<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 {
private:
    static void ConvertStackToPath(std::stack<int> _stack, std::vector<int>& path) {
        path.resize(_stack.size());
        int index = path.size()-1;
        while (!_stack.empty()) {
            path[index] = _stack.top();
            _stack.pop();
            --index;
        }
    }

public:
    std::vector<std::vector<int>> allPathsSourceTarget(std::vector<std::vector<int>>& graph) {
        std::unordered_map<int, std::set<int>> nodeChildrenMap;
        for (int i = 0; i < graph.size(); ++i) {
            for (auto child : graph[i]) {
                nodeChildrenMap[i].insert(child);
            }
        }

        std::vector<std::vector<int>> paths;

        std::unordered_map<int, std::set<int>> tempNodeChildrenMap;
        std::stack<int> _stack;
        _stack.push(0);
        tempNodeChildrenMap[0] = nodeChildrenMap[0];
        while (!_stack.empty()) {
            int node = _stack.top();
            auto& children = tempNodeChildrenMap[node];
            if (children.empty()) {
                _stack.pop();
            } else {
                int child = *children.begin();
                children.erase(child);
                tempNodeChildrenMap[child] = nodeChildrenMap[child];
                _stack.push(child);
                if (child == (graph.size()-1)) {
                    std::vector<int> path;
                    ConvertStackToPath(_stack, path);
                    paths.push_back(std::move(path));
                    _stack.pop();
                }
            }
        }

        return paths;
    }
};
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