<p>Given a directed acyclic graph (<strong>DAG</strong>) of <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>, find all possible paths from node <code>0</code> to node <code>n - 1</code> and return them in <strong>any order</strong>.</p>

<p>The graph is given as follows: <code>graph[i]</code> is a list of all nodes you can visit from node <code>i</code> (i.e., there is a directed edge from node <code>i</code> to node <code>graph[i][j]</code>).</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/28/all_1.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> graph = [[1,2],[3],[3],[]]
<strong>Output:</strong> [[0,1,3],[0,2,3]]
<strong>Explanation:</strong> There are two paths: 0 -&gt; 1 -&gt; 3 and 0 -&gt; 2 -&gt; 3.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/28/all_2.jpg" style="width: 423px; height: 301px;" />
<pre>
<strong>Input:</strong> graph = [[4,3,1],[3,2,4],[3],[4],[]]
<strong>Output:</strong> [[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4],[0,1,4]]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == graph.length</code></li>
	<li><code>2 &lt;= n &lt;= 15</code></li>
	<li><code>0 &lt;= graph[i][j] &lt; n</code></li>
	<li><code>graph[i][j] != i</code> (i.e., there will be no self-loops).</li>
	<li>All the elements of <code>graph[i]</code> are <strong>unique</strong>.</li>
	<li>The input graph is <strong>guaranteed</strong> to be a <strong>DAG</strong>.</li>
</ul>

class Solution {
public:
 
    void fun(int i,vector<vector<int>>&graph,map<int,vector<vector<int>>>&mp,vector<int> &vis){
        if(vis[i]) return ;
        for(auto &child:graph[i]){
            if(child==graph.size()-1){
                mp[i].push_back({i,child});
            }else{
                fun(child,graph,mp,vis);
                for(auto &v:mp[child]){
                    vector<int> temp;
                    temp.push_back(i);
                    for(auto &t:v) temp.push_back(t);
                    mp[i].push_back(temp);
                }
            }
        }
        vis[i]=true;
    }

    vector<vector<int>> allPathsSourceTarget(vector<vector<int>>& graph) {
        // dp on treee
        int n=graph.size();
        map<int,vector<vector<int>>> mp;
        vector<int> vis(n);
        fun(0,graph,mp,vis);
        return mp[0];
    }
};
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