hw7 - CS 473 Algorithms Fall 2010 HW 7(due Tuesday October...

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CS 473: Algorithms, Fall 2010 HW 7 (due Tuesday, October 26) This homework contains four problems. Read the instructions for submitting homework on the course webpage . In particular, make sure that you write the solutions for the problems on separate sheets of paper; the sheets for each problem should be stapled together. Write your name and netid on each sheet. Collaboration Policy: For this home work, Problems 1-3 can be worked in groups of up to 3 students each. Problem 0 should be answered in Compass as part of the assessment HW6-Online and should be done individually. 0. (10 pts) HW7-Online on Compass. 1. (25 pts) Let G = ( V,E ) be an undirected graph with edge costs c e . Given an integer k where 1 k n - 1, describe an algorithm that finds the minimum-cost forest in G that contains k edges. 2. (25 pts) Recall from class the idea of Path-Compression in the Union-Find data structure for maintaining disjoint sets. Prove that if Path-Compression is used then the total time for
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