<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:
    bool CheckDAG(int u, vector<int> &color, const vector<vector<int>> &adj) {  
        color[u] = 1;  // Đang duyệt, đánh dấu màu là 1
        for(int v : adj[u]) {
            if(color[v] == 1) return true;  // is DAG => res 
            else if(color[v] == 0) {
                if(CheckDAG(v, color, adj)) {
                    return true;
                }
            }
        }
        color[u] = 2;  // Đã duyệt xong, đánh dấu màu là 2
        return false;
    }
    void dfs(int u, stack<int> &store, const vector<vector<int>> &adj, vector<bool> &visited) {
        visited[u] = true;
        for(int v : adj[u]) {
            if(!visited[v]) {
                dfs(v, store, adj, visited);
            }
        }
        store.push(u);
    }
    vector<int> Get_Topo(const vector<vector<int>> &adj) {
        vector<int> Topo;
        vector<int> color(adj.size(), 0);
        for(int u = 0; u < adj.size(); u++) {
            if(color[u] == 0) {
                if(CheckDAG(u, color, adj)) {  // is DAG => COOK
                    return {};
                }
            }
        }
        stack<int> store;
        vector<bool> visited(adj.size(), false);
        for(int u = 0; u < adj.size(); u++) {
            if(!visited[u]) {
                dfs(u, store, adj, visited);
            }
        }
        while(!store.empty()) {
            Topo.push_back(store.top());
            store.pop();
        }
        return Topo;
    }

    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>> adj(n);
        vector<vector<int>> adj_group(m);
        for(int u = 0; u < n; u++) {
            for(int v : beforeItems[u]) {
                adj[v].push_back(u);  
                //thằng v đứng trước thằng u
                if(group[v] != group[u]) {
                    adj_group[group[v]].push_back(group[u]);  
                    // => v truoc u => nhóm thằng v đứng trước thằng u
                }
            }
        }
        vector<int> Topo_of_adj = Get_Topo(adj);
        if(Topo_of_adj.empty() == true) return {};  
        vector<int> Topo_of_adj_group = Get_Topo(adj_group);
        if(Topo_of_adj_group.empty() == true) return {}; 
        vector<vector<int>> grouped_item(m);
        for(int u : Topo_of_adj) {
            grouped_item[group[u]].push_back(u);
        }
        vector<int> res;
        for(int g : Topo_of_adj_group) {
            for(int u : grouped_item[g]) {
                res.push_back(u);
            }
        }
        return res;
    }
};

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