<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 {
    vector<int> topological_sort(const vector<vector<int>>& graph) {
        vector<int> vec;
        vector<int> visited(graph.size());
        int cnt = 1;

        auto dfs = [&](int v, int cnt, auto Dfs) -> bool {
            visited[v] = -cnt;
            for (int u : graph[v]) {
                if (visited[u] == -cnt) {
                    return false;
                }
                if (!visited[u]) {
                    if (!Dfs(u, cnt, Dfs)) {
                        return false;
                    }
                }
            }
            visited[v] = cnt;
            vec.emplace_back(v);
            return true;
        };

        for (int i = 0; i < graph.size(); i++) {
            if (!visited[i]) {
                if (!dfs(i, cnt, dfs)) {
                    return {};
                }
            }
            cnt++;
        }

        reverse(vec.begin(), vec.end());
        return vec;
    }
public:
    vector<int> sortItems(int n, int m, vector<int>& group, vector<vector<int>>& beforeItems) {
        for (int i = 0; i < group.size(); i++) {
            if (group[i] == -1) {
                group[i] = m++;
            }
        }

        vector<vector<int>> groups(m);
        for (int i = 0; i < n; i++) {
            groups[group[i]].emplace_back(i);
        }

        vector<unordered_set<int>> group_graph_st(m);
        vector<vector<int>> inner_graph(n);
        for (int i = 0; i < beforeItems.size(); i++) {
            for (int element : beforeItems[i]) {
                if (group[element] != group[i]) {
                    group_graph_st[group[element]].insert(group[i]);
                } else {
                    inner_graph[element].emplace_back(i);
                }
            }
        }

        vector<vector<int>> group_graph;
        for (int i = 0; i < m; i++) {
            group_graph.emplace_back(group_graph_st[i].begin(), group_graph_st[i].end());
        }

        vector<int> group_topo = topological_sort(group_graph);
        if (group_topo.empty()) {
            return {};
        }

        auto build_graph = [&](int group) {
            unordered_map<int, int> idx_map;
            for (int i = 0; i < groups[group].size(); i++) {
                idx_map[groups[group][i]] = i;
            }

            vector<vector<int>> graph(groups[group].size());
            for (int i = 0; i < groups[group].size(); i++) {
                for (int v : inner_graph[groups[group][i]]) {
                    graph[i].emplace_back(idx_map[v]);
                }
            }
            return graph;
        };

        vector<int> answer;
        for (int group : group_topo) {
            if (groups[group].empty()) {
                continue;
            }
            vector<vector<int>> temp_graph = build_graph(group);
            vector<int> inner_topo = topological_sort(temp_graph);
            if (inner_topo.empty()) {
                return {};
            }
            for (int v : inner_topo) {
                answer.emplace_back(groups[group][v]);
            }
        }

        return answer;
    }
};
71462