All Ancestors of a Node in a Directed Acyclic Graph - Solution & Explanation

This approach involves the following steps:

1. Create an adjacency list to represent the graph.
2. Perform topological sorting using a DFS to establish the processing order of each node.
3. For each node, use the established order to determine its ancestors by propagating the ancestors list from predecessors to successors in the order of DFS completion.
4. Finally, sort the ancestors list for each node as required in ascending order.

This solution uses a DFS-based topological sort to process each node in a DAG. We represent the graph as an adjacency list and maintain an indegree count. Nodes with no incoming edges are processed first, during which their ancestors are propagated to their children nodes. This is done until all nodes are processed, yielding a set of ancestors which we then convert to a sorted list for each node to meet the problem requirement.

Here, we reverse the edges in the graph and then perform a DFS for each node to find all reachable nodes, which now represent ancestors. This is an implementation that directly finds ancestors by traversing upwards in the graph via reversed edges:

1. Create an adjacency list but with reversed edges.
2. For each node, perform DFS to locate all nodes that can reach it (which are ancestors in the original graph).
3. Cautiously compile and sort results before returning, ensuring a time-efficient DFS exploration by marking visited nodes.

This solution reverses the direction of edges and applies DFS for each node to find reachable nodes (representing ancestors). Each DFS invocation tracks visited nodes to prevent reprocessing and adds ancestors directly to the current node's list, which is then sorted for output.