# 6ehw3 - Consider the maze shown below. We try to ﬁnd a...

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National Taiwan University Handout #15 Department of Electrical Engineering December 10, 2009 Algorithms, Fall 2009 Yao-Wen Chang Name: Student ID: Web ID: Problem 1. (15 pts total) A group of n girls and n boys are attending a dance class. The instructor wants to pair each girl with a boy in such a way that the sum of the absolute value of the height diﬀerences between partners is minimized. (a) (10 pts) Let A be a tallest girl in the class (there could be a tie), and let B be a tallest boy. Prove that there is an optimal pairing in which A is paired with B . (b) (5 pts) Based on the result of part (a), give an algorithm for computing an optimal pairing. What is the time complexity of your algorithm? Problem 2. (15 pts total)
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Unformatted text preview: Consider the maze shown below. We try to ﬁnd a shortest path from s to t . Formulate this problem as a graph-search problem and give an eﬃcient algorithm for this problem. s t Problem 3. (15 pts total) Apply the accounting method of the amortized analysis to show that the BUILD-HEAP procedure runs in O ( n ) time. (a) (10 pts) Suppose we put \$3 on each node initially. Prove by induction that immediately after calling HEAPIFY( A,i ), the total credit of all the nodes in the subtree rooted at A [ i ] is greater than or equal to h + 1, where h is the height of A [ i ]. (b) (5 pts) Finish the proof that the BUILD-HEAP procedure runs in O ( n ) time....
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## This note was uploaded on 01/01/2011 for the course EE 5503 taught by Professor Yao-wenchang during the Fall '09 term at National Taiwan University.

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