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This document discusses binary search trees (BSTs) and their use for dynamic sets and sorting. It covers BST operations like search, insert, find minimum/maximum, and delete. It explains that BST sorting runs in O(n log n) time like quicksort. Maintaining a height of O(log n) can lead to efficient implementations of priority queues and other dynamic set applications using BSTs.

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CS 332: Algorithms Medians and Order Statistics Structures for Dynamic Sets
Homework 3 ,[object Object],[object Object]
Review: Radix Sort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: Bucket Sort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: Order Statistics ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: The Selection Problem ,[object Object],[object Object],[object Object],[object Object]
Review: Randomized Selection ,[object Object],[object Object],[object Object], A[q]  A[q] q p r
Review: 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
Review: Randomized Selection ,[object Object],[object Object],[object Object]
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]
Structures… ,[object Object],[object Object],[object Object],[object Object],[object Object]
Dynamic Sets ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Binary Search Trees ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Binary Search Trees ,[object Object],[object Object],F B H K D A
Inorder Tree Walk ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Inorder Tree Walk ,[object Object],[object Object],[object Object],F B H K D A
Operations on BSTs: Search ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
BST Search: Example ,[object Object],F B H K D A
Operations on BSTs: Search ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Operations of BSTs: Insert ,[object Object],[object Object],[object Object],[object Object],[object Object]
BST Insert: Example ,[object Object],C F B H K D A
BST Search/Insert: Running Time ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Sorting With Binary Search Trees ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Sorting With BSTs ,[object Object],[object Object],for i=1 to n TreeInsert(A[i]); InorderTreeWalk(root); 3 1 8 2 6 7 5 5 7 1 2 8 6 7 5 2 6 7 5 3 1 8 2 6 5 7
Sorting with BSTs ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Sorting with BSTs ,[object Object],[object Object]
Sorting with BSTs ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
More BST Operations ,[object Object],[object Object],[object Object],[object Object],[object Object]
BST Operations: Minimum ,[object Object],[object Object]
BST Operations: Successor ,[object Object],[object Object],[object Object],[object Object]
BST Operations: Successor ,[object Object],[object Object],[object Object],[object Object],[object Object]
BST Operations: Delete ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],F B H K D A C Example: delete K or H or B
BST Operations: Delete ,[object Object],[object Object],[object Object],[object Object],[object Object]
The End ,[object Object]

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lecture 11

  • 1. CS 332: Algorithms Medians and Order Statistics Structures for Dynamic Sets
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