# hw_07 - CS 473 Fundamental Algorithms Spring 2012 Homework...

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CS 473: Fundamental Algorithms, Spring 2012 Homework 7 (due Tuesday, 23:55:00, March 27, 2012) Collaboration Policy & submission guidelines: See homework 1. Each student individually have to also do quiz 7 online. Version: 1.1 1. ( 30 pts. ) 3 / 4 -tree. Consider a uniform rooted tree of height h (every leaf is at distance h from the root). The root, as well as any internal node, has exactly 4 children. Therefore this three has n = 4 h leaves. Each leaf has a boolean value (0 or 1) associated with it. Based on the values at the leaves we recursively define the values at each node of the tree as follows. The value at an internal node v is 1 if and only at least three of its children evaluate to 1. The evaluation problem consists of determining the value of the root; at each step, an algorithm can choose one leaf whose value it wishes to read. (A) ( 10 pts. ) Consider a tree of height h = 1. Provide a randomized algorithm that in expectation (independent of the values stored in the 4 leafs!) evaluates strictly less than 4 leaves to find the value of the root.

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