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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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This note was uploaded on 09/24/2010 for the course CS 6.006 taught by Professor Erikdemaine during the Spring '08 term at MIT.
 Spring '08
 ErikDemaine
 Algorithms

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