05 - Deterministic Linear-time Selection

05 - Deterministic Linear-time Selection - Part I Divide...

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Part I: Divide and Conquer Lecture 5: Deterministic Linear-Time Selection Lecture 5: Deterministic Linear-Time Selection Part I: Divide and Conquer
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Objective and Outline Objective : We discussed a randomized selection algorithm that runs in O ( n ) on average We now discuss a deterministic algorithm that runs in O ( n ) in the worst case Reference : Section 9.3 of CLRS Outline: Idea and Algorithm Analysis of Algorithm Lecture 5: Deterministic Linear-Time Selection Part I: Divide and Conquer
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Deterministic Selection Algorithm Idea : Question If we follow the Partition idea to solve the selection problem, which step(s) make the worst case running time becomes O ( n 2 )? Ans : We make a “ bad ” split in each iteration Trick : In each iteration, we pick a good element such that it “guarantees” a good split Question How to get such a “good” element in each iteration? Lecture 5: Deterministic Linear-Time Selection Part I: Divide and Conquer
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DSelection(A, p, r, i) 1 Divide the n = r - p + 1 items into n / 5 sets in which each, except possibly the last, contains 5 items . O ( n ) 2 Find the median of each of the n / 5 sets. O ( n ) 3 Take these n / 5 medians and put them in another array. Use
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