All Paths From Source to Target

                                            
const allPathsSourceTarget = (graph) =>{
    
    const target = graph.length - 1;
    let ans = new Set;
    
    const backtrack = (currentNode, path) =>{
        
        if(currentNode === target){
            ans.add(path.slice(0));
            return;
        }
        
        for(let i=0; i<graph[currentNode].length; i++){
            
            const nextNode = graph[currentNode][i];
            path.push(nextNode);
            backtrack(nextNode, path);
            path.pop();
        }
    };
    backtrack(0, [0]);
    
    return Array.from(ans); 
};

This coding challenge involves finding all paths from the start node (node 0) to the end node (node n-1) in a Directed Acyclic Graph (DAG). The approach to solve this problem involves using Depth-First Search (DFS) with backtracking.

Steps to Solve:

1. Initialization:

Define a variable to hold the final result (list of paths). Also, define the target node, which is the last node (n-1).

2. Depth-First Search (DFS) Function:

This function, let's call it DFS, will take the current node and the current path as arguments. If the current node is the target node, add the current path to the result and return. If the current node is the target node, add the current path to the result and return. Iterate over all adjacent nodes of the current node. For each adjacent node. Add the adjacent node to the current path. Recursively call DFS with the adjacent node and the updated path. Backtrack by removing the last node added to the path (to explore other paths).

3. Backtracking:

This is implicitly done by the DFS function by adding and then removing nodes from the current path as it explores different paths.

4. Start DFS:

Begin the DFS from node 0 with an initial path containing just the start node.

5. Return Result:

Convert the result set to an array or list and return it.

Pseudo Code:

                                        
FUNCTION allPathsSourceTarget(graph)
    target = LENGTH(graph) - 1
    result = NEW LIST

    FUNCTION DFS(currentNode, path)
        IF currentNode IS target
            ADD path TO result
            RETURN
        END IF

        FOR each nextNode IN graph[currentNode]
            ADD nextNode TO path
            DFS(nextNode, path)
            REMOVE last element from path (BACKTRACK)
        END FOR
    END FUNCTION

    INITIAL_PATH = [0]
    DFS(0, INITIAL_PATH)

    RETURN result
END FUNCTION

In this solution, the DFS function is defined within the allPathsSourceTarget function and recursively explores all paths from the start node to the target node. By adding and removing nodes from the path within the loop, the function effectively backtracks after exploring all paths from a given node, allowing it to explore all possible paths without revisiting the same path.