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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 6.006 Introduction to Algorithms Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . 6.006 Recitation Build 2008.14 Coming up next... Open addressing KarpRabin coming back from the dead to hunt us Open Addressing Goal: use nothing but the table Hoping for less code, better caching Hashing we must handle collisions Solution: try another location Easy Collision handling taken taken taken taken taken here taken h(x) = standard hash 0 function 1 if T[h(x)] is taken 2 3 try T[h(x)+1] h(29) 4 h(29) + 1 5 then T[h(x) + 2] h(29) + 2 6 then T[h(x) + 3] h(29) + 3 7 8 just like parking a car 9 h(k) grows up to H(k, i) where i is the attempt number frst try T[H(k, 0)] H(29, 0) Collision Handling: Abstracting it Up taken 1 taken 2 taken 3 taken 4 taken 5 taken 6 taken 7 taken 8 taken 9 taken h(k) grows up to H(k, i) where i is the attempt H(29, 1) number frst try T[H(k, 0)] then T[H(k, 1)] H(29, 0) Collision Handling: Abstracting it Up taken 1 taken 2 taken 3 taken 4 taken 5 taken 6 taken 7 taken 8 taken 9 taken h(k) grows up to H(k, i) where i is the attempt H(29, 1) number frst try T[H(k, 0)] H(29, 2) then T[H(k, 1)] then T[H(k, 2)] H(29, 0) Collision Handling: Abstracting it Up taken 1 taken 2 taken 3 taken 4 taken 5 taken 6 taken 7 taken 8 taken 9 taken Collision Handling: Abstracting it Up h(k) grows up to H(k, i) where i is the attempt number frst try T[H(k, 0)] then T[H(k, 1)] then T[H(k, 2)] stop aFter trying all H(29, 3) 0 taken H(29, 1) 1 taken H(29, 4) 2 taken H(29, 9) 3 taken H(29, 2) 4 taken H(29, 5) 5 taken H(29, 6) 6 taken H(29, 7) 7 taken H(29, 8) 8 taken H(29, 0) 9 taken Collision Handling: Abstracting it Up H(k) = <H(k, 0), H(k, 1), H(k, 2) ... > Linear probing, h(29) = 4, H linear (29) = ? <4, 5, 6, 7, 8, 9, 0, 1, 2, 3> General properties? H(29, 3) 0 taken H(29, 1) 1 taken H(29, 4) 2 taken H(29, 9) 3 taken H(29, 2) 4 taken H(29, 5) 5 taken H(29, 6) 6 taken H(29, 7) 7 taken H(29, 8) 8 taken H(29, 0) 9 taken Collision Handling: Abstracting it Up Any collision handling strategy comes to: for key k, probe H(k,0), then H(k,1) etc....
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 Spring '08
 ErikDemaine
 Algorithms

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