Design a linear-time algorithm for solving the, Basic Computer Science

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Design a linear-time algorithm for solving the

1. Prove the correctness of Dijkstra's algorithm for graphs with positive weights.

2. Design a linear-time algorithm for solving the single-source shortest-paths problem for dags (directed acyclic graphs) represented by their adjacency lists.

3. Explain how the minimum-sum descent problem (Problem 8 in Exercises 8.1) can be solved by Dijkstra's algorithm.

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