Count Unique Dependents in a Referral DAG

Given named nodes and a dependency DAG, compute how many unique nodes directly or indirectly depend on each node. An edge [a,b] means a depends on b, so a contributes to b's count, not the other way around.

Implement referral_counts(nodes: string[], edges: string[][]) -> int[]. Return one count per node in the same order as nodes; this parallel-array output is a portable representation of the source's name-to-count map.

Constraints & Assumptions

• Between 0 and 2000 unique nonempty node names and at most 10000 edges. Each edge contains exactly two names.
• Discard an edge if either endpoint is absent from nodes. Excluded nodes must not create paths connecting known nodes.
• The remaining graph is a DAG. Duplicate edges may occur and must not multiply reachability counts.
• Count distinct reachable dependents, excluding the node itself. Shared descendants reached by multiple paths count once.
• Isolated nodes have count zero. Names are case-sensitive.

Example

nodes = ["A","B","C","D","E"]
edges = [["B","A"],["C","A"],["D","B"],["D","C"],
 ["E","ghost"],["ghost","A"]]
result = [3,1,1,0,0]

D contributes only once to A. Ignoring the unknown node does not create an E-to-A relationship.

Explain a topological-order approach and why adding child counts is insufficient when dependency paths merge. Compare set or bitset propagation with performing a graph search separately for each node, including time and memory tradeoffs.