All Paths From Source To Target Problem


Description

LeetCode Problem 797.

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

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

Example 1:

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Input: graph = [[1,2],[3],[3],[]]
Output: [[0,1,3],[0,2,3]]
Explanation: There are two paths: 0 -> 1 -> 3 and 0 -> 2 -> 3.

Example 2:

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Input: graph = [[4,3,1],[3,2,4],[3],[4],[]]
Output: [[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4],[0,1,4]]

Example 3:

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Input: graph = [[1],[]]
Output: [[0,1]]

Example 4:

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Input: graph = [[1,2,3],[2],[3],[]]
Output: [[0,1,2,3],[0,2,3],[0,3]]

Example 5:

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Input: graph = [[1,3],[2],[3],[]]
Output: [[0,1,2,3],[0,3]]

Constraints:

  • n == graph.length
  • 2 <= n <= 15
  • 0 <= graph[i][j] < n
  • graph[i][j] != i (i.e., there will be no self-loops).
  • All the elements of graph[i] are unique.
  • The input graph is guaranteed to be a DAG.


Sample C++ Code

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class Solution {
public:
    vector<vector<int>> ans;
    int n;
    
    void dfs(vector<vector<int>>& graph, vector<int>& path) {
        int node = path.back();
        if (node == n-1)
            ans.push_back(path);
        
        for (int i = 0; i < graph[node].size(); i ++) {
            path.push_back(graph[node][i]);
            dfs(graph, path);
            path.pop_back();
        }
    }
    
    vector<vector<int>> allPathsSourceTarget(vector<vector<int>>& graph) {
        n = graph.size();
        vector<int> path;
        path.push_back(0);
        
        dfs(graph, path);
        return ans;
    }
};




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