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l08-more-trees

# l08-more-trees - CS112 Data Structures Lecture 8 More About...

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CS112: Slides for Prof. Steinberg ʼ s lecture 1 Lecture 8 CS112: Data Structures CS112: Data Structures Lecture 8 More About Trees

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CS112: Slides for Prof. Steinberg ʼ s lecture 2 Lecture 8 Exam in 1 results Exam in 1 results :-( Tentatively adding 15 points (Out of 150) Sakai will stay the raw score
CS112: Slides for Prof. Steinberg ʼ s lecture 3 Lecture 8 Raw Scores Raw Scores 0 2 4 6 8 10 12 68 83 98 113 128 143 158

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CS112: Slides for Prof. Steinberg ʼ s lecture 4 Lecture 8 Review: Hashing Review: Hashing Suppose we want to store a set of numbers add number to set, delete from set, test if in set should all be O(1) If range of numbers is small, e.g. 0 . . 9, we can use a boolean array 0 1 2 3 4 5 6 7 8 9 t f f f t t f t f f What if range of numbers is large, e.g. 0…500,0000? but only a small number of numbers, e.g. 10
CS112: Slides for Prof. Steinberg ʼ s lecture 5 Lecture 8 Hashing Hashing If we use array of 500,000 elements, they will nearly all be false. Idea: divide the range into 500 blocks of 1000 numbers Block 10: (numbers 9,001 to 10,000) Is any set element in this range? True Which one: 9,251 Block 9:

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CS112: Slides for Prof. Steinberg ʼ s lecture 6 Lecture 8 Hashing Hashing Array of 500 objects Insert n: put in object at index n/1000 Lookup n: look in object at index n/1000 is any number in this object? is it the right number? All O(1)
CS112: Slides for Prof. Steinberg ʼ s lecture 7 Lecture 8 Hash Function Hash Function What if numbers not random, eg likely to be near each other? convert n to index in some other way, e.g. index = n mod 500 In general, function that makes each index equally likely: “makes hash out of any pattern in the numbers” - Hash function: converts data to hash code Mapping function: converts hash code to array index. (Why separate this?)

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CS112: Slides for Prof. Steinberg ʼ s lecture 8 Lecture 8 Collisions Collisions Even with 500 indices for 10 numbers, it is possible that more than one number will hash to same index As we reduce number of indices probability of collision grows => must be some way to handle collisions
CS112: Slides for Prof. Steinberg ʼ s lecture 9 Lecture 8 Linear Probing

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l08-more-trees - CS112 Data Structures Lecture 8 More About...

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