lecture 11

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]

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