l06-trees

l06-trees - CS112: Data Structures Lecture 06 Add / Delete...

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CS112: Slides for Prof. Steinberg ʼ s lecture 1 Lecture 6 CS112: Data Structures CS112: Data Structures Lecture 06 Add / Delete / Search Trees
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CS112: Slides for Prof. Steinberg ʼ s lecture 2 Lecture 6 Review: Add / Delete / Search Review: Add / Delete / Search Basic task: Set of data items E.g. “Al”, “Bob”, “Cindy” Operations: Add an item Delete an item Search for an item Goal: minimize worst case O(add + delete + search)
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CS112: Slides for Prof. Steinberg ʼ s lecture 3 Lecture 6 Unordered Array Unordered Array 0 Carol 1 Anne 2 Bob 3 4 numberOfNames 3 0 Carol 1 Anne 2 Bob 3 Alice 4 numberOfNames 4 Add Alice
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CS112: Slides for Prof. Steinberg ʼ s lecture 4 Lecture 6 Unordered Array Unordered Array 0 Carol 1 Anne 2 Bob 3 Alice 4 numberOfNames 4 0 Carol 1 Alice 2 Bob 3 Alice 4 numberOfNames 3 Remove Anne
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CS112: Slides for Prof. Steinberg ʼ s lecture 5 Lecture 6 Unordered Array Unordered Array Insert O(1) if there’s space Delete O(1) (move last element) Search O(n) where n is size of set Overall O(n)
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CS112: Slides for Prof. Steinberg ʼ s lecture 6 Lecture 6 Ordered Array Ordered Array 0 Anne 1 Bob 2 Carol 3 4 numberOfNames 3 Add Alice 0 Alice 1 Anne 2 Bob 3 Carol 4 numberOfNames 4
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CS112: Slides for Prof. Steinberg ʼ s lecture 7 Lecture 6 Ordered Array Ordered Array Remove Anne 0 Alice 1 Anne 2 Bob 3 Carol 4 numberOfNames 4 0 Alice 1 Bob 2 Carol 3 4 numberOfNames 3
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CS112: Slides for Prof. Steinberg ʼ s lecture 8 Lecture 6 Searching an ordered array Searching an ordered array Binary search Binary search requires sorted values each comparison rules out half of the remaining elements O(log(n)) - we will prove this later Find A, find R A D E F G H J M P T ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ 0 1 2 3 4 5 6 7 8 9
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CS112: Slides for Prof. Steinberg ʼ s lecture 9 Lecture 6 Searching an array Searching an array Performance Performance Search among 1 B illion entries Check 1 million entries per second Sequential search 1 billion operations needed Requires 1000 seconds - about 20 minutes Binary search 30 operations needed Requires 30 microseconds 30 million times faster
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CS112: Slides for Prof. Steinberg ʼ s lecture 10 Lecture 6 Searching an array Searching an array Performance Performance Search among 1 M illion entries Check 1 million entries per second Sequential search 1 million operations needed Requires 1 second Binary earch 20 operations needed Requires 20 microseconds 50,000 times faster
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CS112: Slides for Prof. Steinberg ʼ s lecture 11 Lecture 6 Searching + Insert Searching + Insert Performance Performance 1 billion entries, process 1 million/sec Insert O(n) 1 billion operations needed Requires 1000 seconds - about 20 minutes Binary search O(log n) 30 operations needed Requires 30 microseconds Together: 1000.00003 seconds
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CS112: Slides for Prof. Steinberg ʼ s lecture
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l06-trees - CS112: Data Structures Lecture 06 Add / Delete...

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