Compute currency conversions with graphs and topological sort

Q: Compute currency conversions with graphs and topological sort

This question evaluates graph modeling, algorithmic reasoning for chaining pairwise ratios, and understanding of topological ordering and DAG properties within the context of currency conversion, assessing skills in data structures, graph algorithms, and complexity analysis.

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Question

You are given pairwise currency ratios such as "a:b = 1:1.5" and "b:c = 1:1.5". Design functions to: (

store direct conversions; (
answer queries like "A:C" by chaining rates; (
support many queries efficiently; (
when the relations form a DAG with a chosen base currency, compute all currency-to-base rates using a topological ordering; (
explain when a simple map suffices versus when a graph traversal or topological sort is required; (
state time and space complexities and how you handle missing paths or contradictions.

Compute currency conversions with graphs and topological sort

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