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lecture 10

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CS 332: Algorithms Linear-Time Sorting Continued Medians and Order Statistics
Review: Comparison Sorts ,[object Object],[object Object],[object Object],[object Object],[object Object]
Review: Counting Sort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: Counting Sort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: Radix Sort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: Radix Sort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Radix Sort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Radix Sort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Radix Sort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Radix Sort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Summary: Radix Sort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Bucket Sort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Order Statistics ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Order Statistics ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Finding Order Statistics: The Selection Problem ,[object Object],[object Object],[object Object],[object Object]
Randomized Selection ,[object Object],[object Object],[object Object],[object Object],[object Object], A[q]  A[q] q p r
Randomized Selection ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object], A[q]  A[q] k q p r
Randomized Selection ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Randomized Selection ,[object Object],[object Object],[object Object],What happened here?
Randomized Selection ,[object Object],What happened here? “ Split” the recurrence What happened here? What happened here? What happened here? The recurrence we started with Substitute T(n)  cn for T(k) Expand arithmetic series Multiply it out
Randomized Selection ,[object Object],What happened here? Subtract c/2 What happened here? What happened here? What happened here? The recurrence so far Multiply it out Rearrange the arithmetic What we set out to prove
Worst-Case Linear-Time Selection ,[object Object],[object Object],[object Object],[object Object],[object Object]
Worst-Case Linear-Time Selection ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Worst-Case Linear-Time Selection ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Worst-Case Linear-Time Selection ,[object Object],[object Object],??? ??? ??? ??? ???  n/5   n/5 Substitute T(n) = cn Combine fractions Express in desired form What we set out to prove
Worst-Case Linear-Time Selection ,[object Object],[object Object],[object Object],[object Object]
Linear-Time Median Selection ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Linear-Time Median Selection ,[object Object],[object Object],[object Object],[object Object]
The End

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lecture 10

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