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hbs3 - Problem 3[Divide and Conquer Let p = x,y and p = x,y...

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CS 473: Algorithms, Fall 2010 HBS 3 Problem 1. [Recurrences] Solve the following recurrences. T ( n ) = 5 T ( n/ 4) + n and T ( n ) = 1 for 1 n < 4. T ( n ) = 2 T ( n/ 2) + nlogn T ( n ) = 2 T ( n/ 2) + 3 T ( n/ 3) + n 2 Problem 2. [Tree Traversal] Let T be a rooted binary tree on n nodes. The nodes have unique labels from 1 to n . Given the preorder and postorder node sequences for T , give a recursive algorithm to re- construct a tree that satisfies the preorder and postorder sequences. Is this reconstruction unique? Given the preorder and inorder node sequences for T , give a recursive algorithm to reconstruct a tree that satisfies the preorder and inorder sequences. Is this reconstruction unique?
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Unformatted text preview: Problem 3. [Divide and Conquer] Let p = ( x,y ) and p = ( x ,y ) be two points in the Euclidean plane given by their coordinates. We say that p dominates p if and only if x > x and y > y . Given a set of n points P = { p 1 ,...,p n } , a point p i ∈ P is undominated in P if there is no other point p j ∈ P such that p j dominates p i . Describe an algorithm that given P outputs all the undominated points in P ; see figure. Your algorithm should run in time asymptotically faster than O ( n 2 ) Figure 1: The undominated points are shown as unfilled circles. 1...
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