i], inDegMaps[i]);
            if (orders[i].size() < inDegMaps[i].size()) {
                return {};
            }
        }

        unordered_map<int, vector<int>> metaEdges;
        unordered_map<int, int> metaInDeg;
        for (int i = 0; i < n; ++i) {
            int keyCurr = encode(n, group[i], i);
            if (!metaInDeg.count(keyCurr)) {
                metaInDeg[keyCurr] = 0;
            }

            for (int bf : beforeItems[i]) {
                int keyBf = encode(n, group[bf], bf);
                if (keyCurr == keyBf) {
                    continue;
                }
                metaEdges[keyBf].push_back(keyCurr);
                ++metaInDeg[keyCurr];
            }
        }
        vector<int> metaOrder = topoSort(metaEdges, metaInDeg);
        if (metaOrder.size() < metaInDeg.size()) {
            return {};
        }

        vector<int> res;
        for (int curr : metaOrder) {
            if (curr < n) {
                res.push_back(curr);
            } else {
                for (int x : orders[curr - n]) {
                    res.push_back(x);
                }
            }
        }
        return res;
    }
};
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