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 ```text 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. ```hint Counts alone lose overlap information When two direct dependents share another dependent, you need enough information to union their reachable nodes without counting that shared node twice. ```