Скачать или смотреть 2192. All Ancestors of a Node in a Directed Acyclic Graph || LeetCode POTD || Explanation in HINDI

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Approach:-

Initialization:
We start by creating a map to store the sorted ancestors for each node.
We also initialize an array to keep track of the in-degrees of nodes and a map to represent the graph.

Graph Construction:
We construct the graph and compute the in-degrees of each node from the given edges.

Topological Sorting:
We use a queue to process nodes in topological order. Nodes with zero in-degrees are added to the queue initially.

Processing Nodes:
For each node processed, we merge its ancestor list with its children's ancestor lists to update the children's ancestor lists.

Merging Ancestors:
The merge function is used to combine two ancestor lists while maintaining sorted order and removing duplicates.

Result Compilation:
Finally, we compile the results into a list of lists, where each list contains the sorted ancestors of the corresponding node.

Time and Space Complexity
Time Complexity:
Constructing the graph and computing in-degrees take O(m), where m is the number of edges.
The topological sorting and processing of nodes take O(n + m), where n is the number of nodes.
The merge operations depend on the lengths of the ancestor lists, which can be up to O(n). Therefore, each merge operation can take O(n). Since each edge can trigger a merge, the worst-case time complexity can be O(m * n).

Space Complexity:
The space required to store the graph, in-degrees, and ancestors lists is O(n + m).
The queue for topological sorting can take up to O(n) space.
The space complexity for the merged ancestor lists is O(n^2) in the worst case.

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