Added Day-24 Solution

Author: Gangadharbhuvan

Day-24_All_Paths_From_Source_to_Target.py

@@ -0,0 +1,43 @@
+'''
+    Given a directed, acyclic graph of N nodes.  Find all possible paths from node 0 to node N-1, and return them in any order.
+
+The graph is given as follows:  the nodes are 0, 1, ..., graph.length - 1.  graph[i] is a list of all nodes j for which the edge (i, j) exists.
+
+Example:
+Input: [[1,2], [3], [3], []] 
+Output: [[0,1,3],[0,2,3]] 
+Explanation: The graph looks like this:
+0--->1
+|    |
+v    v
+2--->3
+There are two paths: 0 -> 1 -> 3 and 0 -> 2 -> 3.
+Note:
+
+The number of nodes in the graph will be in the range [2, 15].
+You can print different paths in any order, but you should keep the order of nodes inside one path.
+
+
+
+'''
+
+class Solution:
+    def allPathsSourceTarget(self, graph: List[List[int]]) -> List[List[int]]:
+        N = len(graph)
+        paths = [[] for _ in range(N)]
+        # Base Case
+        paths[-1].append([N-1])
+        
+        def dfs(node):
+            # Check if we already have paths available for the current node
+            if not paths[node]:
+                for nbr in graph[node]:
+                    res = dfs(nbr)
+                    # Add current node to each path from neighbour node to target node
+                    for r in res:
+                        paths[node].append([node] + r)
+
+            return paths[node]
+        
+        dfs(0)
+        return paths[0]