closest pair i
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Divide and Conquer. Closest Pair I. Design and Analysis of Algorithms I. The Closest Pair Problem. Initial Observations. High-Level Approach. The Divide and Conquer Paradigm. ClosestPair ( ). - PowerPoint PPT PresentationTRANSCRIPT
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Divide and Conquer
Closest Pair IDesign and Analysis
of Algorithms I
![Page 2: Closest Pair I](https://reader035.vdocument.in/reader035/viewer/2022062305/568160b2550346895dcfd473/html5/thumbnails/2.jpg)
Tim Roughgarden
The Closest Pair Problem
![Page 3: Closest Pair I](https://reader035.vdocument.in/reader035/viewer/2022062305/568160b2550346895dcfd473/html5/thumbnails/3.jpg)
Tim Roughgarden
Initial Observations
![Page 4: Closest Pair I](https://reader035.vdocument.in/reader035/viewer/2022062305/568160b2550346895dcfd473/html5/thumbnails/4.jpg)
Tim Roughgarden
High-Level Approach
![Page 5: Closest Pair I](https://reader035.vdocument.in/reader035/viewer/2022062305/568160b2550346895dcfd473/html5/thumbnails/5.jpg)
Tim Roughgarden
The Divide and Conquer Paradigm
![Page 6: Closest Pair I](https://reader035.vdocument.in/reader035/viewer/2022062305/568160b2550346895dcfd473/html5/thumbnails/6.jpg)
Tim Roughgarden
ClosestPair()
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𝑂 (𝑛)𝑂 (𝑛 log𝑛)𝑂 ¿𝑂 (𝑛2)
Suppose we can correctly implement the ClosestSplitPair subrouine in time. What will be the overall running time of the Closest Pair algorithm? (Choose the smallest upper bound that applies.)
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Tim Roughgarden
ClosestPair()
![Page 9: Closest Pair I](https://reader035.vdocument.in/reader035/viewer/2022062305/568160b2550346895dcfd473/html5/thumbnails/9.jpg)
Tim Roughgarden
ClosestSplitPair(,)
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Tim Roughgarden
Correctness Claim